{ "cells": [ { "cell_type": "code", "execution_count": 304, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "

Lax-Friedrichs, Lax-Wendroff, MacCormack and Beam-Warming Schemes


\n", "" ], "text/plain": [ "" ] }, "execution_count": 304, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML \n", "s=\"\"\"

Lax-Friedrichs, Lax-Wendroff, MacCormack and Beam-Warming Schemes


\n", "\"\"\";\n", "h=HTML(s); h" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Understand the Problem\n", "\n", "## Question\n", "\n", "* What is the 1D velocity for the **1D Burgers Equation** for flow with a step function for the initial conditions?\n", "* Invesgiate the propagation with the:\n", "\n", " 1. LF\n", " 2. LW\n", " 3. MacCormack\n", "\n", "\n", "* $\\Delta x$ = $\\Delta t$ = 0.1\n", "* Change ${{\\Delta t} \\over {\\Delta x}} $from 1 to 0.5 (effect of Courant Number)\n", "* Change to a finer mesh (effect of step sizes)\n", "\n", "## Initial Conditions\n", "\n", "* `t = 0s` and `x = 0m to 2m` $\\Rightarrow$ ` u = 1m/s`\n", "\n", "* `t = 0s` and `x = 2m to 4m` $\\Rightarrow$ `u = 0m/s`\n", "\n", "## Boundary Conditions\n", "\n", "* `x = 0m` $\\Rightarrow$ ` u = 1m/s`\n", "\n", "* `y = 2m` $\\Rightarrow$ ` u = 0m/s`\n", "\n", "## Governing Equation\n", "\n", "* The Burgers Equation is a wave that propagates with different speeds at different points in the solution\n", "* Eventually a shock will be formed\n", "\n", "* In **Non-conservative Form** the Burgers Equation is described as follows:\n", "\n", "$$ {\\partial u \\over \\partial t} + u {\\partial u \\over \\partial x} = 0 $$\n", "\n", "Non-conservative form will not be good at resolving problems with **sharp changes**. \n", "\n", "* In **Conservative Form** the Burgers Equation is described as follows (for the derivation see http://www.thevisualroom.com/conservative_form.html)\n", "\n", "$$ {\\partial u \\over \\partial t} + {\\partial \\over {\\partial x}}{ \\left( {u^2 \\over 2} \\right)} = 0 $$\n", "\n", "Alternatively, one can write this:\n", "\n", "$$ {\\partial u \\over \\partial t} + {\\partial F \\over {\\partial x}} = 0 $$\n", "\n", "where flux:\n", "\n", "$$ F = {{u^2} \\over 2} $$\n", "\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Formulate the Problem\n", "\n", "## Input Data:\n", "\n", "Burgers Equation **does have a temporal component**, so we use `nt`\n", "\n", "* `nt` = ? (number of temporal points)\n", "* `nx` = 51 (number of x spatial points)\n", "* `tmax` = 1.0\n", "* `xmax` = 4.0\n", "\n", "Formulate `nt` based on the CFL Condition `sigma = (dt / dx) = 1`\n", "\n", "## Initial Conditions:\n", "\n", "* $\\forall (x, t) \\quad t = 0 \\land x \\le 2 \\rightarrow u(x,0) = 2 $\n", "* $\\forall (x, t) \\quad t = 0 \\land x \\gt 2 \\rightarrow u(x,0) = 0 $\n", "\n", "## Velocity Boundary Conditions:\n", "\n", "* $\\forall (x, t) \\quad x = 0 \\rightarrow u(0,t) = 2 $\n", "* $\\forall (x, t) \\quad x = 4 \\rightarrow u(4,t) = 0 $\n", "\n", "## Output Data:\n", "\n", "* $\\forall (x, t) \\quad \\ u(x,t) = ? $\n", "\n", "***\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Lax-Friedrichs Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Lax-Friedrichs Numerical scheme\n", "\n", "* For the **one** first derivative of **velocity** in time: 1st order FD in time\n", "* For the **one** first derivative of **flux** in space: 2nd order CD in space\n", "* Replace $u_i^n = {1 \\over 2} (u_{i+1}^n+u_{i-1}^n)$\n", "\n", "## Discrete equation\n", "\n", "$$ {{u_i^{n+1} - {1 \\over 2}(u_{i+1}^n+u_{i-1}^n)} \\over {\\Delta t}} + {{F_{i+1}^n - F_{i-1}^n} \\over {2 \\Delta x}}=0 $$\n", "\n", "## Transpose\n", "\n", "$$ u_i^{n+1} = {1 \\over 2} (u_{i-1}^n + u_{i+1}^n) - {\\sigma \\over 2} (F_{i+1}^n - F_{i-1}^n) $$\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 51\n", " dx = xmax/(nx-1)\n", " tmax = 1.0\n", " sigma = 1.0\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt-1\n", " u(0,n)=1\n", " u(nx-1,n)=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u(i,0) = 1\n", " else\n", " u(i,0) = 0\n", " \n", " F = (u/2)**2\n", " \n", " #Iteration\n", " for n between 0 and nt-1\n", " for i between 1 and nx-2\n", " u(i,n+1) = 0.5*[ u(i-1,n)+u(i+1,n) ] - 0.5*sigma*[ F(i+1,n)-F(i-1,n) ]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def initial_and_boundary_conditions(nx, nt):\n", " \n", " # Initialise data structures\n", " import numpy as np\n", " u = np.zeros((nx,nt))\n", " \n", " # Boundary conditions\n", " u[0,:] = 1.0\n", " u[nx-1,:] = 0.0\n", "\n", " half = int((nx-1)/2)\n", "\n", " # Initial conditions \n", " u[0:half,0] = 1.0\n", " \n", " return u" ] }, { "cell_type": "code", "execution_count": 130, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def initial_and_boundary_conditions_2(nx, nt):\n", " \n", " # Initialise data structures\n", " import numpy as np\n", " u = np.zeros((nx,nt))\n", " \n", " # Boundary conditions\n", " u[0,:] = 1.1\n", " u[nx-1,:] = 0.0\n", "\n", " half = int((nx-1)/2)\n", "\n", " # Initial conditions \n", " u[0:half,0] = 1.1\n", " \n", " return u" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytical(nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D non-linear convection\n", " This is just transporting the ICs with a Courant number of 2 \n", " (effectively a numerical wave speed of 0.5)\n", " \"\"\"\n", " \n", " # Increments\n", " # dx = xmax/(nx-1)\n", " # dt = dx*sigma\n", " # tmax = (nt-1)*dt\n", "\n", " dx = xmax/(nx-1)\n", " dt = dx/0.5\n", " nt = int((tmax/dt)+1)\n", " \n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,int(nt-1)):\n", " u[i:nx-1, n+1] = u[i-1:nx-2, n]\n", "\n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytical_2(nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D non-linear convection\n", " This is just transporting the ICs with a Courant number of 2 \n", " (effectively a numerical wave speed of 0.5)\n", " \"\"\"\n", " \n", " # Increments\n", " # dx = xmax/(nx-1)\n", " # dt = dx*sigma\n", " # tmax = (nt-1)*dt\n", "\n", " dx = xmax/(nx-1)\n", " dt = dx / (((1.1+0.0)/2.0))\n", " nt = int(tmax/dt + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions_2(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,int(nt-1)):\n", " u[i:nx-1, n+1] = u[i-1:nx-2, n]\n", "\n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 215, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot(u,x,NT,u_analytical, x_analytical, NT2, step, dt, dt_lf):\n", " \"\"\"\n", " Plots the 1D velocity field\n", " \"\"\"\n", "\n", " import matplotlib.pyplot as plt\n", " import matplotlib.cm as cm\n", " plt.figure()\n", " ax=plt.subplot(111)\n", " colour=iter(cm.rainbow(np.linspace(0,step,NT))) \n", " for n in range(0,NT,step):\n", " t = n*dt\n", " c=next(colour)\n", " ax.plot(x,u[:,n],linestyle='-',c=c,label='t='+str(t))\n", " t_lf =(NT2-1)*dt_lf \n", " ax.plot(x_analytical,u_analytical[:,NT2-1],linestyle='--',c='k',label='t='+str(t_lf)+' analytical') \n", " box=ax.get_position()\n", " ax.set_position([box.x0, box.y0, box.width*2,box.height*2])\n", " ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n", " plt.ylim([-0.5,1.5])\n", " plt.xlim([0.0,4.0])\n", " plt.xlabel('x (m)')\n", " plt.ylabel('u (m/s)')\n", " plt.show()\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_friedrichs_convection(sigma, nx, nt, xmax, step):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", "\n", " # Increments\n", " # dx = xmax/(nx-1)\n", " # dt = dx*sigma\n", " # tmax = (nt-1)*dt\n", " dx = xmax/(nx-1)\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", "\n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,int(nt-1)):\n", " u[i:nx-1, n+1] = (0.5*(u[i-1:nx-2, n]+u[i+1:nx, n])-\n", " 0.5*sigma*(F(u[i+1:nx, n])-F(u[i-1:nx-2, n])))\n", "\n", " # Lax-Friedrichs with Courant Number = 2\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", "\n", " dt_lf = dx * 2.0\n", "\n", " plot(u,x,nt,u_lf, x_lf, nt_lf, step, dt, dt_lf)" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_cfl(x,u_1,nt_1,u_2,nt_2,u_3,nt_3,u_lf, x_lf, nt_lf, dt_1, dt_2, dt_3, dt_lf):\n", " \"\"\"\n", " Plots the 1D velocity field\n", " \"\"\"\n", "\n", " import matplotlib.pyplot as plt\n", " import matplotlib.cm as cm\n", " plt.figure()\n", " ax=plt.subplot(111)\n", " c_1 = dt_1/(max(x)/100)\n", " c_2 = dt_2/(max(x)/100)\n", " c_3 = dt_3/(max(x)/100)\n", " t_1 =(nt_1-1)*dt_1 \n", " ax.plot(x,u_1[:,nt_1-1],linestyle='-',c='r',label='t='+str(t_1)+' Courant = '+str(c_1))\n", " t_2 =(nt_2-1)*dt_2 \n", " ax.plot(x,u_2[:,nt_2-1],linestyle='-',c='b',label='t='+str(t_2)+' Courant = ' +str(c_2))\n", " t_3 =(nt_3-1)*dt_3 \n", " ax.plot(x,u_3[:,nt_3-1],linestyle='-',c='g',label='t='+str(t_3)+' Courant = ' +str(c_3)) \n", " \n", " t_lf =(nt_lf-1)*dt_lf \n", " ax.plot(x_lf,u_lf[:,nt_lf-1],linestyle='--',c='k',label='t='+str(t_lf)+' Analytical') \n", " box=ax.get_position()\n", " ax.set_position([box.x0, box.y0, box.width*2,box.height*2])\n", " ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n", " plt.ylim([-0.5,1.5])\n", " plt.xlim([0.0,4.0])\n", " plt.xlabel('x (m)')\n", " plt.ylabel('u (m/s)')\n", " plt.show()\n" ] }, { "cell_type": "code", "execution_count": 177, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_friedrichs_convection_cfl(sigma_1, sigma_2, sigma_3, nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt_1 = dx * sigma_1\n", " nt_1 = int(tmax/dt_1 + 1)\n", " dt_2 = dx * sigma_2\n", " nt_2 = int(tmax/dt_2 + 1)\n", " dt_3 = dx * sigma_3\n", " nt_3 = int(tmax/dt_3 + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u_1 = initial_and_boundary_conditions(nx, nt_1)\n", " u_2 = initial_and_boundary_conditions(nx, nt_2)\n", " u_3 = initial_and_boundary_conditions(nx, nt_3)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt_1-1):\n", " u_1[i:nx-1, n+1] = (0.5*(u_1[i-1:nx-2, n]+u_1[i+1:nx, n])-\n", " 0.5*sigma_1*(F(u_1[i+1:nx, n])-F(u_1[i-1:nx-2, n])))\n", " \n", " for n in range(0,nt_2-1):\n", " u_2[i:nx-1, n+1] = (0.5*(u_2[i-1:nx-2, n]+u_2[i+1:nx, n])-\n", " 0.5*sigma_2*(F(u_2[i+1:nx, n])-F(u_2[i-1:nx-2, n])))\n", " \n", " for n in range(0,nt_3-1):\n", " u_3[i:nx-1, n+1] = (0.5*(u_3[i-1:nx-2, n]+u_3[i+1:nx, n])-\n", " 0.5*sigma_3*(F(u_3[i+1:nx, n])-F(u_3[i-1:nx-2, n])))\n", " \n", " # Lax-Friedrichs with Courant Number = 2\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", " \n", " dt_lf = dx * 2.0\n", " \n", " plot_cfl(x,u_1,nt_1,u_2,nt_2,u_3,nt_3,u_lf, x_lf, nt_lf, dt_1, dt_2, dt_3, dt_lf)" ] }, { "cell_type": "code", "execution_count": 178, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_friedrichs_convection_initial(sigma_1, sigma_2, sigma_3, nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt_1 = dx * sigma_1\n", " nt_1 = int(tmax/dt_1 + 1)\n", " dt_2 = dx * sigma_2\n", " nt_2 = int(tmax/dt_2 + 1)\n", " dt_3 = dx * sigma_3\n", " nt_3 = int(tmax/dt_3 + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u_1 = initial_and_boundary_conditions_2(nx, nt_1)\n", " u_2 = initial_and_boundary_conditions_2(nx, nt_2)\n", " u_3 = initial_and_boundary_conditions_2(nx, nt_3)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt_1-1):\n", " u_1[i:nx-1, n+1] = (0.5*(u_1[i-1:nx-2, n]+u_1[i+1:nx, n])-\n", " 0.5*sigma_1*(F(u_1[i+1:nx, n])-F(u_1[i-1:nx-2, n])))\n", " \n", " for n in range(0,nt_2-1):\n", " u_2[i:nx-1, n+1] = (0.5*(u_2[i-1:nx-2, n]+u_2[i+1:nx, n])-\n", " 0.5*sigma_2*(F(u_2[i+1:nx, n])-F(u_2[i-1:nx-2, n])))\n", " \n", " for n in range(0,nt_3-1):\n", " u_3[i:nx-1, n+1] = (0.5*(u_3[i-1:nx-2, n]+u_3[i+1:nx, n])-\n", " 0.5*sigma_3*(F(u_3[i+1:nx, n])-F(u_3[i-1:nx-2, n])))\n", " \n", " # Passing ICs with Courant Number = 2\n", " u_lf, x_lf, nt_lf = analytical_2(nx, tmax, xmax)\n", " \n", " dt_lf = dx * 2.0\n", " \n", " plot_cfl(x,u_1,nt_1,u_2,nt_2,u_3,nt_3,u_lf, x_lf, nt_lf, dt_1, dt_2, dt_3, dt_lf)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lax-Friedrichs CFL Number = 0.5\n", "\n", "Stability condition:\n", "\n", "$$ \\left| {\\Delta t \\over \\Delta x} u_{max} \\right| \\lt 1 $$\n", "\n", "Where $ u_{max} $ is the maximum eigenvalue of the A matrix\n", "\n", "$$ \\left| u \\right| \\le {\\Delta x \\over \\Delta t} $$\n", "\n", "Meaning of $ {\\Delta x \\over \\Delta t} $ is the **velocity of the computated information**, i.e. $1 \\over \\sigma$, so this must be greater than or equal to **the velocity of the physical wave**.\n", "\n", "The effective wave speed is $c = {{u_R + u_L} \\over 2} = 0.5 $ **this is not a stability condition - due to the condition of needing to resolve a wave of length** $2 \\Delta x$\n", "\n", "Lax-Friedichs also adds an artificial diffusion term $({\\Delta x^2 \\over \\Delta t}) {\\partial^2 Q \\over \\partial x^2}$ with an artificial viscosity of 0.5 to the RHS of the FTCS scheme, to stabilize it using standard second order central differencing for the diffusion term\n", "\n", "However, this scheme is still **first order**. The shock is subject to numerical dissipation" ] }, { "cell_type": "code", "execution_count": 172, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Xon+nlSBfND9PihEfYO4JbeW91jcZnDyWPu7CuAxeONLErppXaQrto0/gKtKT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\n7zfnMg2G5ZhsTLTfXMDDqiOJNw9PNG8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nwmXLuH4erDPqGU1Q2r0I2wz5aq3K3GYJgQnK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\nFlX3P/nkk49UfG0YhlVTQvb5559fHRcXdygrK6vZ4MGDV3fq1Gl33759N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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lax_friedrichs_convection(0.5, 101, 2.0, 4.0, 5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lax-Friedrichs CFL Number = 1, 0.5 and 0.25\n", "\n", "* CFL Number effectively reduced the timestep, increasing the number of timesteps\n", "* The numerical diffusion is proportional to the number of timesteps, so that increasing the **CFL number increases the numerical dissipation**" ] }, { "cell_type": "code", "execution_count": 180, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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pX5eRkaGAgACH9ZcuXdK///1vjRw5UpLUpUsXRUVFaeXKlSXqmjRpYv/Z19fX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\nMEPZv7+1jXkkaUK3CVp7ZK3OF533/WQAaMAIlAA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lax_friedrichs_convection_cfl(1.0, 0.5, 0.25, 101, 2.0, 4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lax-Friedrichs CFL Number = 1, 1.28, 2\n", "\n", "* CFL above 1, the solution should be unstable\n", "* However, CFL of 2 **appears** stable\n", "\n", "### Why is CFL = 2 stable for Lax-Friedrichs?\n", "\n", "#### Explanation from Linear Convection\n", "\n", "$$ {\\partial u \\over \\partial t} = -c {\\partial u \\over \\partial x} $$\n", "\n", "With FTBS:\n", "\n", "$$ {{u_i^{n+1} - u_i^n} \\over \\Delta t} = -c\\left( {{u_i^n - u_{i-1}^n} \\over \\Delta x} \\right)$$\n", "\n", "i.e.\n", "\n", "$$ u_i^{n+1} = u_i^n -\\sigma \\left( {{u_i^n - u_{i-1}^n}} \\right)$$\n", "\n", "With $\\sigma = 1$:\n", "\n", "$$ u_i^{n+1} = u_{i-1}^n$$\n", "\n", "i.e. the new value in time equals the upstream value - just propagating the **Initial Conditions** through the domain\n", "\n", "#### Explanation from Non-Linear Convection\n", "\n", "$$ u_i^{n+1} = {1 \\over 2} (u_{i+1}^n + u_{i-1}^n)-{\\sigma \\over 2} \\left( {{(u_{i+1}^n)^2 \\over 2} - {(u_{i-1}^n)^2 \\over 2}} \\right)$$\n", "\n", "At the shock and $\\sigma = 2$\n", "\n", "$$u_{i+1}^n = 0$$\n", "$$u_{i-1}^n = 1$$\n", "\n", "$$ u_i^{n+1} = {1 \\over 2} (0+1)-{2 \\over 2} \\left( 0 -{1 \\over 2} \\right) = 1$$\n", "\n", "i.e. the new value equals the upstream value - similar to CFL = 1 for FTBS (upwind)\n", "\n", "**It's simply a cancellation of terms**" ] }, { "cell_type": "code", "execution_count": 181, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AgDbCn8AayBHWqCjP51l4CQDgDwIrAABtREspCZYoCQYA+IfACgBAG9GcJcHe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\npWfMmLGprKxszyWXXPL4lClTtrQf15un5mTrqT977uabb/7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lax_friedrichs_convection_cfl(1.0, 1.28, 2.0, 101, 2.0, 4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### CFL=2 numerical cancellation of terms for Lax-Friedrichs is not generally applicable and depends on the ICs+BCs\n", "\n", "* This shows for ICs with a slightly higher value, the Courant Number needs to be less than 1 for stability (as it should)\n" ] }, { "cell_type": "code", "execution_count": 186, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dOnUKDz/8sMnrhIWFYceOHbh58yaOHDmCW7duoWfPngBgNLS4tr55eXmhT58+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\nxgEACD+CFQCgDLvdexlnsIwK1g8//FBef/31HsfddFMvfb2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lax_friedrichs_convection_initial(0.5, 1.28, 2.0, 101, 1.0, 4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion from Lax-Friedrichs\n", "\n", "Lax-Friedrichs shows **diffusion error** (acculumated numerical diffusion)\n", "\n", "* Reducing the CFL number reduces the timestep\n", "* Reducing the timestep increases the number of iterations to get to the same point in time\n", "* The diffusion error is proportional to (amplitude ratio) to the power of number of timesteps \n", "* Therefore increasing the number of timesteps increases the diffusion error\n", "\n", "Lax-Friedrichs has best accuracy with **CFL = 1**\n", "\n", "Lax Friedrichs shows **Odd-Even Decoupling**:\n", "\n", "1) The value of the velocity at point $u_i^{n+1}$ does not depend on the value at $u_i^n$. \n", "\n", "2) Since $u_i^n$ depends on $u_{i-1}^{n-1}$ and $u_{i+1}^{n-1}$, then $u_i^{n+1}$ does not depend on these either\n", "\n", "This is similar to the behavior of a collocated grid when pressure and velocity are decoupled. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Lax-Wendroff Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Conservative Form\n", "\n", "$$ {\\partial u \\over \\partial t} + {\\partial \\over {\\partial x}}{ \\left( {u^2 \\over 2} \\right)} = 0 \\qquad\n", " \\Leftrightarrow \\qquad {\\partial u \\over \\partial t} + {{\\partial F} \\over {\\partial x}} = 0$$\n", " \n", "## Non-Conservative Form\n", "\n", "$$ {\\partial u \\over \\partial t} + u {{\\partial u} \\over {\\partial x}} = 0 \\qquad\n", " \\Leftrightarrow \\qquad {\\partial u \\over \\partial t} + A {{\\partial u} \\over {\\partial x}} = 0$$\n", " \n", "* F = Flux for Conservative Form of Burgers Equation\n", "* A = Jacobian for Non-Conservative Form of Burgers Equation\n", "\n", "$$ A = {{\\partial F} \\over {\\partial u}} = u $$\n", "\n", "## Lax-Wendroff Numerical scheme\n", "\n", "* Taylor Expansion to 2nd order term:\n", "\n", "$$ u_i^{n+1} = u_i^n + {\\Delta t}(u_t)_i^n + {\\Delta t^2 \\over 2} (u_{tt})_i^n + O(\\Delta t^3) $$\n", "\n", "\n", "* Replace $u_t$ and $u_{tt}$ by spatial derivatives:\n", "\n", "$$ u_t = - F_x $$\n", "\n", "$$ u_{tt} = -(F_x)_t = -(F_t)_x $$\n", "\n", "$$ {{\\partial F} \\over {\\partial t}} = {{\\partial F} \\over {\\partial u}} {{\\partial u} \\over {\\partial t}} = A (-F_x) = -AF_x $$\n", "\n", "Hence:\n", "\n", "$$ u_{tt} = (A F_x)_x $$\n", "\n", "And:\n", "\n", "$$ u_i^{n+1} = u_i^n - {\\Delta t}(F_x)_i^n + {\\Delta t^2 \\over 2} ((A F_x)_x)_i^n $$\n", "\n", "* For the first derivative of **Flux** in space: 2nd order CD in space between two points\n", "* For the first derivative of **Jacobian times Derivative of the Flux** in space: 2nd order in space between two midpoints\n", "* For the first derivative of midpoint **Flux** in space: 2nd order in space\n", "* For the value of the **Jacobian** at the midpoint: average value\n", "\n", "## Discrete equation\n", "\n", "$$ u_i^{n+1} = u_i^n - {{\\Delta t}} {(F_{i+1}^n - F_{i-1}^n) \\over {2 \\Delta x}} + {{\\Delta t^2} \\over 2} {{(AF_x)_{i+{1 \\over 2}}^n - (AF_x)_{i-{1 \\over 2}}^n \\over {\\Delta x}}} $$\n", "\n", "\n", "$$ {{(AF_x)_{i+{1 \\over 2}}^n - (AF_x)_{i-{1 \\over 2}}^n \\over {\\Delta x}}} = \n", "{1 \\over {\\Delta x}}(A_{i+{1 \\over 2}}^n{{{F_{i+1}^n - F_i^n} \\over {\\Delta x} }}) -\n", "{1 \\over {\\Delta x}}(A_{i-{1 \\over 2}}^n{{{F_{i}^n - F_{i-1}^n} \\over {\\Delta x} }}) = \\\n", "{1 \\over {\\Delta x^2}} \\left( A_{i+{1 \\over 2}}^n{{ ({F_{i+1}^n - F_i^n}) }} -\n", "A_{i-{1 \\over 2}}^n{{ ({F_{i}^n - F_{i-1}^n}) }} \\right) = \\\n", "{1 \\over {\\Delta x^2}} \\left( {{A_{i+1}^n + A_i^n} \\over 2} {{ ({F_{i+1}^n - F_i^n}) }} -\n", "{{A_{i}^n + A_{i-1}^n} \\over 2}{{ ({F_{i}^n - F_{i-1}^n}) }} \\right) = \\\n", "{1 \\over {2 \\Delta x^2}} \\left( {({A_{i+1}^n + A_i^n}) } {{ ({F_{i+1}^n - F_i^n}) }} -\n", "{({A_{i}^n + A_{i-1}^n})}{{ ({F_{i}^n - F_{i-1}^n}) }} \\right)$$\n", "\n", "Hence:\n", "\n", "$$ u_i^{n+1} = u_i^n - {{\\Delta t}} {(F_{i+1}^n + F_{i-1}^n) \\over {2 \\Delta x}} + {\\Delta t^2 \\over {4 \\Delta x^2}} \\left( {({A_{i+1}^n + A_i^n}) } {{ ({F_{i+1}^n - F_i^n}) }} -\n", "{({A_{i}^n + A_{i-1}^n})}{{ ({F_{i}^n - F_{i-1}^n}) }} \\right) $$\n", "\n", "$$ u_i^{n+1} = u_i^n - {{\\sigma \\over 2}} {(F_{i+1}^n - F_{i-1}^n)} + {\\sigma^2 \\over {4}} \\left( {({A_{i+1}^n + A_i^n}) } {{ ({F_{i+1}^n - F_i^n}) }} -\n", "{({A_{i}^n + A_{i-1}^n})}{{ ({F_{i}^n - F_{i-1}^n}) }} \\right) $$\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 51\n", " dx = xmax/(nx-1)\n", " tmax = 1.0\n", " sigma = 1.0\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt-1\n", " u(0,n)=1\n", " u(nx-1,n)=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u(i,0) = 1\n", " else\n", " u(i,0) = 0\n", " \n", " F = (u/2)**2\n", " A = u\n", " \n", " #Iteration\n", " for n between 0 and nt-1\n", " for i between 1 and nx-2\n", " u(i,n+1) = u(i,n)-0.5*sigma*[ F(i+1,n)-F(i-1,n) ] + \n", " 0.25*(sigma**2)*[ ( A(i+1,n)+A(i,n) )*( F(i+1,n)-F(i,n) )-\n", " ( A(i,n)+A(i-1,n) )*( F(i,n)-F(i-1,n) ) ]" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_wendroff_convection_2(sigma, nx, nt, xmax, step):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", "\n", " # Increments\n", " # dx = xmax/(nx-1)\n", " # dt = dx*sigma\n", " # tmax = (nt-1)*dt\n", " dx = xmax/(nx-1)\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " # Lamba function for Jacobian:\n", " A = lambda u: u\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " u[i:nx-1, n+1] = (u[i:nx-1,n] -\n", " 0.5*sigma*( F(u[i+1:nx, n])-F(u[i-1:nx-2, n]) ) + \n", " 0.25*(sigma**2)*( ( A(u[i+1:nx, n])+A(u[i:nx-1, n]) )*\n", " ( F(u[i+1:nx, n])-F(u[i:nx-1, n]) )-\n", " ( A(u[i:nx-1, n])+A(u[i-1:nx-2, n]) )*\n", " ( F(u[i:nx-1, n])-F(u[i-1:nx-2, n]) ) ) )\n", "\n", " # Wave propagating with speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", "\n", " dt_lf = dx * 2.0\n", "\n", " plot(u,x,nt,u_lf, x_lf, nt_lf, step, dt, dt_lf)" ] }, { "cell_type": "code", "execution_count": 194, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_wendroff_convection_cfl(sigma_1, sigma_2, sigma_3, nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt_1 = dx * sigma_1\n", " nt_1 = int(tmax/dt_1 + 1)\n", " dt_2 = dx * sigma_2\n", " nt_2 = int(tmax/dt_2 + 1)\n", " dt_3 = dx * sigma_3\n", " nt_3 = int(tmax/dt_3 + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u_1 = initial_and_boundary_conditions(nx, nt_1)\n", " u_2 = initial_and_boundary_conditions(nx, nt_2)\n", " u_3 = initial_and_boundary_conditions(nx, nt_3)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " # Lamba function for Jacobian:\n", " A = lambda u: u\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt_1-1):\n", " u_1[i:nx-1, n+1] = (u_1[i:nx-1,n] -\n", " 0.5*sigma_1*( F(u_1[i+1:nx, n])-F(u_1[i-1:nx-2, n]) ) + \n", " 0.25*(sigma_1**2)*( ( A(u_1[i+1:nx, n])+A(u_1[i:nx-1, n]) )*\n", " ( F(u_1[i+1:nx, n])-F(u_1[i:nx-1, n]) )-\n", " ( A(u_1[i:nx-1, n])+A(u_1[i-1:nx-2, n]) )*\n", " ( F(u_1[i:nx-1, n])-F(u_1[i-1:nx-2, n]) ) ) )\n", " \n", " for n in range(0,nt_2-1):\n", " u_2[i:nx-1, n+1] = (u_2[i:nx-1,n] -\n", " 0.5*sigma_2*( F(u_2[i+1:nx, n])-F(u_2[i-1:nx-2, n]) ) + \n", " 0.25*(sigma_2**2)*( ( A(u_2[i+1:nx, n])+A(u_2[i:nx-1, n]) )*\n", " ( F(u_2[i+1:nx, n])-F(u_2[i:nx-1, n]) )-\n", " ( A(u_2[i:nx-1, n])+A(u_2[i-1:nx-2, n]) )*\n", " ( F(u_2[i:nx-1, n])-F(u_2[i-1:nx-2, n]) ) ) ) \n", " \n", " for n in range(0,nt_3-1):\n", " u_3[i:nx-1, n+1] = (u_3[i:nx-1,n] -\n", " 0.5*sigma_3*( F(u_3[i+1:nx, n])-F(u_3[i-1:nx-2, n]) ) + \n", " 0.25*(sigma_3**2)*( ( A(u_3[i+1:nx, n])+A(u_3[i:nx-1, n]) )*\n", " ( F(u_3[i+1:nx, n])-F(u_3[i:nx-1, n]) )-\n", " ( A(u_3[i:nx-1, n])+A(u_3[i-1:nx-2, n]) )*\n", " ( F(u_3[i:nx-1, n])-F(u_3[i-1:nx-2, n]) ) ) ) \n", " \n", " # Wave at speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", " \n", " dt_lf = dx * 2.0\n", " \n", " plot_cfl(x,u_1,nt_1,u_2,nt_2,u_3,nt_3,u_lf, x_lf, nt_lf, dt_1, dt_2, dt_3, dt_lf) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Lax-Wendroff CFL = 0.25, 0.5, 1.0" ] }, { "cell_type": "code", "execution_count": 195, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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pKSlJkhQTE6N3331XeXl5WrZsmebMmaMvvviixu/bWhAoAQBAkzqRaZEzskKx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\nbD0m7TEAyIErlABAXtj7lx2xrbU57TEAyIGgBAD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "lax_wendroff_convection_cfl(0.25, 0.5, 1.0, 101, 2.0, 4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion from Lax-Wendroff\n", "\n", "Stability condition:\n", "\n", "$$ \\left| {\\Delta t \\over \\Delta x} u_{max} \\right| \\lt 1 $$\n", "\n", "Where $ u_{max} $ is the maximum eigenvalue of the A matrix\n", "\n", "Lax-Wendroff shows **dispersive errors** $\\epsilon_{\\phi}$ and very little **diffusion errors** $ \\epsilon_D$ and this is because LW is second order:\n", "\n", "* When the leading error term is even ordered (as for first order methods), there will be mainly dissipation error\n", "* When the leading error term is odd ordered (as for second order methods), there will be mainly dispersion error\n", "\n", "Dispersion error depends on:\n", "\n", "* The dispersive errors depend on the wave content of the solution\n", "* Numerical velocity here is lagging\n", "* Oscillations are larger for smaller CFL number - this is the accumulation of numerical dispersion errors\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using MacCormack Scheme\n", "\n", "Lax-Wendroff is ok, but it was quite complex to code, **Because of the need to compute second order derivatives**. MacCormack should be easier\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Conservative Form\n", "\n", "$$ {\\partial u \\over \\partial t} + {\\partial \\over {\\partial x}}{ \\left( {u^2 \\over 2} \\right)} = 0 \\qquad\n", " \\Leftrightarrow \\qquad {\\partial u \\over \\partial t} + {{\\partial F} \\over {\\partial x}} = 0$$\n", "\n", "## MacCormack Numerical scheme\n", "\n", "* Define predicted terms as $ \\tilde{u} $ and $ F(\\tilde{u}) = \\tilde{F} $\n", "\n", "* Predictor step **FTFS** from $n$ to $n+1$\n", "\n", "$$ {{ \\tilde{u}_i^{n+1} - u_i^n } \\over {\\Delta t}} = -\\left( {{F_{i+1}^n - F_i^n} \\over {\\Delta x}} \\right) $$\n", "\n", "$$ \\tilde{u}_i^{n+1} = u_i^n - \\Delta t \\left( {{F_{i+1}^n - F_{i}^n} \\over {\\Delta x}} \\right) $$\n", "\n", "$$ \\tilde{u}_i^{n+1} = u_i^n - \\sigma \\left( {{F_{i+1}^n - F_{i}^n}} \\right) $$\n", "\n", "* Corrector step **FTBS** from $n+{1 \\over 2}$ to $n+1$ using predicted values for time $n+1$ and where the midpoint time is the average of the predicted and current values $ u_i^{n+{1 \\over 2}} = {1 \\over 2} \\left( \\tilde{u}_i^{n+1} + u_i^n \\right) $\n", "\n", "$$ {{ u_i^{n+1} - {1 \\over 2} \\left( \\tilde{u}_i^{n+1} + u_i^n \\right)} \\over {{\\Delta t \\over 2}}} = -\\left( {{\\tilde{F}_{i}^{n+1} - \\tilde{F}_{i-1}^{n+1}} \\over {\\Delta x}} \\right)$$\n", "\n", "$$ u_i^{n+1} = {1 \\over 2} \\left( \\tilde{u}_i^{n+1} + u_i^n \\right) - {\\Delta t \\over 2} \\left( {{\\tilde{F}_{i}^{n+1} - \\tilde{F}_{i-1}^{n+1}} \\over {\\Delta x}} \\right) $$\n", "\n", "$$ u_i^{n+1} = {1 \\over 2} \\left( \\tilde{u}_i^{n+1} + u_i^n \\right) - {\\sigma \\over 2} \\left( {{\\tilde{F}_{i}^{n+1} - \\tilde{F}_{i-1}^{n+1}}} \\right) $$\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 51\n", " dx = xmax/(nx-1)\n", " tmax = 1.0\n", " sigma = 1.0\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt-1\n", " u(0,n)=1\n", " u(nx-1,n)=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u(i,0) = 1\n", " else\n", " u(i,0) = 0\n", " \n", " F = (u/2)**2\n", " \n", " #Iteration\n", " for n between 0 and nt-1\n", " for i between 1 and nx-2\n", " up[i,n+1] = u[i,n] - sigma*(F[i+1,n] - F[i,n])\n", " \n", " u[i,n+1] = 0.5*(up[i,n+1] + u[i,n]) - 0.5*sigma * (Fp[i,n+1] - Fp[i-1,n+1])" ] }, { "cell_type": "code", "execution_count": 197, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def maccormack_convection_2(sigma, nx, nt, xmax, step):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", "\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", " up = initial_and_boundary_conditions(nx, nt)\n", " \n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " up[i:nx-1, n+1] = u[i:nx-1, n] - sigma*(F(u[i+1:nx, n]) - F(u[i:nx-1, n]))\n", " u[i:nx-1, n+1] = ( 0.5*(up[i:nx-1, n+1] + u[i:nx-1, n]) - \n", " 0.5*sigma*(F(up[i:nx-1, n+1]) - F(up[i-1:nx-2, n+1])) )\n", "\n", " # Wave propagating with speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", "\n", " dt_lf = dx * 2.0\n", "\n", " plot(u,x,nt,u_lf, x_lf, nt_lf, step, dt, dt_lf)" ] }, { "cell_type": "code", "execution_count": 201, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_schemes(x,u_1,nt_1,u_2,nt_2,u_3,nt_3,u_lf, x_lf, nt_lf, dt_1, dt_2, dt_3, dt_lf):\n", " \"\"\"\n", " Plots the 1D velocity field\n", " \"\"\"\n", "\n", " import matplotlib.pyplot as plt\n", " import matplotlib.cm as cm\n", " plt.figure()\n", " ax=plt.subplot(111)\n", " c_1 = dt_1/(max(x)/100)\n", " c_2 = dt_2/(max(x)/100)\n", " c_3 = dt_3/(max(x)/100)\n", " t_1 =(nt_1-1)*dt_1 \n", " ax.plot(x,u_1[:,nt_1-1],linestyle='-',c='r',label='t='+str(t_1)+'Lax-Friedrichs')\n", " t_2 =(nt_2-1)*dt_2 \n", " ax.plot(x,u_2[:,nt_2-1],linestyle='-',c='b',label='t='+str(t_2)+'Lax-Wendroff')\n", " t_3 =(nt_3-1)*dt_3 \n", " ax.plot(x,u_3[:,nt_3-1],linestyle='-',c='g',label='t='+str(t_3)+'MacCormack') \n", " \n", " t_lf =(nt_lf-1)*dt_lf \n", " ax.plot(x_lf,u_lf[:,nt_lf-1],linestyle='--',c='k',label='t='+str(t_lf)+' Analytical') \n", " box=ax.get_position()\n", " ax.set_position([box.x0, box.y0, box.width*2,box.height*2])\n", " ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n", " plt.ylim([-0.5,1.5])\n", " plt.xlim([0.0,4.0])\n", " plt.xlabel('x (m)')\n", " plt.ylabel('u (m/s)')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 202, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def maccormack_convection_cfl(sigma_1, sigma_2, sigma_3, nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt_1 = dx * sigma_1\n", " nt_1 = int(tmax/dt_1 + 1)\n", " dt_2 = dx * sigma_2\n", " nt_2 = int(tmax/dt_2 + 1)\n", " dt_3 = dx * sigma_3\n", " nt_3 = int(tmax/dt_3 + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u_1 = initial_and_boundary_conditions(nx, nt_1)\n", " u_2 = initial_and_boundary_conditions(nx, nt_2)\n", " u_3 = initial_and_boundary_conditions(nx, nt_3)\n", " up_1 = initial_and_boundary_conditions(nx, nt_1)\n", " up_2 = initial_and_boundary_conditions(nx, nt_2)\n", " up_3 = initial_and_boundary_conditions(nx, nt_3)\n", " \n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " # Lamba function for Jacobian:\n", " A = lambda u: u\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt_1-1):\n", " up_1[i:nx-1, n+1] = u_1[i:nx-1, n] - sigma_1*(F(u_1[i+1:nx, n]) - F(u_1[i:nx-1, n]))\n", " u_1[i:nx-1, n+1] = ( 0.5*(up_1[i:nx-1, n+1] + u_1[i:nx-1, n]) - \n", " 0.5*sigma_1*(F(up_1[i:nx-1, n+1]) - F(up_1[i-1:nx-2, n+1])) )\n", " \n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt_2-1):\n", " up_2[i:nx-1, n+1] = u_2[i:nx-1, n] - sigma_2*(F(u_2[i+1:nx, n]) - F(u_2[i:nx-1, n]))\n", " u_2[i:nx-1, n+1] = ( 0.5*(up_2[i:nx-1, n+1] + u_2[i:nx-1, n]) - \n", " 0.5*sigma_2*(F(up_2[i:nx-1, n+1]) - F(up_2[i-1:nx-2, n+1])) ) \n", " \n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt_3-1):\n", " up_3[i:nx-1, n+1] = u_3[i:nx-1, n] - sigma_3*(F(u_3[i+1:nx, n]) - F(u_3[i:nx-1, n]))\n", " u_3[i:nx-1, n+1] = ( 0.5*(up_3[i:nx-1, n+1] + u_3[i:nx-1, n]) - \n", " 0.5*sigma_3*(F(up_3[i:nx-1, n+1]) - F(up_3[i-1:nx-2, n+1])) )\n", " \n", " # Wave at speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", " \n", " dt_lf = dx * 2.0\n", " \n", " plot_cfl(x,u_1,nt_1,u_2,nt_2,u_3,nt_3,u_lf, x_lf, nt_lf, dt_1, dt_2, dt_3, dt_lf) " ] }, { "cell_type": "code", "execution_count": 203, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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58mS98847kqSKigq9//77mjRpkiTVOhX4rbfe0t13361hw4ZJkqKjo3XFFVdI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\nLCwM7tGjx54rr7xy/4IFCx5piuIAAED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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "maccormack_convection_cfl(0.25, 0.5, 1.0, 101, 2.0, 4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusion from MacCormack Scheme\n", "\n", "$$ \\left| {\\Delta t \\over \\Delta x} u_{max} \\right| \\lt 1 $$\n", "\n", "Similar behaviour to the Lax-Wendroff Scheme i.e.\n", "\n", "**The higher the CFL number, the more dispersive errors are accumulated**\n", "\n", "However, MacCormack is much easier to program\n", "\n", "If dispersion errors caused oscillations - the overshoot may make the solution more unstable" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Which scheme is the best for CFL = 1?" ] }, { "cell_type": "code", "execution_count": 208, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def scheme_comparison(sigma, nx, tmax, xmax):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u_1 = initial_and_boundary_conditions(nx, nt)\n", " u_2 = initial_and_boundary_conditions(nx, nt)\n", " u_3 = initial_and_boundary_conditions(nx, nt)\n", " up_3 = initial_and_boundary_conditions(nx, nt)\n", " \n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " # Lamba function for Jacobian:\n", " A = lambda u: u\n", " \n", " i = 1\n", " # Lax-Friedrichs\n", " for n in range(0,nt-1):\n", " u_1[i:nx-1, n+1] = (0.5*(u_1[i-1:nx-2, n]+u_1[i+1:nx, n])-\n", " 0.5*sigma*(F(u_1[i+1:nx, n])-F(u_1[i-1:nx-2, n])))\n", " \n", " # Lax-Wendroff\n", " for n in range(0,nt-1):\n", " u_2[i:nx-1, n+1] = (u_2[i:nx-1,n] -\n", " 0.5*sigma*( F(u_2[i+1:nx, n])-F(u_2[i-1:nx-2, n]) ) + \n", " 0.25*(sigma**2)*( ( A(u_2[i+1:nx, n])+A(u_2[i:nx-1, n]) )*\n", " ( F(u_2[i+1:nx, n])-F(u_2[i:nx-1, n]) )-\n", " ( A(u_2[i:nx-1, n])+A(u_2[i-1:nx-2, n]) )*\n", " ( F(u_2[i:nx-1, n])-F(u_2[i-1:nx-2, n]) ) ) ) \n", " \n", " # MacCormack\n", " for n in range(0,nt-1):\n", " up_3[i:nx-1, n+1] = u_3[i:nx-1, n] - sigma*(F(u_3[i+1:nx, n]) - F(u_3[i:nx-1, n]))\n", " u_3[i:nx-1, n+1] = ( 0.5*(up_3[i:nx-1, n+1] + u_3[i:nx-1, n]) - \n", " 0.5*sigma*(F(up_3[i:nx-1, n+1]) - F(up_3[i-1:nx-2, n+1])) )\n", " \n", " # Wave at speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", " \n", " dt_lf = dx * 2.0\n", " \n", " plot_schemes(x,u_1,nt,u_2,nt,u_3,nt,u_lf, x_lf, nt_lf, dt, dt, dt, dt_lf) " ] }, { "cell_type": "code", "execution_count": 209, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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55s+fr8jISL3//vsexy0Wi15++WVdcsklcjgcmjlzpvvY/v37dc0116h169Zq\n06aNbr31VuXn59e7xnfffaeQkBAdO3bM3fbFF18oKipKu3bt0q9+9Stt3bpVYWFhatWqlSRpypQp\nmjdvnrv/e++9pz59+ig8PFxdunRxh97U1FR169ZNdrtdnTt31iuvvNL4TTUBAREAAACAJGn58uXq\n0KGDVq9ercLCQj344IOSpIiICDkcDq/bggULvJ5r06ZNiomJkcPhqHfM6XQqJydHvXv3drf16tVL\nu3fvbrC2Tz75RLm5uRo1apRuuukmvfbaa/X6rFmzRtu2bdOXX36pt956y2NE8pFHHlFOTo727Nmj\nzMxMzZ8/v97n27Ztq+HDh+utt97yuCcTJ05Ujx499PLLL2vQoEEqLCx0h8hTp6empaVp8uTJeu65\n55Sfn69NmzapY8eOkqTo6GitWbNGBQUFSk1N1X333aft27c3+H3NQkAEAAAAfMz8+fPdwePUzVuo\naah/Q31/iOPHj8vpdHrdHnrooXr9s7KyNHPmTC1atMjr+YqKiiRJ4eHh7ja73a7CwsIGa3jttdc0\nevRoBQUF6aabbtIHH3ygI0eOePSZPXu27Ha74uLidPXVV2vHjh2SpM6dO+vaa6+Vv7+/Wrdurfvu\nu08bN270ep2kpCT9+c9/liRVV1frjTfe0KRJkySp0am3r776qqZNm6Zrr71WktSuXTtdeumlkqRR\no0bpoosukiQNGzZMCQkJ2rx582nPZwYCIgAAAOBj5s+fL5fLVW87XUA8077N7ciRI0pISNDdd9+t\n8ePHe+0TGhoqSSooKHC35efnKywszGv/0tJS/fWvf9VNN90kSerTp486duyolStXevRr27at+2eb\nzeYOorm5uZowYYLat2+v8PBwTZo0SUePHvV6rbFjx+rrr7/WgQMH9I9//EPh4eHq37//GX33rKws\nde7c2euxtWvX6ic/+YkiIyPlcDj097//vcEazERABAAAAODmbTXP0NBQhYWFed2eeeYZdz+n06mE\nhAQlJiZqzpw5DV7D4XAoJibGPcInSTt37lSPHj289n/nnXdUUFCgGTNmKCYmRjExMcrMzPQ6zdTb\nd/ntb38rPz8/7dq1S/n5+Vq+fLlqamq8fubkCOWf//xn/fnPf1ZSUtJp782p4uLitG/fvnrt5eXl\nGjdunB566CEdPnxYTqdTo0aN+kGLATU3q9kFAAAAAPAd0dHR7kVdTjo5Enc6BQUFGjFihIYMGaKn\nnnqq0f4JgSyUAAAgAElEQVRJSUlKSUlR//79lZOToyVLljQY+F577TVNmzZNTz75pLstKytLAwYM\n0K5du7wGy1PDV1FRkcLDw2W325Wdna1nn3220dqSkpJ05MgRPf300+72tm3bKisrS5WVlfL393df\n5+S1pk2bpoSEBN1www0aPny4cnJyVFRUpHbt2qmiokKtW7eWxWLR2rVr9dFHH6lnz56N3qeWxggi\nAAAAALc5c+YoJSVFDoejwWcIvXnnnXe0bds2paamukcX7Xa7srKyJEkrVqzwCHLJycnq3Lmz4uPj\ndfXVV+vhhx9WQkJCvfNmZ2dr3bp1mjVrlqKiotxb3759NXLkSC1btsxrPaeO9j322GP64osvFB4e\nrtGjR2vcuHGnHQ288sorZbFY1K9fP48X2F9zzTXq3r272rZtq6ioKPd1Tp5rwIAB7gVoIiIiNHz4\ncGVkZCgsLEwvvPCCbr75ZrVq1Uqvv/56vVeAnMl7GFuC4YvDmmfDMAzX+f4dAAAA4NtOvBuwyX6D\n53dY3/fTn/5Ut9xyi6ZOnWp2KU2qsT/LBEQAAACgEQTEC8vnn3+uESNGKDMzUyEhIWaX06Qa+7PM\nFFMAAAAAOGHy5Mn62c9+pueff/5HFw7PBCOIAAAAQCMYQcSPBSOIAAAAAIAzQkAEAAAAAEgiIAIA\nAAAATrCaXQAAAABwoXE4HIWGYYSZXQcuPA6Ho/B0x1mkBgAAAGhEUy9SA/gqppgCAAAAACQREAEA\nAAAAJxAQAQAAAACSCIgAAAAAgBMIiAAAAAAASQREAAAAAMAJBEQAAAAAgCQCIgAAAADgBAIiAAAA\nAEASAREAADSTqiqzKwAAnC0CIgAAaHJbtkiXXCK5XGZXAgA4GwREAADQpFwuac4c6b//lXJyzK4G\nAHA2CIgAAKBJffihdPiwNGyY9NVXZlcDADgbBEQAANBkampqRw9TUqQ+fQiIAHC+sZpdAAAA+PH4\ny18kq1W68Ubp+HFp0yazKwIAnA1GEAEAQJOorJTmzZOefloyDKlnT0YQAeB8Q0AEAABNIjVViouT\nfvrT2v3u3aW9e3ndBQCcTwiIAADgnJWWSo8/Xjt6eFJIiNSunbRvn3l1AQDODgERAACcsz/8QRo4\nsHY7FdNMAeD8QkAEAADnJD9fWrCgduXSunr2lL78suVrAgD8MAREAABwThYulK6/XurWrf4xRhAB\n4PxiWkCcOnXq/0VHR+f27Nmzwb827r333hcuvvjib3v37r1z+/btl7dkfQAAoHG5udKLL0rz53s/\nTkAEgPOLaQHxtttuS/3ggw9GNnT873//+6h9+/Z1+fbbby9+5ZVXpt95550vtWR9AADg9DIypPvv\nl269VYqP996nSxcpJ0cqKmrZ2gAAP4xpAXHo0KGbHQ6Hs6Hjq1atGjN58uTXJOmKK6741/HjxyNy\nc3OjW65CAABwqspKacMG6aGHpB49pH79JD+/2ncfNsRqlS67TNq9u8XKBACcA6vZBTQkOzs7Ni4u\nLvPkfvv27bOysrLaR0dH59btG9G2rfvnoNBQBYWGKiwyUpFxcfXOW5CXp2NZWfXa6U9/+tOf/vS/\noPobJ1uM0/YPjWytyLg4HbFE67+ZoWrdyl+XXWpV719my/mfvcq3WPXs4q4K9g+WJPXv31833HCD\nxzl69pRWrfpca9eucbclJCRo8ODB9a4H+IoNGzZow4YNZpcBtDifDYiS5HK5jFP3DcNweet3akAE\nAABnwP03ak3tzzU1ksslQ55/1Vpc1bJUlOriws1KuGuoAkNrVFVTpey92corOaLiymKtO7BOIzqP\nUI+oHl4v1bOn9PnnUteutftffPGFsrKyCIjwacOHD9fw4cPd+8nJyeYVA7Qgnw2IsbGx2ZmZme5/\nEs3KymofGxub7a3vgR07Wq4wAAAuNC6XlJAgZcVKM2fWtiV8f/hfWf/SHe/foRJ7iaYMmVLv4z17\nSmvWDNAbbwyQJC1fvlwfffRRCxQOADhbPvuaizFjxqxatmxZkiR99tlnP4mIiDjubXopAABoZoYh\nLVokPfGE5Ky/fMAV7a/Qv6f/W0M6DFH/V/pr8dbFqqqpch8/uZKp68TgZJ8+fZSYmNhS1QMAzoLh\ncnmdtdnsJk6c+PrGjRuvysvLax0dHZ2bnJz8WGVlpb8kzZgx42VJmjlz5u8/+OCDkSEhIcWpqam3\n9e3b94u65zEMw2XWdwAA4ILyq19JwcHS4sUNdvn26LeasXqGCsoLtGTMEvVp20cul9SmjbRrl8RT\nIThfGYZR7/En4MfItIDYVAiIAAC0kMOHpe7dpU8/lS65pMFuLpdLqTtS9Zt//EaZ92XK5m/T1VdL\nc+bUzlQFzkcERFwofHaKKQAA8DFRUbXvuHjwwdN2MwxDUy+fqgHtBmjVN6skfT/NFADg2wiIAADg\nzN17b+1LDf/5z0a7Tuo1Sct2LpMk9epFQASA8wEBEQAAnLnAQOnZZ6X775eqq0/bNbFrorZmbVVu\nUS4jiABwniAgAgCAs/Pzn0utWkmvvnrabiEBIRp76Vi9vut1de8u7d1bmymPHj2qxadZ6AYAYB4C\nIgAAODuGUbuS6WOPSfn5p+16cpppaGjtCqb79klFRUV6/vnnW6hYAMDZICACAICzd/nl0qhR0lNP\nnbbb8I7Ddbj4sHYd3uWeZhoUFKTy8vIWKhQAcDZ4zQUAAPhhcnJqlycdNMj78c6dpeef1+x/zpZL\nLgVs/B9ZLNJ99x1Xx44ddfz48ZatFzgHvOYCFwoCIgAA+OF275b+85/67aWl0h13SPn52n14t0b8\neYQWxh7UW2/6aeXKMkVERKisrKzl6wV+IAIiLhRWswsAAADnse7da7e6amqkW26RqqvVPaq7okKi\nVBK9QV9+ea0CAwNVUVEhl8slw+D3bQDwJTyDCAAAmp7FIoWFuRexSeqdpA3HlunQIamkxNATTzyh\nmpoak4sEANTFFFMAANA8LrpI+vhjqVMn5RblqusfuqrDX7P0pz+EaOBAs4sDzg5TTHGhYAQRAAA0\nj4gI6cRCNNGh0RocN1j2ge/qq69MrgsA0CACIgAAaB6nBESp9p2Ih2OWERABwIcREAEAQPOoExDH\nXjpWh5Smbd/kmFgUAOB0CIgAAKB51AmIwf7BuqHLjdpRvdLEogAAp0NABAAAzcPh8AiIkjT9ikkq\nu2SZnn32ZWVkZJhUGACgIQREAADQPOqMIErSVR2HyRp2XK+kvqwDBw6YUxcAoEEERAAA0Dy8BESL\nYVGPmlt0rNKp8vJykwoDADSEgAgAAJpHRITkdNZr7hp1icpdVSorKzOhKADA6RAQAQBA8/AygihJ\n9mCbXH4iIAKADyIgAgCA5tFAQAwLtKnG4mKKKQD4IAIiAABoHg0FxCCb/C9tpZ49e5pQFADgdAiI\nAACgeZxmiqnROUS9e/c2oSgAwOkQEAEAQPNoICCG22yqMkpMKAgA0BgCIgAAaB5hYVJpqVRV5dEc\nbrOpmoAIAD6JgAgAAJqHYUjh4VJ+vkdzeEiwqi0ERADwRQREAADQfLy8C9ERalONHwERAHwRAREA\nADQfL88hRoTYVPNdkd577z2TigIANISACAAAmo+3gBgaKB2u0urVq00qCgDQEAIiAABoPl4Cos1m\nSEaASsqYZgoAvoaACAAAmo+XgOjvL0mBKiwuNqUkAEDDCIgAAKD5eAmIhiHJCFIRAREAfA4BEQAA\nNB+Ho15AlCSLJUjFJaUmFAQAOB0CIgAAaD5eRhAlyWIP19CRI0woCABwOgREAADQfBoIiP5hEeoz\n7CoTCgIAnA4BEQAANJ+ICMnprNfs57Ipv4RVTAHA1xAQAQBA82loBNFlU0EpAREAfA0BEQAANJ+G\nAqJhU2EZi9QAgK8hIAIAgObTQEAMMGwqLGMEEQB8DQERAAA0n4ZGEGsC9Mnf3jahIADA6RAQAQBA\n8wkJkSoqardTBBlB+urDj00qCgDQEAIiAABoPoZRO4qYn+/RHBwQpuqqKrlcLpMKAwB4Q0AEAADN\ny8s0U1tAmAxDqqqqMqkoAIA3BEQAANC8vATEYP9gGVY/lZWVmVQUAMAbAiIAAGheERGS0+nRFGy1\nyfDzU3l5uUlFAQC8ISACAIDm5WUEMSTApshhlykoKMikogAA3hAQAQBA8/ISEEMDbbL1i1VoaKhJ\nRQEAvCEgAgCA5tVAQCyvKTGpIABAQwiIAACgeXkJiGFBNlW4CIgA4GsIiAAAoHl5CYj2YJsqRUAE\nAF9DQAQAAM3L4fAaEKsMAiIA+BoCIgAAaF5eRhDDbTaV78rTnj17TCoKAOANAREAADQvb1NMbcGq\nTi8mIAKAjyEgAgCA5hURITmdHk2OEJvkX63y8nKTigIAeENABAAAzcvbCGJIgGR1qbik2KSiAADe\nEBABAEDz8hIQbTZDslhVWFJoUlEAAG8IiAAAoHkFB0vV1VJZmUeTLP4qKikyry4AQD0ERAAA0LwM\no3YUMT/f3RQcLKmjXT369jCvLgBAPQREAADQ/OpMMw0OltQ2Upf0vsS8mgAA9RAQAQBA83M4PAKi\n1Sqp0qaC0hLzagIA1ENABAAAzc/LQjWWapucxQREAPAlBEQAAND8vLwL0a8mWMcJiADgUwiIAACg\n+XkZQbS6bMovISACgC8hIAIAgObnbYrpsXJtXPNPkwoCAHhDQAQAAM3PS0A0Ciq0Y9NnJhUEAPCG\ngAgAAJqftymmfjaVl5ebVBAAwBsCIgAAaH5eAmKAfwgBEQB8DAERAAA0vzrvQZSkQGuIKioqTCoI\nAOANAREAADQ/LyOIgQGhqiIgAoBPsZpdAAAAuAB4CYhh9nayDr7MpIIAAN4QEAEAQPOLiJCcTo8m\ne3iUArp2MKkgAIA3TDEFAADN7+QIosvlbrJZbSqtKjGxKABAXQREAADQ/IKCJMOQysrcTSEBNpVV\nExABwJcQEAEAQMuo8xxiSKBN5TUERADwJQREAADQMuoExFACIgD4HAIiAABoGXUCYligTcc//q+q\nq6tNLAoAcCoCIgAAaBkOh2dADLapLO2oysvLTSwKAHAqAiIAAGgZdUYQ7UE2ySoCIgD4EAIiAABo\nGXUDoq02IJadsrIpAMBcBEQAANAyIiIkp9O9G24LlvxcBEQA8CEERAAA0DLqLlJj85esUlFJkYlF\nAQBORUAEAAAto05AtNkMGYOCZLPbTCwKAHAqAiIAAGgZdQJicLDk1yNctggCIgD4CgIiAABoGV4C\noiptKqksMa8mAIAHAiIAAGgZDQTE0qpS82oCAHggIAIAgJbhcHgExKAgMYIIAD6GgAgAAFqGlxHE\nmnICIgD4EgIiAABoGeHhtQHR5ZJ0IiCm52v7tu0mFwYAOImACAAAWkZgoGS1SiW1I4Z+fpIOHdfu\nL/eaWxcAwI2ACAAAWk6daaYWS6AKi5hiCgC+wnq6g5WVlf4fffRRwqZNm4YdOHCgo2EYrvj4+IPD\nhg3bNGLEiA+tVmtVSxUKAAB+BE4GxNhYSScCYnGxyUUBAE5qcATxiSeemDdgwIDPV69efUPXrl33\nTp069f8mT5782qWXXvrN+++/P7p///7bUlJS5rZksQAA4DxXdwTRL0jFxbzmAgB8RYMjiL179945\nd+7cFMMwXHWPTZ069f9qamosq1evvqF5ywMAAD8qdQKin1+QSkoJiADgKxocQRwzZsyquuGwpqbG\nUlBQYJcki8VSM2bMmFXNXSAAAPgRqfMuRFt0N7XpFmdiQQCAUzW6SM3EiRNfLygosBcXF4f06NFj\n12WXXbZnwYIFD7VEcQAA4EemzghiWJtLFHZRaxMLAgCcqtGA+PXXX3ez2+0F7777buJ111239sCB\nAx2XL18+qSWKAwAAPzJ1AmKQn01FFaxiCgC+otGAWFVVZa2srPR/9913E0ePHv2+v79/pbfnEgEA\nABoVESE5ne7dID+bSgiIAOAzGg2IM2bMeLljx44HioqKQocNG7bpwIEDHcPDw/NbojgAAPAjU2cE\nMdg/WCWVBEQA8BUNBsQtW7YMdrlcxr333vtCdnZ27Nq1a6+zWCw18fHxB9etW3dNSxYJAAB+JOoG\nRKtNpVUERADwFQ0GxGXLliX17dv3i/Hjx7+5dOnSKd99911bSTIMw+Xv71/ZciUCAIAfjToB0VVy\nTN9t2WdiQQCAUzX4HsQ//vGPv5KkPXv2XLZ27drrpkyZsvT48eMR11xzzbqRI0d+cOWVV37q5+dX\n3XKlAgCA816dgGhUFKtg53cmFgQAOJXhcp35ejMlJSW29evXX7127drrtm7dOujf//53v2as7YwY\nhuE6m+8AAABM9O230nXXSftqRw3HTFmptf+cpsqsUpMLA07PMAy5XC7D7DqA5nZGAdHpdDoyMzPj\nqqqqrCf/j9GvX79/N3t1Z4CACADAeSQvT+ratfZ/Jf3yzjV6452fq/q7CpMLA06PgIgLRYNTTE+a\nN2/eE0uXLp3SqVOn/1gslpqT7evXr7/6XC/+wQcfjJw1a9bz1dXVfrfffvuShx9++H9OPb5hw4bh\nY8eOfa9Tp07/kaRx48b9be7cuSnnel0AAGCS8HApP19yuSTDUHhouFxVNY1/DgDQIhoNiG+++eb4\n/fv3dw4ICGjSf9qrrq72mzlz5u//+c9//jQ2NjZ7wIABn48ZM2bVZZddtufUflddddXGVatWjWnK\nawMAAJP4+0uBgVJxsRQaqoiQCAIiAPiQRt+D2L17991Op9PR1BdOS0sb2KVLl30dO3Y84O/vXzlh\nwoQ33nvvvbF1+zGUDwDAj0xEhOR0SpKiW8dKQyUeFwEA39DoCOJvf/vbpy6//PLtPXr02BUYGFgu\n1T73d66jetnZ2bFxcXGZJ/fbt2+f9a9//euKU/sYhuHasmXL4N69e++MjY3NXrhw4YPdunX7uu65\n5s+f7/55+PDhGj58+LmUBgAAmtPJlUzj4tSmlUNGPz9V1lQqwC/A7MoAtw0bNmjDhg1mlwG0uEYD\nYlJS0rLZs2c/06NHj10nn0E0DOOc/5nvTM7Rt2/fLzIzM+NsNlvJ2rVrr0tMTHw3PT39krr9Tg2I\nAADAx53yqovgYMmvxqaSyhICInxK3UGH5ORk84oBWlCjATE0NLTo3nvvfaGpLxwbG5udmZkZd3I/\nMzMzrn379lmn9gkLCys8+fN111239q677nrx2LFjrVq1anWsqesBAAAtpE5AtFTXBsSIoAiTCwMA\nNBoQhw4dunnOnDlPjxkzZtXJKaZS7ejeuVy4f//+27799tuLDxw40LFdu3aH3nzzzfGvv/76xFP7\n5ObmRkdFRR02DMOVlpY20OVyGYRDAADOc3UDYlVtQAQAmK/RgPjFF1/0NQzD9dlnn/3k1PZzfc2F\n1Wqt+v3vfz9zxIgRH1ZXV/tNmzbt1csuu2zPyy+/PEOSZsyY8fJf//rXX7z00kt3Wq3WKpvNVvLG\nG29MOJdrAgAAH3BKQAwKkgwCIgD4DON8XzXMMAzX+f4dAAC4oMybJwUESPPm6csvpX53xOqDpct0\n7WXXml0Z0CDDMFhdHxeEBl9zsXTp0ilVVVUNjjBWVFQEpKam3tY8ZQEAgB+tiAhp61Zp+XIFf/iu\nqnYf1ZH3/iYtXy6tWCEVFZldIQBcsBoMgEVFRaEDBgz4vGvXrnv79++/LSYmJsflchnfffdd223b\ntvXfu3dv1zvuuONPLVksAAD4EbjmGmnHDumjjxRc7JBh8VPB9i+k3YXSpk21DybeeKPZVQLABem0\nU0xdLpfx6aefXvnJJ58MycjI6CBJ8fHxB4cMGfLJ4MGDtzTF6y7OFVNMAQA4fx09KrXuEqFnX52r\nB298ULr9dumKK6Q77jC7NMADU0xxoTjtIjWGYbiGDBnyyZAhQz5pqYIAAMCFIzhYkmFVYemJN1tF\nRtamRgCAKRp8BhEAAKC5BQVJMvxVWHziucPWraW8PFNrAoALGQERAACYxmKRLPH9FOCw1TYwgggA\npiIgAgAAU/m37SNLWEDtTmQkI4gAYKLTPoMoScnJyY/VbTMMw/Xoo48+3jwlAQCAC4m/bCooO/EM\nYuvWjCACgIkaDYghISHFJ1crLS0tDV69evUN3bp1+7r5SwMAABeCAMOmorLc2h2mmAKAqRoNiA8+\n+ODCU/d/85vfPJuQkPBR85UEAAAuJIEWm4rKS2p3WKQGAEx11s8gFhcXh2RnZ8c2RzEAAODCE2ix\nqbiitHbH4ZDy86XqanOLAoALVKMjiD179vzq5M81NTWWw4cPR/H8IQAAaCqVh3cr+6sDtTt+fpLd\nLh0/XjvdFADQohoNiO+///5od2ertSo6OjrX39+/snnLAgAAF4qq4//R0f253zecnGZKQASAFtdo\nQOzYseOBFqgDAABcoAL8Q1RaXv59AwvVAIBpeA8iAAAwVaB/iCorK75v4F2IAGAaAiIAADBVUECo\nKitOCYi8CxEATENABAAApgoODFV15SnLGzDFFABMQ0AEAACmio8fIqO73/cNvAsRAExDQAQAAKaK\nb99XNZ2qvm9gBBEATENABAAApgoLClalq1Qul6u2gYAIAKYhIAIAAFOF2qyyyKqK6hML1TDFFABM\nQ0AEAACmCg6W/FzBKqksqW1gBBEATENABAAApgoKkvxqbN8HREYQAcA0BEQAAGCq0tJsVX9S/n1A\nbNVKOnZMOvlMIgCgxRAQAQCAqWpq8lX1ZfH3ATEgoHbeaUGBuYUBwAWIgAgAAEwVFhYkV5W+D4gS\n00wBwCQERAAAYCq7PUiqdnkGRBaqAQBTEBABAICp7PZAqYqACAC+gIAIAABMZbcHyVVVo9Kq0u8b\nmWIKAKYgIAIAAFNFRAQpoG8/RhABwAcQEAEAgKlCQ/3k17Evi9QAgA8gIAIAAFMFBUnVZTZGEAHA\nBxAQAQCAqYKDpapSAiIA+AICIgAAMFVQkFRTZlNxBVNMAcBsBEQAAGAqw5CssqmwjBFEADCb1ewC\nAAAAjMyNyj0U+H1DZCQjiABgAkYQAQCA6WqObtfRXOf3DSdHEF0u84oCgAsQAREAAJjOYglUcWnx\n9w02m2SxSCUlDX8IANDkCIgAAMB0Fr8glZSWejayUA0AtDgCIgAAMJ3VEqTSsjoBkYVqAKDFERAB\nAIDprNZglREQAcB0BEQAAGC6dhdNkKuN4dnIFFMAaHEERAAAYLr2cSNU5ajybGQEEQBaHAERAACY\nLiTApvKaOiuWMoIIAC2OgAgAAEwXGuglIDKCCAAtjoAIAABMFxoUrEpXqVwu1/eNBEQAaHEERAAA\nYLqQYD/5KUBlVWXfNzLFFABaHAERAACYLifnn7Lssaq06pRXXTCCCAAtjoAIAABM53R+KddBqaTy\nlOcQCYgA0OIIiAAAwHTBwUEyKv08AyJTTAGgxREQAQCA6Wy2IKmqTkAMDZUqKqSysoY/CABoUgRE\nAABgupCQIBmVFs+AaBi1o4hMMwWAFkNABAAAprPZAqW6AVHiOUQAaGFWswsAAAC47LK+CvpPRwIi\nAJiMEUQAAGC6jh0vUmD7i+oHRBaqAYAWRUAEAACmCwqSXBU2RhABwGQERAAAYLrgYMlVblNpZann\ngchIRhABoAUREAEAgOmCg6WaimDvU0wZQQSAFkNABAAApgsOlqrLmGIKAGYjIAIAANNVVBxXyc5N\nKqlikRoAMBMBEQAAmM5qrVRl1jZGEAHAZAREAABguvDwQKm6ioAIACYjIAIAANPZ7UGSq0rFFUwx\nBQAzERABAIDpAgL8JVeNCkqKPQ+Eh0vFxVJlpTmFAcAFhoAIAABMZxiGZPirsKjI84DFIjkc0rFj\n5hQGABcYAiIAAPAJoXGzVFxdWv8AzyECQIshIAIAAJ8Q0fZmlbvK6x8gIAJAiyEgAgAAnxBstdVf\nxVRioRoAaEEERAAA4BNsVptKq7wEREYQAaDFEBABAIBPsAUQEAHAbAREAADgE0ICbCqvYYopAJiJ\ngAgAAHzCd5kvq/xwqWpcNZ4HGEEEgBZDQAQAAD4h78iH8sv3V1lVmecBRhABoMUQEAEAgE/w9w+U\ntSqw/kqmjCACQIshIAIAAJ8QEBAkv6oAAiIAmIiACOD/27v74Krre0/gn5MEeZbwoAEJbVDC5Ukg\nHSCde4ugFKm4Rm07XrAqe0tZWkdZ7Y6jvet02x3r6u20tchMF7utBb0LOt1exUKpaA04OBgcgxZB\nCUU0QYgiRh5EyMPZPzhoJEFOaB4O4fWaOWN+5/c5h8/5zkfgze/hAGSErl27RVZdlzhce/izO5xi\nCtBuBEQAICN07do1ErVdmh5B7Ns3oqYmoqGh+RcC0GoERAAgI0yYcGN0y+/fNCDm5ET07n0sJALQ\npgREACAjjBp1SXTrPyAO1R5qutNppgDtQkAEADJC9+4RPY4WxBt732i6041qANqFgAgAZIRu3SL6\nH5wSa99a23SnI4gA7UJABAAyQvfuEX0+mBLr3loXyWTyszsdQQRoFwIiAJARunePSOz/QvQ8p2ds\n3bv1szsFRIB2ISACABnhb39bHzt2LIkpX5wSa3eecJqpU0wB2oWACABkhPff3xF79z5zLCCeeB2i\nI4gA7UJABAAyQq9eXaO29uOYUnAsIH7mOkRHEAHahYAIAGSEXr26RV3dxzE0d2jkZOVExb6KT3c6\nggjQLgREACAjnHtut6ivPxKJRKLpdYgCIkC7EBABgIzQq1fXqK//OCKi6XWITjEFaBcCIgCQEUaP\n/ofIzv5+RERMKZgSpTtLP70OsX//iP37j/23ucfcuR3YOUDnkdPRDQAAREQUFAyM2tprIiKisF9h\nNCQbYscHO+KifhdFnHNOxLvvRhw50vSFR49GjBsXsW1bxPDh7dw1QOfiCCIAkBG6dIlIJiNqa+PY\ndYgFJ5xm2qtX80cPBw2K+O53Ix54oOOaB+gkBEQAICMkEhHdu0ccPnxsu9nvQzyZm2+OWLbMjWwA\n/k3uzHUAABH2SURBVE4CIgCQMZoExJ1pBsSBAyOuvTZi8eK2aw7gLCAgAgAZo3FAHDFgRByuOxxv\n1byV3otvvz1i0aLmr1MEIC0CIgCQEerq6mL//ps/CYiJRCIu+eIl6Z9mevHFEaNHRzz2WNs1CdDJ\nCYgAQEbIzs6ODz/833H4cPKT51p0HWJExPe/H/Hznx+72w0ALSYgAgAZIZFIRCLRJfbvP/rJcy26\nDjEiYsaMY197UVra+g0CnAUERAAgY2RldYsPP/z4k+3R54+Omo9rYtf+Xem+wbFrEX/+8zbqEKBz\nExABgIzRpUu3ePTRI9HQcGw7K5EVk784uWWnmd5wQ0RZWcQbb7RNkwCdmIAIAGSMAQO6xttvfxzz\n58cnIbHF1yF27x7x3e9GPPBA2zQJ0IkJiABAxvi3f7s//vCH3NiyJeKWW47da6bF1yFGRNx8c8Ty\n5RF797ZNowCdVIcFxNWrV39txIgRrxcWFlbcf//9dzZXs2DBgoWFhYUV48aNe6W8vLyovXsEANrX\n7NmzY/Dgc+NPf4p4+eWI226LuPj8sVF9qDr2HNyT/hvl5UVce23E4sVt1yxAJ9QhAbG+vj77lltu\nWbR69eqvbdmyZdSyZctmb926dWTjmlWrVs3cvn37sIqKisKHHnrov3zve9/7VUf0CgC0v3PPjVi9\nOmL9+oi77syOrwz5Sqx7a13L3uT22yMWLYo4cqRtmgTohHI64hctKyubNGzYsO0FBQU7IyJmzZq1\n/Mknn7x65MiRW4/XrFixomTOnDlLIiKKi4tfrKmpya2urs7Ly8ur7oieAYD2lZsb8fTTEZddFtG/\n+5RY22dtXDf6uvTf4OKLI4qKIgoKIs45p+n+7OyIMWMiiosjvvzliIkTjyVTgLNYhwTEXbt2DR4y\nZEjl8e38/PyqF198sfhUNVVVVfnNBcQf/ehHn/w8derUmDp1apv0DQC0vYaGhli5cuUn23fcEfHf\n7s2KF7f/R/Tb97Um9cmGhqh45aUmzyciEYXXzYuYebBp/WuvHLsLTk1NxLMbIh5fGYmaD6Iw/8KI\nwRdEnHdeROLYiVbJZDIqdm7/9A2yIiKRiERWdhQWjojIyo7IzjpWn8iKZLIhKra/3kw/EYWFo479\n0Lifk9YnonD4qKafN9kQFRVb1bdx/Xvv7on6+vomz0Nn1yEBMZFIJNOpSyaTn/kt9GSvaxwQAYAz\nWzKZjIceeugzz108OBnry7LjoYEPNa1vSMaHT21s+kaJROQmJzZfv6aZ+pxE5BY1RNS9GXGk4rP1\nf93c/Pv3q/x0O5n8tP6FpoEjEhG5PSqaPJ1sSMaH609S332b+o6sn9YoULbwDGc4U3VIQBw8ePCu\nysrKIce3Kysrh+Tn51d9Xk1VVVX+4MGD0/yWXADgTJWdnR1PPfVUy170yxb+Ii2t56yX+F3i1EXQ\nCXTITWomTJjwUkVFReHOnTsLjh49es5jjz32zyUlJSsa15SUlKxYunTpTRERGzZs+HJubm6N6w8B\nAADaToccQczJyalbtGjRLTNmzPhzfX199ty5c38zcuTIrYsXL54fETF//vzFM2fOXLVq1aqZw4YN\n296zZ89DDz/88L90RK8AAABni0QymdblgBkrkUgkz/TPAABAZkskEk3ujwGdUYecYgoAAEDmERAB\nAACICAERAACAFAERAACAiBAQAQAASBEQAQAAiAgBEQAAgBQBEQAAgIgQEAEAAEgREAEAAIgIAREA\nAIAUAREAAICIEBABAABIERABAACICAERAACAFAERAACAiBAQAQAASBEQAQAAiAgBEQAAgBQBEQAA\ngIgQEAEAAEgREAEAAIgIAREAAIAUAREAAICIEBABAABIERABAACICAERAACAFAERAACAiBAQAQAA\nSBEQAQAAiAgBEQAAgBQBEQAAgIgQEAEAAEgREAEAAIgIAREAAIAUAREAAICIEBABAABIERABAACI\nCAERAACAFAERAACAiBAQAQAASBEQAQAAiAgBEQAAgBQBEQAAgIgQEAEAAEgREAEAAIgIAREAAIAU\nAREAAICIEBABAABIERABAACICAERAACAFAERAACAiBAQAQAASBEQAQAAiAgBEQAAgBQBEQAAgIgQ\nEAEAAEgREAEAAIgIAREAAIAUAREAAICIEBABAABIERABAACICAERAACAFAERAACAiBAQAQAASBEQ\nAQAAiAgBEQAAgBQBEQAAgIgQEAEAAEgREAEAAIgIAREAAIAUAREAAICIEBABAABIERABAACICAER\nAACAFAERAACAiBAQAQAASBEQAQAAiAgBEQAAgBQBEQAAgIgQEAEAAEgREAEAAIgIAREAAIAUAREA\nAICIEBABAABIERABAACICAERAACAFAERAACAiBA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "scheme_comparison(1.0, 101, 2.0, 4.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Conclusion of the Best Scheme\n", "\n", "MacCormack is the best scheme:\n", "\n", "* less diffusive than Lax-Freidrichs \n", "* less dispersive than Lax-Wendroff " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Beam-Warming Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Beam-Warming Numerical scheme\n", "\n", "* Taylor Expansion to 2nd order term (replacing $ u_t $ with the average):\n", "\n", "$$ u_i^{n+1} = u_i^n + {\\Delta t \\over 2}[(u_t)_i^n + (u_t)_i^{n+1}] + O(\\Delta t^3) $$\n", "\n", "* Replace $u_t$ by spatial derivatives:\n", "\n", "$$ (u_t)_i^n = - (F_x)_i^n $$\n", "\n", "$$ u_i^{n+1} = u_i^n - {\\Delta t \\over 2}[(F_x)_i^n + (F_x)_i^{n+1}] $$\n", "\n", "* Taylor Expansion of $F^{n+1}$\n", "\n", "$$ F^{n+1} = F^n + {{\\partial F \\over \\partial t} \\Delta t} + O(\\Delta t^2) $$\n", "\n", "* Replacing the derivative of F with the Jacobian and using **Forward Differencing in time for the velocity gradient** (to avoid a second order derivative in space for F):\n", "\n", "$$ {{\\partial F} \\over {\\partial t}} = {{\\partial F} \\over {\\partial u}} {{\\partial u} \\over {\\partial t}} = A_i^n {{\\left( {{u_i^{n+1} - u_i^n}} \\right)} \\over \\Delta t} $$\n", "\n", "Hence:\n", "\n", "$$ F_i^{n+1} = F_i^n + {{A_i^n u_i^{n+1} - A_i^n u_i^n} \\over \\Delta t} $$\n", "\n", "And:\n", "\n", "$$ u_i^{n+1} = u_i^n - {\\Delta t \\over 2}[2(F_x)_i^n + {\\partial \\over {\\partial x}} \\left( {A_i^n u_i^{n+1} - A_i^n u_i^n} \\right)] $$\n", "\n", "* For the first derivative of **Flux** in space: 2nd order CD in space between `i+1` and `i-1`\n", "* For the first derivative of **Jacobian times the Velocity Difference** in space: 2nd order in space between `i+1` and `i-1`\n", "\n", "## Discrete equation\n", "\n", "$$ u_i^{n+1} = u_i^n - {{\\Delta t \\over 2}} {(F_{i+1}^n - F_{i-1}^n) \\over {\\Delta x}} - {{\\Delta t} \\over 2} {({A_{i+1}^n u_{i+1}^{n+1} - A_{i-1}^n u_{i-1}^{n+1}}) \\over {2 \\Delta x}} -{{\\Delta t} \\over 2} {({A_{i+1}^n u_{i+1}^n - A_{i-1}^n u_{i-1}^n}) \\over {2 \\Delta x}} $$\n", "\n", "$$ - {\\Delta t \\over {4 \\Delta x}} \\left( A_{i-1}^n u_{i-1}^{n+1} \\right) + \n", "u_i^{n+1} + {\\Delta t \\over {4 \\Delta x}} \\left( A_{i+1}^n u_{i+1}^{n+1} \\right) = \n", "u_i^n - {1 \\over 2} {\\Delta t \\over \\Delta x} (F_{i+1}^n - F_{i-1}^n) + \n", "{\\Delta t \\over 4 \\Delta x}(A_{i+1}^n u_{i+1}^n - A_{i-1}^n u_{i-1}^n) $$\n", "\n", "## TDMA\n", "\n", "For a description of this, see:\n", "\n", "http://www.thevisualroom.com/tri_diagonal_matrix.html\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 101\n", " dx = xmax/(nx-1)\n", " tmax = 2.0\n", " sigma = 1.0\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt-1\n", " u[0,n]=1\n", " u[nx-1,n]=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u[i,0] = 1\n", " else\n", " u[i,0] = 0\n", " \n", " #Lambda function\n", " F = (u/2)**2\n", " \n", " #Lamba function\n", " A = u\n", " \n", " #Iteration\n", " for n between 0 and nt-1\n", " for i between 1 and nx-2 \n", " \n", " a[i] = - (dt / (4 * dx)) * A[i-1, n]\n", "\n", " b[i] = 1\n", "\n", " c[i] = (dt / (4 * dx)) * A[i+1, n]\n", "\n", " d[i] = u[i,n] - 0.5 * (dt / dx) * (F[i+1, n] - F[i-1, n]) + \n", " (dt / (4 * dx)) * (A[i+1, n] * u[i+1, n] - A[i-1, n] * u[i-1, n])\n", " \n", " #Corrections for BCs:\n", " \n", " d[1] = d[1]-a[1]*B1\n", " d[nx-2] = d[nx-2]-a[nx-2]*B2\n", " \n", " #Built-in solver:\n", " \n", " l_and_u = (1, 1)\n", " abc = np.matrix([c[1:nx-1], b[1:nx-1], a[1:nx-1])\n", " RHS = d[1:nx-1]\n", " u[1:nx-1, n] = linalg.solve_banded(l_and_u, abc, RHS)\n", " " ] }, { "cell_type": "code", "execution_count": 213, "metadata": { "collapsed": false }, "outputs": [], "source": [ "try:\n", " import numpypy as np # for compatibility with numpy in pypy\n", "except:\n", " import numpy as np # if using numpy in cpython\n", " \n", "## Tri Diagonal Matrix Algorithm(a.k.a Thomas algorithm) solver\n", "def TDMAsolver(a, b, c, d):\n", " '''\n", " TDMA solver, a b c d can be NumPy array type or Python list type.\n", " refer to http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm\n", " '''\n", " nf = len(a) # number of equations\n", " ac, bc, cc, dc = map(np.array, (a, b, c, d)) # copy the array\n", " for it in xrange(1, nf):\n", " mc = ac[it]/bc[it-1]\n", " bc[it] = bc[it] - mc*cc[it-1]\n", " dc[it] = dc[it] - mc*dc[it-1]\n", "\n", " xc = ac\n", " xc[-1] = dc[-1]/bc[-1]\n", "\n", " for il in xrange(nf-2, -1, -1):\n", " xc[il] = (dc[il]-cc[il]*xc[il+1])/bc[il]\n", "\n", " del bc, cc, dc # delete variables from memory\n", "\n", " return xc " ] }, { "cell_type": "code", "execution_count": 249, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_oscillatory(u,x,NT,u_analytical, x_analytical, NT2, step, dt, dt_lf):\n", " \"\"\"\n", " Plots the 1D velocity field\n", " \"\"\"\n", "\n", " import matplotlib.pyplot as plt\n", " import matplotlib.cm as cm\n", " plt.figure()\n", " ax=plt.subplot(111)\n", " colour=iter(cm.rainbow(np.linspace(0,step,NT))) \n", " for n in range(0,int(NT),int(step)):\n", " t = n*dt\n", " c=next(colour)\n", " ax.plot(x,u[:,n],linestyle='-',c=c,label='t='+str(t))\n", " t_lf =(NT2-1)*dt_lf \n", " ax.plot(x_analytical,u_analytical[:,NT2-1],linestyle='--',c='k',label='t='+str(t_lf)+' analytical') \n", " box=ax.get_position()\n", " ax.set_position([box.x0, box.y0, box.width*2,box.height*2])\n", " ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n", " plt.ylim([-0.2,1.8])\n", " plt.xlim([0.0,4.0])\n", " plt.xlabel('x (m)')\n", " plt.ylabel('u (m/s)')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 260, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def beam_warming_convection(sigma, nx, tmax, xmax, step, B1):\n", " \n", " from scipy import linalg\n", " \n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", " \n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Coefficients\n", " a = np.zeros(nx-2)\n", " b = np.ones(nx-2)\n", " c = np.zeros(nx-2)\n", " d = np.zeros(nx-2)\n", " \n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " # Lambda function for Jacobian:\n", " A = lambda u: u\n", " \n", " # index of space\n", " i = 1\n", " \n", " #index in TDMA\n", " m = 0\n", " \n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " \n", " a[m:nx-2] = - (dt / (4.0 * dx)) * A(u[i-1:nx-2, n])\n", " \n", " b[m:nx-2] = 1.0\n", " \n", " c[m:nx-2] = (dt / (4.0 * dx)) * A(u[i+1:nx, n])\n", " \n", " d[m:nx-2] = ( u[i:nx-1,n] - \n", " 0.5 * (dt / dx) * (F(u[i+1:nx, n]) - F(u[i-1:nx-2, n])) + \n", " (dt / (4.0 * dx)) * (A(u[i+1:nx, n]) * u[i+1:nx, n] - \n", " A(u[i-1:nx-2, n]) * u[i-1:nx-2, n]) )\n", " #Correction for BCs (other BCs = 0):\n", " d[m] = ( u[i,n] - \n", " 0.5 * (dt / dx) * (F(u[i+1, n]) - F(u[i-1, n])) + \n", " (dt / (4.0 * dx)) * (A(u[i+1, n]) * u[i+1, n] - \n", " A(u[i-1, n]) * u[i-1, n]) - a[m]*B1 )\n", " \n", " u[1:nx-1, n+1] = TDMAsolver(a, b, c, d)\n", "\n", " \n", " # Wave at speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", "\n", " dt_lf = dx * 2.0\n", "\n", " plot_oscillatory(u,x,nt,u_lf, x_lf, nt_lf, step, dt, dt_lf) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beam-Warming with CFL = 1" ] }, { "cell_type": "code", "execution_count": 268, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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+8Y9/9uMf//hnz9T5BUEQhNVxJArQJFzT9Vm6FnecNa+QrN5ZA2g0oFIB4Gii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F7j6XjqrD0aYHd25pw1N0/UO7rPaGuLUQE+moJq6qwND9F5ht28gY8iq2N747k1a+1kZs0o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\ndfVoICtDvVNy1ZeXo8Wfn6H87PTzPu/f329RZ8/5u6nXn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beam_warming_convection(1.0, 101, 2.0, 4.0, 5, 1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What happens if the grid density is increased?\n", "\n", "* Oscillation density increases\n", "* Scheme is still stable, but oscillatory" ] }, { "cell_type": "code", "execution_count": 300, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Hjqw778iRI1x++eVbPs8HP/hBPvnJT/KpT32Kubm53X8h5zgq1hRFUfYobkJn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L3aLvbmfbKtyEbBRt3azcJTTIbD+leUK15vw7YpCXxdrldXldXv9F1o9MrL385S//yI033vj1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qJgna8mjdSNZMmhSMJKhmGCekCVmT5VJjhsaSrCEJyMacyEtK1txMI43X9sYZsJiQVau7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\nG41MUMOYqvbEI+2foTVDqaAPMo6gHZ9qxxHPMn/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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beam_warming_convection(1.0, 201, 2.0, 4.0, 5, 1.0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusions from Beam-Warming\n", "\n", "The method is stable but oscillatory because of the absense of damping, so introduce a damping function onto the RHS:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ D_e = - \\epsilon_e(u_{i+2}^n - 4u_{i+1}^n + 6u_i^n - 4u_{i-1}^n + u_{i-2}^n) $$\n", "\n", "For the **solution point** $i=1$, the value of $u_{-1}$ is unknown, so set it to the value at $u_{0}$ (as no periodic boundaries are used).\n", "\n", "For the **solution point** $i=nx-2$ the value of $u_{nx}$ is unknown, so set it to the value at $u_{nx-1}$ (for the same reason)\n", "\n", "\n", "## Pseudo Code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " epsilon = 0.125\n", "\n", " for i between 1 and nx-2\n", " ipos[i]=i+2\n", " ineg[i]=i-2\n", "\n", " ipos[nx-2]=nx-1\n", " ineg[1]=0\n", " \n", " for i between 1 and nx-2\n", " \n", " D[i] = -epsilon*(u[ipos[i],n] - 4*u[i+1,n] + 6*u[i,n] - 4*u[i-1,n] + u[ineg[i],n])\n", " \n", " # D[i] = -epsilon*(u[i+2,n] - 4*u[i+1,n] + 6*u[i,n] - 4*u[i-1,n] + u[i-2,n])" ] }, { "cell_type": "code", "execution_count": 244, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def damping_function(u, epsilon, nx, n):\n", " \n", " ipos = np.zeros(nx, dtype=numpy.int)\n", " ineg = np.zeros(nx, dtype=numpy.int)\n", " \n", " for i in range(1,nx-1):\n", " ipos[i] = i+2\n", " ineg[i] = i-2\n", " \n", " # Set the values at the extremities to the boundary values \n", " ipos[nx-2] = nx-1\n", " ineg[1] = 0\n", " \n", " D = np.zeros(nx)\n", " i = 1\n", " D[i:nx-1] = epsilon * (u[ipos[i:nx-1],n] - 4*u[i+1:nx,n] +\n", " 6*u[i:nx-1,n] - 4*u[i-1:nx-2,n] + u[ineg[i:nx-1],n])\n", " \n", " return D" ] }, { "cell_type": "code", "execution_count": 295, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def beam_warming_convection_damping(sigma, nx, tmax, xmax, step, B1, epsilon):\n", " \n", " from scipy import linalg\n", " \n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = dx * sigma\n", " nt = int(tmax/dt + 1)\n", " \n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", " \n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " # Coefficients\n", " a = np.zeros(nx-2)\n", " b = np.ones(nx-2)\n", " c = np.zeros(nx-2)\n", " d = np.zeros(nx-2)\n", " \n", " # Lambda function for Flux:\n", " F = lambda u: u**2.0 / 2.0 \n", " \n", " # Lambda function for Jacobian:\n", " A = lambda u: u\n", " \n", " # index of space\n", " i = 1\n", " \n", " #index in TDMA\n", " m = 0\n", " \n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " \n", " D = damping_function(u, epsilon, nx, n)\n", " \n", " a[m:nx-2] = - (dt / (4.0 * dx)) * A(u[i-1:nx-2, n])\n", " \n", " b[m:nx-2] = 1.0\n", " \n", " c[m:nx-2] = (dt / (4.0 * dx)) * A(u[i+1:nx, n])\n", " \n", " d[m:nx-2] = ( u[i:nx-1,n] - \n", " 0.5 * (dt / dx) * (F(u[i+1:nx, n]) - F(u[i-1:nx-2, n])) + \n", " (dt / (4.0 * dx)) * (A(u[i+1:nx, n]) * u[i+1:nx, n] - \n", " A(u[i-1:nx-2, n]) * u[i-1:nx-2, n]) - D[i:nx-1] )\n", " #Correction for BCs (other BCs = 0):\n", " d[m] = ( u[i,n] - \n", " 0.5 * (dt / dx) * (F(u[i+1, n]) - F(u[i-1, n])) + \n", " (dt / (4.0 * dx)) * (A(u[i+1, n]) * u[i+1, n] - \n", " A(u[i-1, n]) * u[i-1, n]) - D[i] - a[m]*B1 )\n", " \n", " u[1:nx-1, n+1] = TDMAsolver(a, b, c, d)\n", "\n", " \n", " # Wave at speed 0.5\n", " u_lf, x_lf, nt_lf = analytical(nx, tmax, xmax)\n", "\n", " dt_lf = dx * 2.0\n", "\n", " plot_oscillatory(u,x,nt,u_lf, x_lf, nt_lf, step, dt, dt_lf) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is the effect of damping?\n", "\n", "* Damping reduces the oscillatory response, although the scheme is implicitly stable" ] }, { "cell_type": "code", "execution_count": 303, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zleeryUiwOFxhOFlj6JZo0SvJQVayg97JFpOz3cS5Gm5/7Rm7QNZxWBZdPS4O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\nK2QYuLLzCSitg4ppR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "beam_warming_convection_damping(0.5, 101, 2.0, 4.0, 10, 1.0, 0.125)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What happens if the BC on the LHS is set to zero?\n", "* Solution is invalid" ] }, { "cell_type": "code", "execution_count": 298, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ERERERCQBKayJiIiIiIgkIIU1ERERERGRBKSwJiIiIiIikoAU1kREREREupicnBzWr18f\nd71t27YxduxYUlNTGTduHAUFBS2W9fl83HLLLXTv3p3u3btzyy234Pf7P023uxyFNRERERGRLsYw\nDEzTjKtOIBBgypQpTJ8+nfLycmbMmMGUKVMIBoNRy8+fP5/S0lL27t1LUVERR48eZf78+R3Q+65D\nYU1EREREpAuZNm0axcXFTJ48GbfbzZIlS2Kql5+fTygU4s4778RutzNnzhxM02xxhK6wsJCbbroJ\nl8tFWloaN910E4WFhR15KRc8hTURERERkS5k5cqVZGdns3btWvx+P3PnzsXj8eD1eqPeFi9eDETC\n14gRI5q0NXLkyBYD2PXXX89zzz1HeXk5ZWVlPPfcc9xwww1n/fouJLbz3QERERERka7mxsr3OqSd\nNa7RHdJOeXl5m2UqKytJT09v8lhaWlqL69B+8IMf8NJLL5GRkQHANddcw+233/7pO9uFKKyJiIiI\niJxjHRWyziW3243P52vyWEVFBWlpaVHLT506lUsuuYQ1a9YQDoeZO3cut9xyC3/+85/PRXcvCJoG\nKSIiIiLSxRiG0eS+y+XC7XZHvS1atAiA3Nxctm/f3qTe9u3bGTp0aNTXePnll5k9ezYpKSmkpqYy\ne/ZsXnzxxbNzQRcohTURERERkS4mKyuLoqKixvuVlZX4/f6ot3vvvReAiRMnYrVaWb58OXV1dSxf\nvhyLxcKkSZOivsaIESP44x//SG1tLTU1NTzyyCOMHDnynFzfhUJhTURERESki5k3bx4LFy7E6/Wy\ndOnSmOrY7XZWr15NXl4eXq+XvLw8Vq9ejc0WWVm1atUqhg0b1lj+iSee4MMPP6RPnz707duXffv2\nsWLFirNyPRcqI97zFc41wzDMRO+jiIiIiHRup84dM9ouGXN7+g4rbWrrc6eRNRERERERkQSksCYi\nIiIiIpKAFNZEREREREQSkMKaiIiIiIhIAlJYExERERERSUAKayIiIiIiIglIYU1ERERERCQBKayJ\niIiIiIgkIIU1ERERERGRBKSwJiIiIiLSxeTk5LB+/fq4682aNYshQ4ZgtVpZsWJFq2Xr6uq49dZb\nSU9Pp1evXixbtqy93e2yFNZERERERLoYwzAwTTPueqNGjeKhhx5izJgxGIbRatn58+dTVFREcXEx\nGzZsYPHixbzyyivt7XKXpLAmIiIiItKFTJs2jeLiYiZPnozb7WbJkiUx173jjjuYNGkSycnJbZbN\ny8vjvvvuIz09nSFDhjBr1iyeeOKJT9HzrkdhTURERESkC1m5ciXZ2dmsXbsWv9/P3Llz8Xg8eL3e\nqLfFixfH/RplZWWUlJQwcuTIxsdGjBhBYWFhR17KBc92vjsgIiIiItLVLOCFDmnnfr7cIe2Ul5d3\nSDsNKisrAUhPT298LC0tDb/f36Gvc6FTWBMREREROcc6KmQlKpfLBYDP5yMzMxOAiooK3G73+exW\np6NpkCIiIiIiXcyZm4O4XC7cbnfU26JFi+Ju3+v10qtXL7Zt29b4WEFBAcOGDfvUfe9KNLImIiIi\nItLFZGVlUVRUxKRJk4BPpi22JRgMEgqFCIfDBAIBamtrSUpKiroz5PTp01m4cCHjxo2jpKSERx99\ntM3t/qUpjayJiIiIiHQx8+bNY+HChXi9XpYuXRpzvWuvvRan08mbb77JrFmzcDqdbNq0CYBVq1Y1\nGTlbsGABgwYNon///kycOJF77rmH6667rsOv5UJmtOd8hXPJMAwz0fsoIiIiIp3bqXPHWj84LL72\n9B1W2tTW504jayIiIiIiIglIYU1ERERERCQBKayJiIiIiIgkIIU1ERERERGRBKSwJiIiIiIikoAU\n1kRERERERBKQwpqIiIiIiEgCUlgTERERERFJQAprIiIiIiIiCUhhTURERESki8nJyWH9+vVx15s1\naxZDhgzBarWyYsWKVsvOnTuXwYMHk5aWxqWXXsrKlSvb290uS2FNRERERKSLMQwD0zTjrjdq1Cge\neughxowZg2EYrZZ1uVysXbsWn8/HihUruPPOO3njjTfa2+UuSWFNRERERKQLmTZtGsXFxUyePBm3\n282SJUtirnvHHXcwadIkkpOT2yw7f/58Bg8eDMBll13G+PHjFdbipLAmIiIiItKFrFy5kuzsbNau\nXYvf72fu3Ll4PB68Xm/U2+LFiz/1a9bU1PD2228zbNiwDriCrsN2vjsgIiIiItLVPF/5+w5pZ7Lr\n9g5pp7y8vEPaacltt93GqFGjuO66687q61xoFNZERERERM6xjgpZncFPfvITdu3axYYNG853Vzod\nTYMUEREREeliztwcxOVy4Xa7o94WLVrU7te5//77eeWVV1i3bh0ul+vTdrvL0ciaiIiIiEgXk5WV\nRVFREZMmTQKgsrIypnrBYJBQKEQ4HCYQCFBbW0tSUlLUnSEfeOABnn76aTZt2oTX6+3Q/ncVGlkT\nEREREeli5s2bx8KFC/F6vSxdujTmetdeey1Op5M333yTWbNm4XQ62bRpEwCrVq1qsoHIz3/+cw4c\nOMBFF13UIaN0XZHRnvMVziXDMMxE76OIiIiIdG6nzh1r/eCw+NrTd1hpU1ufO42siYiIiIiIJCCF\nNRERERERkQSksCYiIiIiIpKAFNZEREREREQSkMKaiIiIiIhIAlJYExGRs+K1iloeORbbuT0iIiLS\nnMKaiIicFXmlVWz01Z7vboiIiHRaCmsiItLh/KEwG321HAyEzndXREREOi2FNRER6XCvVtQy2ung\nYCBEPIfCmqbJy8FSwhfgQbI6HFdEROKlsCYiIh3uhfIavpPpxGZAWSgcc71DZh0P1R1gV7jqLPbu\n3Ks8soHKknXnuxsiIo1ycnJYv3593PVmzZrFkCFDsFqtrFixIqY6J0+epHv37owfPz7u1+vqFNZE\nRKRDVYXCbPLVcV16Cn3s1rimQhaGKrFjkB88eRZ7eG6FQ3VUHt1AsPpg/JUrSzu+QyIigGEY7Rrx\nHzVqFA899BBjxozBMIyY6txzzz3k5ubGXF4+obAmIiIdar2vjrGpDrw2C32TbHGFtd2hKm62Z7G5\nvpyAGfuIXCKrObEFqz2d+ro4g1f5YXhyVuS/HaX4445rS0Q6rWnTplFcXMzkyZNxu90sWbIk5rp3\n3HEHkyZNIjk5OabymzdvprCwkJkzZ2o6eDsorImISId6obyGG7wpAPR1WDkU58jaVXYvA60pbAlV\nnK0unjOmGaLq2EbS+n2VUKAMM54AWvwuWO1Q8I+O6cy/XoD//AqcPNYx7YlIp7Vy5Uqys7NZu3Yt\nfr+fuXPn4vF48Hq9UW+LFy9u1+uEQiHmzJnDgw8+2MFX0HXYzncHRESkffbtM0lJgaysxJlWUhM2\n2eCrZWHfdCAS1mIdWTsRDlBthuhrJDHR1o384Ek+b/N+qv5UUccmPuYLDMGO9VO11R41J7dhdWSS\n5B6IxeYkHPRhdXhiq1z8Llz5PdiyCj7zHXDGWC+aA0XwyELo0QcO7YNuPWKv+6tfgdsNP/xh+19f\nRJopeXduh7TTa0zso2KtKS8v75B2Trd8+XKuuOIKRo8eTUFBQYe33xUorImIdFLPPB3G54Nf/Zcl\nYdYBbPTVMjzFTqY9Eoz6OqxsrQrEVHdXqIpcqwvDMLjS5uGPdQepMIOkG/Z29eUoPp7hHSqpYwR9\n6E3sYae0/hAmJt1tfdv12hDZ/bHq6AbS+k4GwJaUQX3didjCWn0dHNkF1/4YThbDjhfg8qnt60hN\nFSz6Icz4Mex+Dw7theGXxVY3GITly6G+HiZNgmHD2tcHEWmmo0JWojp8+DC/+93v2Lp16/nuSqem\naZAiIp3Unj1w8CAk0s/BteU1fPnUFEiAvo7Y16ztCleSa00FwGlYGWdLZ1Owfb/pfZ8j5PEWk7iE\nIfTkOJUx1zVNk52B13mn9hXKQ+2fMljn2w2GBYd7MABWRyahWNetHS6EzAGQlAojb4Rdr0CwJv5O\nmCY8dD9cMhKu/Tr0GRAJa7F67TUYOBAWLYKZMyOhTUQuCGf+ks/lcuF2u6PeFi1aFHf7W7ZsoaSk\nhNzcXHr16sWPfvQjtmzZQu/evbV2LQ4KayIinVBlpUmFD26/w0LeijCh0Pn/wVcXNnmtopYvpZ8e\n1mKfBtkwstZgoq0b+fXx7QppYvIvPuIlCvkun2E4feiOK66wdjJcgmmGGZ08iS21L1Ed9sXVhwZV\nRzfgyprQ+IXImtSN+roTsVUufhf6jY38Ob0X9BkOu1+LvxMvPQ37P4LZ/y9yv2+cYe3JJ+GWW+D7\n3wePB+LYhEBEEltWVhZFRUWN9ysrK/H7/VFv9957b2O5YDBIbW0t4XCYQCBAbW1t1PB1ww03sH//\nfgoKCigoKOAXv/gFo0ePZtu2bQkzG6QzUFgTEemE9u6BgQPgiisgxQkb8z99WDtWHeb1g/Uc8IUJ\nheNv73V/HUOS7fR0fLI2LNNmoToUprqNs9aqzBBHwnUMtHwS9EZZ3RwzAxwM18b0+kFC/I1tfMgx\nvs/n6HNq2mMkrPljvo69wZ3k2IfR0zaAi+1jeKvmRQJmXcz1AQKV+wgFKkj2jmx8zJaUQSgQY/gs\nfheyR39yf9RXIxuNhOIY2fpwOzz9v3Dvckg6tWtbPCNrfj+88AJ885tgGPDoo/Df/w27dsXeBxFJ\nWPPmzWPhwoV4vV6WLl0ac71rr70Wp9PJm2++yaxZs3A6nWzatAmAVatWMezUdGmHw0GPHj0ab+np\n6Y2PSey0Zk1EpBMq2mMycKCBYRh8b4aFJUvCfH68icPRvt9W7qsI8401NfRMNThcaXKy1qSPy6B/\nmoWcdAsD0g2m5tpJsbXc/trTdoFsYDEMejtsHAqEuDil5d8Pvh+q4iKrE7vxSRmrYTDe5mVjsIyp\nSb1a7b+PWp7hHTJJZQZXNNlMpDtuSmMcWasJV1Jaf5CRqRMAGOAYTpXp453al7k8+StYjdg2Kak8\nuoHUHldhnFbempQR2zTIihIIVEemQTbocVFkhK3odRg8oe02fGWw+C64YwH07v/J41l9ofQIBANg\nd7TexurVMH48dO8eud+/PyxcGJkO+e9/g01fIUQ6sxtvvJEbb7wx7nr5+fktPjd16lSmTo2+vnbG\njBnMmDEj7tfr6jSyJiLSCe0pgoGDIn++NNdg0CB48cX2ja7trQjz9TU1/HCMg+dvdrJ1eiq7b03l\n8S+l8L1hdgakGzxcEKTgWMujY0HTZF15LTd4mp+7E8tUyMJQJbkWV7PHG6ZCtrW+4RUKGUgmX2VU\ns10fvTipoJYgbU/HLA7uprftIuzGJ0FmqONK7CRRUJcf0zqL+tpjBKv248xsuomHLSkztmmQB96D\n7DFgnPEjetRX4b2/R9ahtSYchqU/hc9dD1de2/Q5uwO694aS4rb70TAF8nSzZoHLFRlhExGRs05h\nTUSkE9pzamStwS3TLPztOZPKyvgCW1F5mG/8o4a7xjqYNvSTXReTbQYXey1cm2Pj+yMcDM20UFHX\nctub/XX0T7LS19F8tCWWsLY7VMnQU5uLnG6QJQUHFnaHq1qsa2KylxNcRg4GzUf+rFjohpMTtNwG\nQNgMsb9+FwPsTXc8NAwLo5O/QFW4nA8Cb7faBkDl0Xyc3T+HYWk6cmVYnWCGCddXt95A8buRsHam\nfqemRR54r/X6f/8T1NXA9LujP98nBw7va72NI0dgyxaYPLnp44YBjz0Gv/mNpkOKiJwDCmsiIp1M\nba3JsWPQr98nj2VnG1x2ucFzz8Ue1j4uC/PNNTX8+DMOpua2vj2+N8mgrJWw9kJ5DV85Ywpkg0hY\na3mtVdAMUxSuYXCUsGYYBhPsXjYEW17rdRQ/Thyk0XxUr0Es69ZK6vfisnhwW7s1e85m2Lks+Usc\nqv+I4uD7LbYRClRQW76D1O6fjXot1rbWrdUHIjtB9h3Z/DnDgNFfhW1/b/U6WPcsfP9nYG1hmmIs\n69aeeQamTAGns/lzOTnwy19qd0gRkXNAYU1EpJPZtw/69gPbGevHvvMdg1fXmZSWth3YPioL883n\na7jncgffubTtc8w8yQbltdHbDZkmL5XX8mVPS2Gt9e37PwpX09eShLOF9WATbN3YXF9OwIw+DXMf\nJ8gho9X4N3rZAAAgAElEQVT+x7JubV9wZ7NRtdMlWZxcnvJldte9QXU4evCrOvYvUrqNw2JrHjyh\n4ay1VtatleyCbtmQ7I7+/KDPR9a0Hfso+vOH9kKgFgZe2vJr9MlpO6xFmwJ5utmzITUVli1rvR0R\nEflUFNZERDqZPXtMBg1sPt0vI8PguusNnnm69bD24cnIiNrPLnfwzUtiO3Dak2RQ3sLI2luVAXrZ\nrfRPij6S09Y0yF2hKi61Nl+v1qC7xUGONYV3QtG30I8lrGW2sX1/RaiUatNHlnVAi2UAXBYPLouX\nGrN5WAuHaqg+8TapPa5qsb41KZNQa+vWit+F7LEtP2+1wcgpsG119Off2Qhjr46MwrWkrZG13bvh\n8GGYOLHlMhZLZDrkAw/A8eMtlxMRkU9FYU1EpJPZUxQ5pziam2822LLFpLg4erAqrQ7zredruO9K\nB1+PMahB62HthTMOwj5T22GtkqGthDWIjK5FmwoZxmR/TCNrrYe1fcGd9LfnYjlzU48oHEYyAbP5\ncQI1J7aS5L4YW5K3xbpWRxtnrbW0Xu10l14Dh3ZERtjO9M5G+MyE1uv3GQAHWwlrq1bBd78L1jZ2\nvhwwIDIlsjiGzUpERKRdFNZERDqZoiKTgYOij5y4XAZf+5rByrzoUwY3HgwxrqeFmwfHHtQAPMlQ\nHuW4s7Bp8mJ5DV+Osgtkg54OK8frQwSj7GIYNk12h6rItUSfNtjgczYPO0J+fGbTNVJHqMBNMi6S\nWq2fQSrlVBOi+fsSMOsoqS8i25bbahsNooU10zSpLt2MM8patdPZkjII1bWwZs13DOr80L2FJN7A\nngK518GOF5s+Xl0ZOVtt5BWt1/dkRs5r85U1fy4cjoS11qZAni4zUyNrIiJnkcKaiEgnEgyaHDwY\nGdBoyZduMPjoYzh0sHk42lIS4vJesZ0VdrqWNhh5+kQ1/Rw2LkpuOfzZDYMeNislUUbXisO1pBs2\nPJbWw6PTsDLWlsbr9U0Dxt4YRtUAbFhJI4WTUXaEPBh8nx62bJItUTbTiCJaWAtU7ok852o9aEU2\nGGlhzdqBd6HfqOZb9kfTcwiUH2z62LZ/w6WjIbmN6zCMU1Mh9zV/bvPmyFq0kVE2OIkmMxNKYzg7\nTkRE2kVhTUSkEzlQDD17QlJSy2uSHA6DMaMNduxoHq7eKgm3K6xF22DkeDDEA4d9LMr2tFm/pamQ\nu8KV5EbZBTKaK20ettY3XbcWy3q1BtGmQpqmyb5gITmtbCxypmhhrbr0DZyZV2K0tlYMsDo8hIJ+\nzHCUXRTbWq92upR0qDljDd87G2HchNjq9xkQffv+ho1F2riORt27K6yJiJxFCmsiIp3ImeertWTY\nMNixs+ljJ2tNSqrCXJoR/z/90daszT9YwbcznOSmtD2lsqXt+3eFqshtY71ag+6Gg7LTpkGGCHOA\nsk8V1o6HDmA17HgtPWNqAxrCWs0n/Qj6qfN9QEq3cW3WNQxrJLCduX1/KAiHd0LfUbF1Ijkdais+\nuR8Owzv/gnFXx1Y/2iYjdXXw179G1qvFSiNrIp1WTk4O69evj7verFmzGDJkCFarlRUrVrRZ/rXX\nXmPMmDG4XC769evHs88+257udlkKayIinUjRHhg4qO1yQ4cZ7NxhYp62TuztIyHGZFmxWWIcNTnN\nmWFtg6+Wt6sC3N2zhS3mz9AnqfnImmma7ArFPrLmMWxUmMHG+yVU4MGJE0crtT4Rbfv+fcGd5NiH\ntjkidrozR9ZqTmwh2TMci63lTVZOZ3VkUH/murWSXeDpAylpsXUiJQ1qKqDh77doF7jSoGe/1us1\niLZ9/0svRVJ+dnZsbYDWrIl0YoZhNPkZEatRo0bx0EMPMWbMmDb/7dy1axdTp07lgQcewOfzsX37\ndsaOjXEGgQAKayIinUqsI2tZWQYOBxw69Mljb5eEuKxn/FMgAdwOqKmHYMikOhxmXnE5i/p5cFpj\n+zHS12Hj0Blh7bgZpB6TXkbrm4M0SDdsVJj1jV8u9nKCATGOqkHzg7Grwz7KQkfpY7s45jYA7KeF\nNdMMU136Js7MK2OuH9lk5IzRqOL3Yp8CCWBPjkxVDJ4Kje/kxz6qBtF3hGzrbLVoNA1SpFOaNm0a\nxcXFTJ48GbfbzZIlS2Kue8cddzBp0iSSk1veWKrBwoULue2227j++uuxWCx4vV4GtrSdsUSlsCYi\n0kmEQib79kZ2TI/F8OGR0bUGW0pCXNarff/sG4ZBmgN8AfhtiZ9RqQ4mpbf9g7pBX3vzkbVdoUpy\nLa6YR7WSDSsWDGpO7egYz3o1iJy1doIqwqfqH6r/mF62QdiM+HbGPH1krc73ARZbKo7UGEe0aNhk\n5Izt+w/EsGX/mVI8n0yFfDsfPtPKuWhn6t0fjh6A0Km/k/JyePVV+PrX4+uDpkGKdEorV64kOzub\ntWvX4vf7mTt3Lh6PB6/XG/W2ePHidr3OW2+9hWmajBgxgt69ezNt2jTKyqLsRCstin6CqYiIJJyS\nEvB4I9vzx2LYMNj6LnzxS1BTb7LrRJgxPdo3sgaRHSHf8QdYdaKa9Zf2iKtutA1GCuOYAtkg3bBR\nbtbjMOAgZXyD2AOOHSsukiijhgxSOVz/McOSPh/X6wM4jJTGsNawsUg8bEkZVJ/aPRKAylKoLoPu\nMcxvPV1yWmSTkZAVSoojO0HGKikF0jPg2CHolQ3PPAPXXQeetjeLaUJhTaT9fn9Tx7Rz++oOaaa8\nvLxD2jndgQMHePLJJ1m3bh29evVixowZzJkzhyeffLLDX+tCpbAmItJJFBWZLR6GHc3QYQYrVoQx\nTZNtx8IM6WYhxR7/erUG6cmw6GgF9/RKo4c9vtDXx2HlcKCesGliOTWStitcxfX2zLjaaVi3FqSK\nDFwkE9+oWMNUSEc4QMCspZulV1z1Aew4CFFPsK6UQOU+PDlT46pvPfOsteKtkY1FLHEG6YZ1azt2\nwqjPgi2+96Jxk5Ge/eDhh6E9vznXmjWR9uugkJXInE4nM2fO5KKLLgLgZz/7Gddcc8157lXnommQ\nIiKdxJ49MCiG9WoNTl+39lY7z1c7XZU3QL0JUzNjO4/sdE6rBafVQml9ZAqiz6ynNBxggCW2TTka\npBt2ys169sW5Xq1BwyYjh09NgYxnY5EGhmFgN5KoLN1MSrcxWKyxrblrENlg5MQnC/v3bolvvVqD\nFE8krMW7Xq1BwyYj77wDPh984Qvxt5GRASdPRnajFJFO5cx//1wuF263O+pt0aJF7XqNESNGdERX\nuzSFNRGRBHC0qu0vu3uKmm4uUlgd5GBdlPO6TtOwbi2yXq39Ye1oMMQedw3fsLsbR8bidfpUyN2h\nKi6xpmKNsy3PqU1G4l2v1iATF8dNP4eDH9PHdlHc9Rs4TAd1J7bGPQUSwGJNwmJNIhz0waGdcLIY\nBl4RfyeS06DyJBS8AWOvir9+w1lrDz8M//EfYGnHVwK7HdzuyJo3EelUsrKyKCoqarxfWVmJ3++P\nerv33nsbywWDQWprawmHwwQCAWpra1vcVXLmzJk8/vjj7N27l+rqahYtWsTkyZPP+rVdSBTWREQ6\nkGma1IXi2wp5x/EQY1dWs+N480OjT293z2nb9leHw8woOsHc4ta/JA8bBgU7TbYeDfGZnlaOhOt4\nvO4Q4Ti3a/7lwQouDSXjDLY/8J1+1tquUCVDYzxf7XQew0aZGeAQ5WTTLe763XFRFi4lRAiPJb51\nd6fzVlZBkhd7Sla76luTMgjVHoPXH4HPzozs7hivlDT4qDASujzxB1f6DoCiD+C55+B734u/fgNN\nhRTplObNm8fChQvxer0sXbo05nrXXnstTqeTN998k1mzZuF0Otm0aRMAq1atYtiwYY1lZ86cyfTp\n07n88svJyckhJSWF5cuXd/i1XMgU1kREOtDMlXVc9vsqgjEGNtM0+enmGhyj/PxPYW2L5Y4dA4cD\nPJ7ISNSDRyoZ7rJQHAzwb39di/WGDjN4syhMz1QDbzI8WHeAdcETvBSMfVOIE8EQRdZDjE+2NDsY\nOx59HTYOBkLsClWyvv4kl1nT424j3bBxnAqycJPUjmXX3XFh1h+ndzunQDb2o/wYZsal7a5vS8qA\nwnXg9MLA+EfnAEhJhw92w2cmtK9+7xz499twzTXQM/ZDwZvRJiMindKNN97I/v37KSsr4+677465\nXn5+PuFwmFAoRDgcJhwOc9VVkdH9qVOnsnPnzibl58+fz7Fjxzh27BgrVqwgPT3+f/u7MoU1EZEW\nLP6wnKLKYNsFT3n+nXreH1ZM/5t281//ajl4nW71x/WUZh/ntuH/5r2Mwxypij66tmcPDDo1qlZc\nV88TpX5Gd9vIl/sVsOhwRYtTULKyDPzeMMPcVvLrywiFTzIz9DFPBQ5xOBxbH5+uLuaaHh9hXPwu\nZcHY349D4cPsrn+/8X5fh5UPwlU8ULuXHyf1Z4C1+Xo1f+gkb9Q8T224Kmqb6YYdn8XXZAqkaZpU\nHt1IbcX7UeuczmHa8NZXkWbrFzlQOlAd8/U0qK89hr2umoA7/s1JGtjCKdh2bYLPfz9yXlp7pKTD\nnr3tW68GkNETdh+CGTPaV7+BzloTETlrzlpYu/XWW/+UlZV1dPjw4TtaKvPDH/5w+cUXX/zRyJEj\nC95777049hwWka7KNM0Wg0lLNlcd4zflL1MVan191+nu2vkhE60Psq7iGaqDbderqArzi5OH+K33\nOZb4/sGu3tsoKm99HVpV0OT+D8r5lfs5fvS3v7Lc+mfu/OBk1LKnr1dbcKiCO3q8xex//JUfvbiK\n/um7ec3XcvAK9wmTHgyzsnYfP9j0OF948GFmH3ud/6ktJtTGe1lBDZknX+JHc3/DzL/mwSUF1NPy\ndM0GB8NHseT9lH6/uZuimq0AGEl17Es9ytykHEbZ0pq/VqiUraXPkPvQE+ws/VvUv2ePYSNoVDaG\nNdMM4zv4D+p2vUrFrhXUVuxqtV/l4WNYsFJtGrDhd7DiVnj/n5HgFgvTpO5feYSsPQgYsQfXMyV/\n8B6B3tngbeN8ttb6VVEJgQAMzG1fJ7ZuBdMCg7PbV7+BRtZERM6asxbWZs6c+fjLL7/8xZaef/HF\nF2/4+OOPL/roo48ufuSRR2bdfvvtvz9bfRGRs8vEJER8u8EdC5WyumYtxfUHY67zVt1HPFv9GM9U\nP86++qMx1Xn8xPtYjz/Gd/b+k38ee5iKUMtTBhv833c/YLZlJfagyQ2lO3ny8DNt1pmxtpTfXfQU\n/YsO0v39Y/wysIb7Pvqg1bVhv3m3hvty/8ykjW9S220IV25+jxnJKyisCjQru2ePycBBBv/y1ZJi\nbOf/vPoXanoOIGxP4b9ef4w/nvg46muZpskRR4hD/Y5w39t59Hp2C5ath/j8Q3/m8mOvszp4rMX+\nhTHJP/BXvvmLR6myOui55m1uW/0wa8wCTFq+roPmCZIe+gE9/7KFlI0f0/e+u3jdt4F/Wg9SfdzL\nSJu7WZ3y0HF2HljJVVMWkfaTvzH2+nso/mhls3KphgGWOrLphmmGqNj/LLYVT9Hthl/T48u/peav\ni6jzfdBi3w7Vf0xKyEPWmiXwP6vgV5tg1f/Cq0ugLvpoXqPqKsK/nkPykkfoe/9jePNWgi+Gw13D\nYVi6BO66C3btgiPvYz26n6p+LUw9NE3Iz4cbb4xs3vGXv0Qv9/5O6Olp/8jcI4/AZ0dHzmj7NLRm\nTUTkrDlrYW38+PGbvF5viz/F1qxZc+OMGTNWAFx++eVvlZeXe44ePdq+ldoXkFDIpLzcpLLSpK7O\nJBTnRgUiDcrMGt4Ll+A3Y5vqVmZW83L4Q5aEXueJ0LscMMta/UIOUGUGeCJYyKLgWh4M/JU/BLbi\nN1sPQ9WhOh6rWsvrNc9x2PTzTu0LPF31PMFwy/WCoSAP+tZyKLie9/w92R9IZ2vtap6v3trqay0s\n+Tdjyv6Co6Keh17+LsOOH2T7wd9SEvC1XOftncxw5HHc0Y0Rg+ext9tXub58Byv3tHyA52Mbqvjp\nuD/Rb/9hsg7X4HEPoXfBAe535PHwB9HD0H5fmKy0v/DV/I1sTbqOtC/P58job3P95jfYtucx6s8I\nXkV7oN8Ak98f+oDfbP4j/m6ZHN9sUv5RFka9yR8KlvJsafNRuf0+E3efau6sfIT+f/43lf1G8Idf\nrSHkM/nqskc5fHg9+0I1Ufv47uGXmHzfMk727sHri//Cn+78T/q+/C5XPrqU9UQPRAfMk6QsmUnm\nS9vh3XKMd05gy9/D5ffOY1b1AYr9zTcoKQsd5cOdf+CzX/wvjKIy+Ne/oCxI9oT/pOLlXzcZYau0\n+KkNO7CFTcqL8nDOXYJz4d8wfnIrxhc/h+eOpzDv+h51vg+bvY5pmpSVbefqR54i9c482PohXDEC\n/vsF+O1z8NQPoaSFkbl9H8D3roOH/4LxoR82HSJpw7tw2xdh5TLwR9nopbwUHloM2T3hgfmw/u8w\naRJcNQmz2EvId0bACQRg5UoYMwZuuw1uuAFefRV+/GP49a+bj7Jtfxu6Jcc+Kni6iorIxiJf+WJk\n+/5PQ9MgRUTOGiPe6UTx2LdvX87kyZOf37Fjx/Azn5s8efLz8+bNe+Czn/3sZoBrrrnmtV//+tf3\njB07tsm3L8MwzGHZfQnXR6ZpdHf3o0daNt1Se/K1zzRfDHmisoS/vbOs2eOJXr601uR9n0nBscO8\n/9FvMYn8/A0DBpCSnMUlF92F1QCbAVYDrBaoqy2h8KPfYjEiv1y1ELm5nT357NC7sBlgOfVLVxPw\nVZfwxq7/4czv4K6Unlwx9K7G+2FMKpNMjtYfZuuO3xKwmQSsELCaBC1gTcui24Q5GKfaMQDDhHrf\nEco2/i+GGXnMcup5hyuLPp+7E0sYrGbkcWvYIOgr4cCbv2v2/iSl9mTAFT9s8ljIauIPHWL/W78j\nZDcxLSZhC5gWE2tGD9K/fhthq0nYZkb6ZUKo9Bi+5x7+5A3AwDDB6u1Bt5tui/TdNMAEIwz1J45S\ntubhyP1TdQwTbJ4eZH75DjAis4YstjD29ABm1WGO/PnRxvcAI/JfR7fu9JsxE4sjjJEUwuIIY7GH\nCZYdZf8jKzHDBmbIwKw3CIcsONJ70Pdr/4EZtEBKCCMlhCUlRH3FEQ48/gQWayQ2hesthIMW7O4s\n+n5lNmaFA+OkHTOtHjOjDoe9iGPPPkqKI4jNEiYYtmA3wiT3yODimdMoP5xOVWEGlg/TAIOanF2U\nvPE7nKm1WC1hasM2qgIOPH3S+cJPvkyo3sKRfZlUrc+m2/tphCuO8sauZQSyq0jt7ceVVEdKfYBe\n3VMY/X++Tv/Uckptqew42Q//M8Po8V4172z/LSETKpJDWEceoa/rBMlZGfiv/jkVrwwg9YZ9fGvY\nVtLCtfz7+RzeX7wOx6kPbW3I5FhvH0PHV3D9D7/IhtdG8OPUV7A5AqzLuARnUjFP/fdbdNs6AOtp\nv3uyJPXg0qcv4RuVb3OywsOBP/8Al+HgNX8h/tBswhaDk3tGkuxPbfz/8eZxd/H6mAK+N+zPfODo\ni/Wx26muLeTpN1dwPLuEi90fUxLuTvLu3Cb//5bV19H7jv8h+0gJ4X8d5OfPZxIMpeFK2oXH/TG+\n7h7qSm5i+qhPtj0GeO/Gf/Dtt//IT1+tovroZ0g+lWFCvQu40lFC71nz6L7uOwBU1Zs8vSdMz88X\nYNl4C0GbHX+RF0JHCNiSGJtp5fZpg/F1SyPjhgdxnDocuaSkhP+4bwnu2rfoW1hEwJ7Gny+diNm9\nJy/99D8ZuuBm7OE6/vfe/8vt2V+m9MhRli2L/HvlryrBtXEddW4ngcnf5w+XXc78gWl4t+/mh0/9\nhpKrh7P95rtZv+zZxmvymTUkvfEC2WWV3F1mwVjwS3ZcfxXub32N7COHOTymN9M8/RnhvZSkU9vE\n15pVJPt38esX3sV0pGBsKcTIyIBAgOJrRvO/b75P8HOXYht3PYZhZR8nKMl08PdJg+k2fTHGkQqM\nvIfhK9MoKSlh2fdvgVc3YnqSCX91Ctb0PvTs2ZO7776bisOv4/zxHGyrCymfNJTaxStYtuJJOLAP\nXnwB6kMwojc9r/gcd//3E5FDqk0T/rES5t3D4YMVLLkoA9ugAdRaXVg2vYUjZKPnpf25u48FvnIL\nXD0Ztr8J+Wsp+ds6lu07CaNHwueugo92QPEH9MxI5y7PxZivvYRx8zcwbpkOW7ZQ8tvfsiw5GT7z\nGRgwoHHErGdyMnevWQOXXQYPPhjZLr+6ipJvXcGyujoY8RWwfLLZSsP1nqmkpKTx75f33oMDB2B0\nLj0rT3D38xtbL3+aZu0//jhs3EjJAw80KZ+bm8v3Ps0ukyJnWX5+Pvn5+Y33FyxYgGma7d956AyG\nYZhn83u2XBgMw2j1cxf/Vlod6MyOGYYR9RN9sweO95nS5LH0VA/OzOZl65JtZGY2fyIRy4fTTHYf\nNyk8ZlJTD0O7G3xtqIM36H5ayciXdHeKl+vGWAiZEApHbvVhOFnpgKpMQmbkO0XIhLAJzmQP3TyR\nMuHTAlW9xUZ6Wmbj/Ya/gNQUD8npJnvcIT5wh9jnCpESMnCeNAkf7oYrZJAcMkgOgSNo4KzOYPSB\npMbMZwKmAZXVTgrCWYSNSL9NSyRwJpPB4EorYQNCBqf+a1JlseNLzTztaiNsaWnUDKijwhukxhWi\nJjVMvT2M/VAd4UMeHAEDS72BxQQjbJAUyKDfnhSsQQNryDj12iaBqloO1EWmGp3+abPVZNCnOJlT\nOa0xhNVWphCyd8c0zEh5A7CFSeqeSvccPzZPAJunDktSiFCFg5riMP4eHjBPtXPqv3aPCyNsIVxh\nhzoLoTor1FoIHrNDyQAMmwn2MIYjhCXJxOpKx0ivx2ILQ60Vs8oOpclwOBN7eT9cqbXYnAFMJ4Rt\nYRzdLfQbWoJhN7E4wqRaAngdtVQc9lPp7EZdaSo1R51Y661UOetJsiZRVZVC94EnuGjYwVPvtUHV\nsQoq9rqoOdkDDrtwljtIrzew7s3gw7QrCF95hKyLjtF/9hYqgkkU7w2Q+Xc/NiMM1U56GfUEj/Ui\nvHk0tuNfY2ePCpImv8PE/u/jv30vbx1O5oPFNtLSqhnuOUpSuJ7Dxy8mfeMobqzIxW6Bmucu5aN/\nDKJ29mZGXPke+796mF3vDcQsTabX+H2MTDlBlbMv3j9+gV98ZgUV+ydQ6evLlwf/jfdraunb06R2\n8gH25g+he42Tw2Y9I77xId/2lVNWOgDjre+R3TOShK5NzWLlGzfQbfS/GTJqNwdKxuAt70G6M513\nx27l1ty/stU5iJ7P/QfOHnvpGbqfnb2PUVoznp1ZaYxzvM/xyw/gPTIEZyaYZoikKcvpW3qUrB0n\neCNwN+ne1099yq7iSCCT4dVbCV/2L5LT78ZiOgDYP3AzP/p4Ff/KuoQjx3uQm/XJh9MMTKL40q3c\nte+v5I/JILn4Oo6chMysSuak/5pVXicVxRfTx3iHN+3foay/g4HW90jafBzv6DqOrPsx2V/6LRgG\nNpuNHo6PuWT3AaqT03h6zM1MyEzFnZHBbyrg6aXrqL73i/znwl/w4v/zcnnyJWRmZhL0HSPjn/+k\nLiudv4/+OvMOHoIl3+RnycksWHY/J+6bT69f/YITJ36JmTGS7oabk2E/vV/5O0nlVXgO12E88Gt2\n3vptFtfu46cb8tn+0/+g9xMvcX3voxy80Um3jLHUmpUY2/IZvLaA8LAcrBu3Q9KpA6YdDlKeyyf1\nGxNJ3rSLUIUPy9dmss9q47o975OxaAX0cGNsfRsGDI38f22zkXn19TB8DOaf/gB5fyH89S/iGTIE\ntrxA2rTvwfEqgkvn8/Ds0dx6omfk3+fMTBg+Cv7xLLy9HU9VCJ67F7LHwcJfwz93Yo7ohfn96+n+\nYR1WRzrh0j0cmHUtvXebeF55BXpdD0UfwvPfhLT+8OJmbMPHkfnN0ZB2an1ehgfKPsaTnILx52c4\n8cav8P7bxHrPPTBiBLZnniHz7beb/bzwZGbCpk3wrW/BV74CzzwN//gTtkuGk3nwY0hzQfInxyB4\nPJ5mbTS+P5mZkR8WO3dG2vK68by3r/XyZ/bnzPZPrVk7vfzx48dZtGiRwpoktAkTJjBhwoTG+wsW\nLDh/nRFpwXkbWbvtttv+MGHChPxvf/vbzwAMGTLk/Y0bN16dlZXVZCGKYRhm7WdzSPr3p5ymkUBK\nSkz++Mcw7++GK64wmDjRYOgwsFg67Jc5MasMmLy2v57ni+p5/VDkHKavDLJxfY4Nb/K57U95fZhX\nKmpYU1bD25UBxqclcZU7iYFJNgYk2+htt7b7MN541JlhCkOVbAv52RbycSwcYJDVySCLk0GWFAZZ\nnfQykuI+zDdePmrYSjFbOUAWbrLpRpgwIcKEMKk/9ecwYXrhYTA98OJss10Tkz1hHyFCXGzxYtD0\nOo7W76feDOKyeHBZPFgNG1VmkBfr9/ERpYw20/GG9lBrVjE86SoyrM13xKs3AxQECtgb3EG9xcQR\nrgdrNjcmfwGb4Wixbx8ETvDP4D/JMsvxkUSKUU+69bN8IeSirOhPpPX9Cindxkau4/+zd97hUdTb\nH35n+27apkEKJXSQKtKrIFLUUAQERJoFVISLFVHxgiIgRdSrol4QEFFR+QFSBAsoIIIivQYCSSAk\nkN63zvz+GEBKQmBndyLXfZ9nH3EzM+c7yZb5zDnncyQ3xRnbyUv7gaPBIeREBPLDyTvoUnU3d6Qm\nYbK2IrZKn1Lt2fNLHPx4biF35CXxa2E8+YUaekWt5tfwBjxYZSQUZsHKidB2JLgdsH0xUrN+TLQE\n87jjR/KCbqNZ9aH8duRtoorTidl/FlO3Z6Ba8yviHDki8e3PP/Cs/mOSG9SiZrvp5OUkYF47hRMx\nVXnz0xm89pqOuErFsGA63Psg1GrI3G12WpvepM3efdh6PM+G326ns/QkRq2LjLj+VJ4zkzf7LqDz\nvjO01mYAACAASURBVAaUBEu8GFXMprDvsH49G6FZJLnNmlHprmmcPfw1UQvfpdCu5Z4hn1DlTCRf\nDg7GIUq0P3yO+XGhNDVJOF7uhfl8HslvLKGaxozw/ECKa0Qw+eHFtD90jAEjB8H33+POyCR7+DAK\nB/XDMrItlebMJb1xTU49/QZNXnwCy9ls+C0LzcSXKXxyDOOLjzLWWI07dMEcIo30Lz6gy6OzEBpF\nsu/jZ4j6bguVp3+Hu1sLdN9sLXUos1tykfz5eGo8sRCxbiWyu9Yj4t2fcXdvim75z2C+tv8NAKcD\ncdjdCKt+hTsbwdbDuOpGUrJwLkJ0BPvt+6lt16LTmAmtORyN9sKcs22b4cFB4HIBonwX5+P5lLSr\nTVHGVsLrjUcQNDi3zSc/cy/hvT+AwiJ47TVYsgTatYPdu+G996DPlTcZ+eUDELTw6yHQ6cnu2xBz\nRAvMoU3KfE9cgcsFD4+E79bCkB4w+W34ZQ50HAOV697YMQB27oShQyEhAUqKYFRnWP6n571vv/0G\nEybIx73AqVOn6NKlC0lJSZ4d04+fCqC8DIcHx/Nn1vyUS3mvuwoTa+vXr7/nvffee2r9+vX37Nix\no82ECRPe3rFjR5trFigIkrtWGJoTWT5bp5rs2SMx7y2R/v0FevQUMKksiC5S4JB4bbudbxNdFSrQ\n7KLEtzklrM4p5vdCBx2CjfS2mrk7xESAVr3JEqdFGztcuex1F3DCXUxNjZlmumCaaYOorbH4XJhd\nREIihWx+J5mTZNKEGFpQnUjKuCD1Ik7JwQH7VvLc5wnShFEg5VAs5mMSLARqQgm8IOxOO49Sy9CM\nmvomaITrD0iWJJFUdzKBmmCsmmuH9opuO4LGcI2g2ug4QKr7NAOMXTAWnSX31FJCqg3EZG14zTHc\nznzyz6whq+Ao50MDiMrOIzTqHkIrd7zu2lxuN/9NW869WfvkmJFNeCxmKDhLYNXLUKsdNB8gb5x/\nHja9jRuB1+q1YLj7D0T0CE47EXvOYu34KNTpVGqciS+4Cbz/R1489F+yq1clJD2ds5ER/OR6k8x9\nRiZN0sCsCVBYAElHIX44hfGP0HJFHp/Xf5vGe4+QawzDZLTxQ9P7ue+1OTzR7A3efKozB2YJIMLR\nfg62nnHzWfUDFL/5JMZaIThaNMO07Q+Ks508NHoRt1tjOPl6AIuXaBAEgaWZRazPLeGL2hHkuPLQ\nT+2P5VQmCAIlNSM4/9IXPPbTCTY+ej/a//4X7r0XgM5Lj/HW12NpnpzBuWmDqPz110gON5JOA1sz\n0D47EcaP521bMkY0PGGS3Q4lJBazg+JtaTzefyQagwBZxTgf64PhnW+u+J2dp4AciinETgE2CsRs\nIv5cR5sB78H5QpKeu5/cyR9yuyEUAIdkJ9udRrAmDIvmSpdJ5/zJ6Gb8B1v3epx76i6Cg+qiM0Xy\nuzGf2qb6hGYn4rJlEFb7UQSN/sJOTpgwBvRGmPMfRMFNxuFZhNZ4CENgDXkTdzF5a/5FRGQbaP+I\nvN/Ro7B+PTz66F/ZtIukHYaNs2DI+yDo4N+PYK9swjl4KIFRXa77WgVkk5I1n8Ly+WCpDRt+kcsP\ni7ZCs3iIa1n+MS7yyCNQty5MnCj///AO8NY3EOHhrLUTJ6BHD0hMvPRUQUEBy5Yt4/HHH/fsmH78\nVAB+seanIqgwsTZkyJAvfvnll86ZmZkRlStXPjd16tR/O51OPcCYMWM+Anjqqafe27BhQ8+AgICi\nRYsWjWrevPnuUk5AEsPMCFk3Pwvn74QkSaxaJbF6tcTzz2lo2KhiRBrAH+luxv1oo2MVLS+1Maou\n0ABESWJlTgkzz+ZT26TjgTALd4eYCFRRoAGcdBez3JHOEbGIjrpQmmmDaKgNxFKOCPEmEhJp5HGC\nDA6ThguRVsTRlFiM6FVZQ7Y7nT22H4nUVuU2Yzt0ghxXlESKpXwKxVwKxRzsUgk19I2xaJSLR1ve\nEXJOLkFrCMFkbYLJ2hi9peoVws2We4i8lK+x1ngIY1Dt6x7PXnCcrLSNWCM7YbnBTIUoikxL/wGT\nUMKzleLRCsCGGWC2wp1jr8w0iG7Ytxr3nlV80bAF9UNzqfLbKSo3H4DQ+N4yY/y2XeKr1W545Adm\nbl9EZmQYHzScQtrUSF56WUPtg4tgy3qYuQzysuHdl8BWwtudXuN7o5E5ofOpmpLGwuY9GD99ETPi\nHqHZ4AHcW0vHtjfBlg2dpkvc9VUxr7Y1Ul1KptKMYQRJTpxOiXtHfkyn2rV4NTaY0Y+JvD74EFEL\npuOY/CrtpDA+qhHGHQEGTjpTiJz7OBq3yOnnPuDUWSONu3WhyjP/grFjL51Pm8+K6NT7LMO/WEfD\nV94g84m7CXSmoVuegH7cc/D00+xw5bLInsrblvqYL3svpZHHf907CUioxvh/DcDdqxump9++9PMi\n7GzgMMlkE0UwQRgJwkQgRkRnGo7ze2h5rgrvNWhAU8FGtJBPljuVQjEPqzaSAnc2tQ23U0PfBI3w\n12eJ6Laz3/ErQdpwahmaArCeg4QTQCupOrmnliFJbkJrDkMo5b1fcHYjLnsGoTUeuvScJEl8n/0+\n3TceQmg+AOrfVfoLQJLgwDr48yvoOh6qt5CfL8xHfL4f9paNMD/8TpmvHwDST8M7L4EkwvjpEFMd\nVq6Us3lHD0Oj+tAjHjp0gLZt4XoDZ/PyIC4Ojh2DSpXk5yYNg8FPQlMPh3Pn5kL16vKx/fi5hfGL\nNT8VQYVm1ryBIAiSqNPgLCjEYLp2gOqtgN0u8d5/JFLPSkyapCEysmKEmtMt8fafDj477GJWZyM9\nalRMy+KWfBvTUvPRCfBqbAhtgoyqr+H4BZF2Qiyin74yPfURGAX1hGIRdhLJ5ATnSSQTCwZqE0ld\nKhFH+DWlib5ClEROOHeT5DxIY2NnonU1VIlryztKXvKXhNYahSDosOXupyRnP5LoxBzaGJO1CS57\nNgWpawmt9TCGgHJmUZWHvUiepVWnI1hCy95u2wLIToF7XwVtGe+PzFPkf/cWUkkWzgb3EdHxweuG\ndrslxj4p0mWsky8j95FbGMLzJ+qw6w94td+fMPsZmLMcKsXKO4girFuG+8sPeL3GGI4MbUJcVCpT\npy9lZ2grlrd8ig/ulkv2drwNuaeg5zuwOcXFy1vtbB5s4aWEEwz5eQbvNR9Ghr4Ja28PQxAEPpyZ\nw7D3WhPQoyN8+y0Hho5k7iPjWNxYNnDa7UpARKSFWJPDne9Ce3sz6n1wpQFQz2+KefJOF9+aTzP/\njBbd0IfgyGGEqa/Bc8+RKzr5V8lRJppqcJs2kKv5j203yTaYY/2rZFRC4iBn2cgRmhBDF+qh50rR\nJEkSu+0/kOM+T5FUjCCEUV8fR7g2llBNJTSCliIxj/32X3BKdpoa7yREK/f/uiU3PxQtobPlAcwa\neU2/k8R5CriPxkiii+zET9AaQgip9sAVNwzcjhwyjswjssHTaA1Xvna+L1pMZ1t7jGumQc9JEFX/\nypMtyZdnuZXkQrdnIOTKkmHbqV/RT3ka7ciXoUufiy8YKC6AwnwozIOje+HL92HgaIgfAdqrxOQP\nH8DxdEhH7mv74w95enqLFtC4sfxo1AgqXzBb/uADeSzA5eMA3nsVataHe67/Wi4TSQKDAQoL/+o5\n9OPnFuSfJtbi4uL45JNP6Nq1603tN3r0aLZs2cLx48f55JNPGDFiRJnb5ufn8+STT7Jx40YAevTo\nwfz58wkK8n3F0K3C39pg5IYR4OCeX2netltFr+SmOX9eYvp0kerVBGbM0GA0VoxQO5UnMu5HG8FG\nge8HmqkcoG4GC+BQsZNpZ/NItruYFBPCfVZTqf1EvuSou4jljnSSxRLu11fmeVOcqiLtLLls4DDn\nKaAGEdQmkq7Uw3oDvWbepljMZ4/tJzSClk7mgZg0AarEtecfk4VazZEYAqoDoLfEEhjdE5ctHVvu\nAfJSViC6bYTVeRy9WeFED9ENP84FW6Gc3ajZFpr1BWvsldvtXwtn9kK/N8sWagARNQgeMhfxzD40\nF7Mk10GrFejTR2DvWj2DHmlMkygd896EiY9lwNxn4Zk3/xJqIPdtxQ9D26wdI6Y8T8k7W3G6jRRW\nieWZ2DH82PGvi2GdCVwXJh50qaajbpiTj/c5eeq2GnQseZ3gQgMLq4TI7zNJov/ah0mo1o3bF34A\nZ89y29PP8EavDpx4+11qD+hLc11dkCRso0Zw1hxAm7ffuuZ8rEaB4GILsQFGNtW00mP7dlkgtG+P\nJEnMt5+miy6sVKEG0Nxdh3OB28mkkAgCycfGOg6QSwlDaEEspZtjCIJAU2MX8sUsfnK5KQbqGq78\nGwZoQmhjiueM6xg7bOuoqqtHXUMLMt2pBGnCLgk1gEgCOUSafGyNjtCaI8g+/hEFZ9cRHHvfpe3y\nU9cRUKnDNUINQC+YsFvDMHYZDxvfhP6zIfCCIUfqQfhpnlwe2+MF0F6bJddF1yV3xJ2EL5oNX7wH\nBXlyD5nZAoEh8iMiCmZ8BtXKyCxHREGABdqNlP/f4ZCdHvfskU1EVq6EAwdAp5OFW0ICLF585TGq\nxCmz7xcE2WQkKwtiYjw/jh8/flTlgki46f2aNWvG4MGDmThxYrnXcVOmTCEzM5NTp04hiiL9+/dn\nypQpzJ0719Nl/+O4NcRakBF+WwO3mFg7cEBi7hyR+/sLxMcLqgsTkO9Gf3nUxRs77Dx9h4FRjfWq\nmHRcTrFbZPKZPH7IszEhKoiHIgIuWbOrRZbo4GP7GU6IxQwwRPGSrgZ6FUWaEzc/k8A+znA3DWhE\nzBVW82pgl0ooFHMoEHMoFHNIdZ2glr4ZtfRNVXtt2vOPkZv0hSzUAuOu+JkgCOjN0ejN0QRFd0eS\nJO+s6/fPwe2EvtPBUQwH18Oql6ByfVm0RTeApD9gzwroNxOMNyBadQY0ZfUIJeyHP7fINu5BsvDo\nepfAF19IDHeZObJTokplB7VXTIB7H4Jm7Us/TtVapP17GQkffsBQ3TG6VX+dmZ3NV5Qt60zgumyM\n3tT2Ru75ppj+dS2sqB3Bg8sd3N7uQiZm9mxCStJ4sf4yFkgSQkwM2uVfcvjrNTR6fgIsWwLvvAOL\nF1Nw8BDrPltFN8O1AiPUJJBrlxhsiGKuLZmuljD07eVz2OzK4axk5zlDXJm/ulp6C0fOV2ZjzGHq\nE8UmjtGS6jzAHeW+J3SCnjBtFFYxi7PuwlK3EQSBqvr6VNJW46DjV34p/gqTYCFGV+eK7SIJIoMC\nJCQEBDRaI2G1HyEr4QMKtQEERnXBUXgSR2ES1uoPlBrLgAkHNqh+BzSJh+9mQJ9psHclHPkBuoyH\nareXeT5aQyiOUAHp3ZUIxcUQFAKWoGuzZ9fDHALZpy9blAFat5YfF5EkOHtWFm2pqdDlqh652Bqw\nd/uNxyyNC46QfrHmx8+twbBhw0hJSSE+Ph6tVsu///1vnnvuuRva98knnwTAZDKVu+2hQ4fo168f\ngYHyzbK+ffuyZs0azxf+D+SWEGtSqJlKxw5V9DJuiuxsiTdnijz3vIZmzSommyZJElO2y8YD3/Q2\nUz9cvT6si5yxuxh1MpsGZj2/NqxMkMo9aW5JYoMzky8c6fTSR/CsKQ6DiiIN4BSZrOEAsVh5gk4E\noE6ZkE0s5rhzF/nubArFHCREAjVhBGlCCdRYaWuKJ1h7remHr7DnJ1wQaiOuEWql4RWhdmIbnNgK\n/efI2TJzMLQcDM36wbFNsOkd+WI3Lw3ueQWCFWbxCnJh5r+g1m3ysOTeIyB+OEZLAD17CaxcKXHw\ngMS06rNBDIP+j133cG2rmni12RN8rYXmoRrujrvyI1trvFKsVQ/WMLyhnjd2OBhcX0ejCC0mnSCX\nvc2bh+H339FMNZKaClWqyPt06n8fXWo0ZsWqRUQ3awbBwfxr6VoeqxpJaViNkGOXaKANJFZjZJMr\nmx76CDJEB5/YU5lqrnXdGyGV9Bp2nw/nzuhEdgspDKc1lQkuc/tS1yDoyJNc193GqLFwh+luzrmS\nOe74kxhdzSt+HoDsSlqM49J7UqMLIKz2aLIS3kejM1OU8RvBsfcgaEp3MDUIZhwXh8436wdZyfDZ\nYxBZGwa+df2SW+SMnlYfjNssoLNWv5FTvxZTMNjK6RUTBIiNlR+lEVsDzih0XL4o1vz48XNLsHTp\nUrZt28bChQsvlUFardYyv3snTZrECy+8cNNxevTowYoVKxg8eDCSJLFixQr69u2raO3/NG4Jseas\nHExoUmpFL+OmWLxIonsPoUKF2rTfHOxMc7Oyr5mQCii//K3AzuOnshkbFcRjkQGqZxaT3CW8Z09B\nh8B0S22qadTtebTh5EeOcpzz3EMj6qFQCNwE+e4sfretJ1pXi3qGlgRqQjEK5grJ7gLY84+Tm/Q5\noTWHX3LT8zkZJ2HrxxA/VRZpl6M3QqNecFt3OLVTzqbdjPV5aUiSbALRvgc88iKcTZJL28Z0hwGP\ncU+3wTz2pJ4BEWsIT94Gc78u1ar+cgRB4LEmemb/7uDz+64V+cEJP1E5qQik+EtmKOOaG+j0ZTHZ\nNolW0Vo5k/Lgg7B0KVStSuPGIgcPSFSpIm9v1AiMqR7B8yPH8dkjIznlEjlUYqFjGb2kVqNA7gV9\ncim7pgvjXXsK8YZIammvX9KrEQQq6/R0s7emnsmExoP+zBBBR245Yu0ilXXVqay7VggJCEQQSAaF\nV9xA0RpCCKv9GFkJ76M1RmAKLTszZhBMf4k1QYA7n4TkP6FmG7jBm0JaYzhuexY6YymDOm8Ec4jc\nG6eEylUgJwMcdjB4eDMpIgIyMq54aurUqTzzzDP+3hQ/fsqid/3yt7kRvj3qlcPk5uZ65TiXM3bs\nWL777jvCw+Wbw926deOJJ57wepz/ZW4JsVZYJZKQw6fL3/BvwsGDEocPS7z3vvp9YSALtRk7HWxN\ndbM8Xn2hJkkSSzKLmJtWwPtxoXQKLj9N7k3sksiXjjR+dGXzkCGau3XhqpZ+Skgc5RzfcYi6VOIJ\nOmFSydUR5Dlpe22baGTsQKy+Tvk7eAFncSrFmb+BoEPQ6OXHhX9LkkjRuc1YawzHEFiz/IN5g5I8\n2DgTOo6GiOuIQ41Wtuj3BuuWQfY5mHjB3TAmDp6dA0kJsOwdrKsX81rjQdQ5+inCjCUQeGPZpAfq\n6YivpcOiv+o1nJhI7FuDCZZioMVU2Rnwnnuw6AUmtzXwxA92Hq0PPPCA7ObYTS4jb9QI/twNPXv9\ndajB4QG8m17InpqxbMgroZ8ZdGW8Z6wmgbOFco/DxezaFFsidklkgP7GbkhUMWg57xBo4KETrSzW\nnB7tezmRF8RaHFdmmHWmSMLrPoWg0V73BodBMOGULktt6ow3/XrSGsJx2bM8z7ebQ+TXuxK0Orlv\nMi0Zqnt40yIy8prM2oIFC3j44Yf9Ys2Pn7Lwksj6OzN06FDq1avHt99+iyiKPPfcczz00EMsX768\nopd2y1AxauImyaxdC01WUUUv44ZwuSQ++lDkkUc0FTZDbc4fDn5KdvPlfeYKmZv2fEouizOKWFMv\nUnWhluguZlzxEc5LTt4116eHPkJVoZZJIcv4nc0c436acR+NVRNqkiRx0rGfffafaWW+Rz2hVnKO\n7BML0Oit6IzhaLRmkCREdzEueyYu23lCa47AGKSSUHO75HlWdTpC7Q7qxEw8DMs/gOfngf6qkrm4\nuvDy+/DiuzTQ7EM39lX5uRtEEIRrhZrDAUOGkDdsMt823wMvvSTPzGrTBjZupHdNLS+1NtDp3UkQ\nFgaTJl3atVZtgeSkKxvKjRqBcVGBzEnL5/+ySxgQVnYWWs6s/bX/EEM0x93FTDBVv+F5hFUMOs44\n3De0balrEPTkSS6PGuMvJ5IgMiko9Wc6U0SppiKXYxBM2C8Xax6gu5BZ8xjzDZRB3gixNZSZjJRS\nBmkymbDb7QoX5sePH19x9c2owMBAgoKCSn3MnDnToxgbNmxgzJgxmM1mAgICGDNmDOvXr/fG8v8x\n3BKZtawm7aibt6Kil3FDrF0rER4BbTwcV6OUebscrDvp5pveJsLM6gq18043j57MJkKvYW29SNVn\npm135fKB7TSPG6vQQX/9iyxvY8fFFo6zh9N0pDatiFPVQESU3By0/0q2mEYHc79rBgP7Cpc9m+wT\nHxMUey+W8PKdEb3C/jWQekC2SY+qL/cH6S4TSNs/Ab0JWnpoQ36zFBfJ9vuPvQzR1crerm4TmPyh\nd2K++ipUqkTxkHG4nhegf3/o1w++/homTEAIC+Opu++GdWtg164ryi0DAqColHtfQ8IDeDe9gBCt\nhobmsm8wWC8YjFykvjaApQGNb8pVtYpRq0isGQUNOgRKELHgeS9uBIEkcM7j/Q2CiTxRWZ+W1hiO\nszjF8wPoTCABTpv8uveUKjUgNcnz/SMi4PjxK54ymUzYbMrErB8/fnxH5cqVSUxMvNSzVlhYunHT\n1TidTtxuN6Io4nA4sNlsGI3GUisRmjRpwn//+19mzZqFJEl8/PHHNG3a1Kvn8b/OLZFZq9llINhc\nnE37e5dCZmVJfPO1xOjRmgrpDXpvt4P/O+7kq94mIizq/mnTHG76JWTSIcjIghphqgo1SZJY7khn\ngf0MU821VBVqEhIHSOV9fqEIB0/SibbUVFWoOSU7v9vWUyIV0F5FoeZ25pN94iMCK3dRT6id2gn7\nVsulZkXZ8OtCWDQM/m8ibF8EO5fC6b3yTCuNSoY6H70GDVtAp7IHY3uVH36Q+88WLUJnFv4yGNFo\nYNAg2a79iSfg++/hm28g9Mr3g8UCxSXXHtaoEZhW1cqz0cHX/fwKNV4p1oCbHn9RxaDljOPGes7K\n4mb61soiCCNFODzeX+5ZK+WXeRPojHIZpMcIgpxdU9q3pjSzFhl5Tc+a0Wj0izU/fv7GTJo0iWnT\nphEaGspbb107qqUs7r77biwWCzt27GD06NFYLBa2bt0KwLJly2jUqNGlbRcvXkxCQgKxsbFUqVKF\npKQklixZ4vVz+V/mlsisRVWKQrLoSfnxC2KG3bwTjVos+kSiZy+BmBj1hdqHex18cdTJij5mKlWA\nUBtwPJMh4RaeilK3N8EuibxrT+ac6GCOuR5hGvV6w7IpYjX7ceBiIM2pirrZPKfk4LTzKCed+4jS\n1eA2Qzs0Kjldiq5iso9/jDmsJQGVVCo1zE2FXz6AXi/LZiB175Sfd9rg/HFIPyoPtO710o3Z75eH\n3QYvDwejWR5Y3K47WK6aHfbTSjhxEN76Rnm8GyEjA0aOhE8/hchItOevdIMEZNv3hx6SH6VgMsk+\nEm63hFZ75WfVPdbyTXispYi1m0UugyxWdIyLfWsxCtxVjeiw4Xnvm9yzpqzM76LBiKJRFeYQefB2\ncCXPF1K5Kmxa7fn+ZZRB+sWaHz9/X3r37k3v3r1ver+ff/65zJ8NHTqUoUOHXvr/unXrsmHDBk+W\n5+cCt4RYA5BCTIQf/L2il1Em+/dLHDsmMW68+snKn5JdLDjgZHU/M1EqD7tOvyDUBleAUMsSHbxh\nO0msxsR0cx1VLfmTyeZrdtOemrSmhkeOdp5SJOZxynmAM84EInVVaW66mzBtlGrxRbed7BMLMAbX\nJTDqLnWCOkpgwwxo9dC1ro16E8Q2lh/eZPFsiIyBjvfAz9/CwhnQvCPc2Rtubw/pZ2DRLHhjiSzo\nlFJUJNcoloUkyUJt+HC4S/6960zgvkmtoNEIGI1gs10/XFlYTVxyg/QUObPmeRkk/NW3pgQTeux4\nfgxvZNY0WjMIOkRXIVq9h5+hphCwKcysBQRBcen9ezdEKWJt3LhxVK/u4UgCP378+PED3EJizR0R\nSHiiwjkwPsLplPj4I5FHHtVgVNl5MaNY5Lmf7cy/20RsYMUItUHhFsapLNSOu4uYbjvFvfpI+usr\nqVp2up9UNnKYfjSjNqXPovI2kiSR5T7LSed+ctzpVNM3oLPlAcyawPJ39uY6RCc5JxejM0cRFBuv\nzu9dkmDzuxB9G9x2t+/jAezcBH/8DG+vlF0b23WH/BzYtgG+/hDefRmMJhg2wXP3vMvZu1c2B2nd\nWnZu7NcP9Fdlid99V74Yfu21S09dPRT7RgkIgOJiz8RayIXMmpJMUIxeyzmnG5cklek6We46bmDW\nWnkY0OHAdWkw9k3vf7l1vwIumox4LNa8UQYZGAxFCsXaVWWQgwYNUrYmP378+PFz64g1W0woAWf+\nngM3166RqFRZvs5SE0mSeGaznUH1dbSJUXfg9Tmnm4HHMxkYbmG8ykJttyufefZknjJWpbXOqlpc\nCYmfSWA/qYygDZVQ57zdkovdth8pFHOoaWhCc1M3dIJ65Z4AoqsIZ/EZis5vQ6O1EFJtgHoCec8K\nuT+t2zPqxMs6B++/CpP+c6W9fnAo3DNEfpxNhuQEaNNNebySEhg6FD74AIKC4P33YcIEGDMGRo+G\n6GjYswemTYMdO64QcTqjZ2LNbJbFmicYtQJ6DRS7IMDDl6FBIxCu05DudFPF4NnX0I0Mxi4PDQJ6\ndNhxeeTaqsOAGzei5EYjeP4ZrNEHIboUOB6bQ5Q7QloClYu1zEz55koFzXP048ePn/9FbhmxlhsX\nQ+zRXRW9jGvIzJRYsUJi9hz1TUUWHXSSZZN4toWh/I29yDmnmwEJmQwIs/AvlYXaNmcOHznOMMlU\ng9u06mWVXLhZzX5yKeZR2l8xRNencSUHv9s2YBRMdLY8oOiC8EYR3XacxSk4i87gLD6Ds/g0oqsY\nvSUWQ2ANAqO6IahVcpqyBw6sg/5zQKuCQHW7Yd5EuPdBaFD2MGRiqssPbzBxIjRuDKNGyRe5AwfC\ngQOyeLvtNujeXc68vfMO1Kp1xa46E7g8aJmyWDwXa3DBEdImEXD1SIGb4KJ9v6diLUTQcVZhvxiA\n6ULfmidiTRCES9k1k+B5n6RGa0J0KyinNIdAsRfEWkkhiGK5w9pLX4NZvpFQWCjfdPDjx48fJB2r\naQAAIABJREFUP17hlhFr5+o3pcoXWyt6Gdfw2WcSvXoJREerK9SOZrl5a5eDb/tZ0GvVi53plEsf\n+4eZ+Ve0ul/IG52ZfOFI53VTbeK0XugRukGKsPMluwjBzHDaoFdgFX4zOCQbO0vWEayJoImxoyoC\nye3IJSvhfTR6K4aAqpisDQmK6YHWGKGeQLtIfjpsehu6T4TA8PK39wYrF8qCbcAYdeJt2ACrVsG+\nfVdmIxo3hvnzYeZM2UykUSN48NpRBJ6WQVosUKJArIUaBXLsErEKPgIq6TVkOEWP97cKeg6Lyudv\neqdvzYYJz8WaoDUjKRFrpmDIOeP5/iAPxjaawFZ8rZHOjXIxu+YXa378+PHjNW4Zsabv0A8K5mIv\nKcZotlT0cgA4c0biz10SH36k7kWszSUx9kc7L7cxUtOqXmy7KPHIyWzuCTExIVode/iLrHCcY4Mz\nk+nmOsRo1MlqAaSTz3J20YRY7qSuR30tnlAiFrLDtpYobRz1Da1Vydq6nYVkn/gYS2QHAit39nk8\n3C7Y9SU4iuV6Pp1Rnpd28d8H1sEdD0DMbb5fC0DCfli9RHZ21KogyDMy4JFH4LPPrrHXv0RICIwb\nV+YhNBc+wUXXX/++ESwWgeISCTx8PV/MrCnBqtWQ6/ZcrHmjZw0uOkIqF2tK0GjNiG4FxzCHQIkX\nBmMHBENRvudi7aJ9f40aytfix48fP36AW2TOGkCT29uCVsPBnT9U9FIu8eUXEn36CAQEqJtVm77D\nQS2rwOD66mltSZJ4ISWXSL2GiTHqCTVJklhsT2WTK5uZKgu1Q6SxlJ10pR5dqKeaUCsS89hesooq\nuro0MLZRRaiJbhs5iQswWRurI9QAflsE5xLAGgumC3fibQWyRX/6EajVHhrd451YogiJh6CkjExM\ncSHMeRae+DdERnsn5vWQJHj0UblXrUsXRYfSGW++FNJikWd5e4rVCLkKKxBDtBryXEoyazpyRc9t\n9y9iQoddiX0/JhwoE2uKM2tmL7hBAliCoOjGhuKWylWOkGvWrGHTpk3K1+XHjx8//2BumcyaIAhI\nwUZ0O7+DO/tU9HJITpY4cEBi7FPq6t3NKS7Wn3Lxw0CLqj1y888XcqTEyaq6EWhUiuuWJObbT5Mk\nljDDXIdgQZ2Xq3iZkchDtCKaEFXiAuS7s9hpW0ddwx1U1zdUJaYkOslJXITeUoXA6J6qxOToT3I/\nWv/Z3pmJVh7/twBWLwZbCVStCQ2aQ4M75P+GV4L5U6FZO9n1UQ0WLICUFPjqK8WHulgKabiJX6O5\njMHYN4o3Zq2F6DTkK8isWTXKrfsBjOj/Fpk1V0m65wcwB3spsxYkZ9Y85Sqxtn37doKCgujatavy\ntfnx48fPP5RbRqwBiKFmIhOOVvQyAPjic5F+9wuYzeoJpqwSiWd/tvOfu4yEmtSL+31uCf89X8ja\nepFYtCoNXZYk3rEnkyO5eN1cG7MKxhoANpz8H3tx4OIxFY1EJEkizX2SA/atNDK0J1ZfR6W4bnJO\nfYZGH0Rw1fvVuQFw7hj8tgT6vqGOUDuy50J54woICZOHWB/ZDT+vhvlT5D4dcyC89bV34n30Ebz3\nnmy/P3iwbBJyOQkJ8NJLsGULGJW/vjzpW/OWwYgSrFqBVIfnYi0QLcUos/8H5Zk1vRfEmqA1KzMY\nMXmrDNK7s9b8Q7H9+PHjRzm3TBkkgCMqhJDktIpeBicTJY4dg1691BNMkiTx7M827q+jo32sehr7\nSImTZ1JyWVgznFgPXdtuFulCRi1LcvKKqaZqQi2TQhbwK6GYGUZr1YRakZjP77b1JDh20dLUQ0Wh\nJpKX/BVILqzVB6tjIFKUDRtnQZdxEFrV9/EKcmHuc/DU63J5o8EIt90B/R+DV+bD0u0wdSHMWOqd\nwdb798Mrr8Abb8hDrrt3h6ZNYcYMOHUKnE546CGYMgUaNFAeD9B6YN+v1GDEK5k1rYY8l+fH0AgC\nQYKOfIXZNaWZNaM3BmPrTMrKIPUmkERwKqxNDQhSZt9/sWftAiaTCbtduWOnHz9+fENcXNxNlyon\nJCTQp08fKlWqRHh4OD179iQhIaHM7e12Ow8//DAhISFER0czb948pcv+x3FLibXCqpUwpeVW9DL4\n/HOR/gMEVQdgrzzu4nS+xAut1LPpz3K6GZGYxWtVQmgeoE5cSZJY6EjllFjCy6aaGFVyIDzOeRbx\nG+2pRS8aoVXhrSFKbo47/mRb8QrCtTF0Mg8gTKtCvxTy7zn/zBpc9iysNYYj3Iw7hae4nbDxTWjY\nA+Ja+j6eJMF/XoHWd0HrMsqwNBqoWkueoaaUi/PSZs+G3r1h7ly51PE//4HTp+VBjHXrytmHJ59U\nHu8COhO4PelZ84IbpBJCdBryFJRBgmwykisp61szXpiz5ineMxhRINYEwUuz1hSKtasya0aj0Z9Z\n8+Pnb4wgCEjSzX2W5+Xl0bdvXxISEjh37hytWrWiT5+y25OmTJlCYmIiKSkpbN68mVmzZrFx40al\nS/9HcUuJtfN16qLJUnCF4QWOHZM4dQq6d1dPqJ0vFpmy3cG8rkYMKtn0X3R+7Bdm5v4w9dw3P3ek\nc9BdyBRzLSwqZdQOkMpq9jOYFtyOCtkeIMt9ll+KvybbfY6Olv7UNtyuygw1SXRSkrOXnMQFOApP\nEFbrYTRaFTKIkgRbPoSAMGg+0PfxANYtg4w0GPmcOvFefFHOlo0Y8ddzGg106iTPTEtNlXvVli71\n6tBgj8ogzQLFxZ6LLW+UQYYodIME2b5fad+aYoMRweyVMkhJiRskeKcUUmlmzV8G6cfPLcOwYcNI\nSUkhPj6eoKAg5syZc0P7tWzZklGjRmG1WtHpdEyYMIFjx46Rk5NT6vaffvopkydPJiQkhPr16zN6\n9GgWL17sxTP53+eW6lnLa9IJ8j+v0DV88bnIwIECBoM6okmSJCb+YufBBjqaRKojXiRJ4sXTuYTp\nNUxU0aJ/heMc2125TLfUJlAlM5E9nGYzxxhGKyrj+3MVJTcH7Fs5706hkbEDUdoaPu8TkyQRZ1ES\nxVl/Ysvdj95SFUv4HZisjRE0KmVqD66H8yfg/pleFSplcvIIfPk+zPoS9Cqc44YNsHKlPLy6rPPT\n6+Guu7weWudBGaRZac+aUfCCG6SgOLNm9YJ9v9IySL1grPjMGlwwGVHoCBkQJJcOe0pExBVlkO3b\nt6dmzZrK1uTHjx+fsHTpUrZt28bChQsvmQBZrdYyr0kmTZrECy+8cM3zW7ZsITo6mtBSRtDk5OSQ\nlpZG06ZNLz3XpEkTVq5c6aWz+GdwS4m1hl3uB/tjJJ9KoHqNuqrHP3xYIjUV7uqmXlZt9QkXp/Ik\nPuyuXvnjwowi9hc7WFM3UjXnx3WODDY6M5lhrkOIoFcl5k6S+I2TjKAN4Xg4V+gmcEsudtk2okFL\nF8tgdIJv/6aS6KLw3CZKsnYhaPSYw1oQ2eA5tAYV3C1FNxTnQnE2ZCbBn1/LQk2vwjDzkiKY/TSM\nfhliqvs+3uXz0sLCfB/vKnQmD637FRmM4JU5a/kKetbAO2WQJnTYKjyzZkJy25Ak0fPeUXOw8jLI\ngGBIO+35/pGRV2TWGjduTOPGjZWtyY+f/2W8dY11k6WMZZGbe3M3a86cOcNTTz3FW2+9VerPCwvl\nUSAhIX9ddwQHB1NQoCCD/w/kumLN6XTqv//+++5btmzplJSUFCcIglS9evXkTp06benRo8dGnU6n\n3Df5JggJDUUKMJC++Suq13hFzdAALFsmMmiQgF6vjoDJKBZ59VcHn95jwqhS+eOvBXbeTS9Q1fnx\nR2cW/+c8x3RzHcJVyvRsI5HdpDCSNljxfZmnS3Lwu+07TEIAzYxd0fi4F092eVwKkkhozeHozLG+\nzeCdS5AFWVG2LNBsBfLstIAwsIRB9xcgOMo7sSRJnptW1uDqD1+D21pAp/u8E6+8tTzyCAwbpnhe\nmqd46gZZUsHW/cEXetYkSfL4tWkV9OQqLoPUV3jPmiBoEDRGJLcdQefhDQ2zVXlmzRLoVTdIP378\nlIOXRFZFkJGRQffu3Rk7diyDBg0qdZvAQPlGeH5+PhEREYDc8xYUFKTaOv8XKFOsvf7665NXrFjR\nv23btr+1atXq965du24SRVGTlpYWvWbNmviXX375jQEDBnzzyiuvTFNzwZLVROTBP9QMCcD+/RJZ\nmdClq3rlj5O22hlUX0ezSuqUP56xu3jiVDbvx4VSzahO0nWbK4fPHGd5w1yHyioMvJYuzFA7TDoj\naUswJp/HdEh2dpasJVgTThNjJ5+7LkqSm9xTnwMSobVGIvi6Fy4/HTbMgBaDILK2LNDMIaDxQVxR\nhJnjYdcvEBEFlWKhcpW//puVLlvzz/WSDf/27fKXaevWoCvlPfHRR3Iv2jffeCeeB3jqBlmkYCi2\nNwxG9IKASSNQKEoEeXgzKkTQkSoqE0pGhZk1HXpE3LglN1oF7zWNzoToLkHjqVgzeWHWWkCwMrEW\nFga5ueB2l30zxY8fP38brr5RFhgYWObNs5dffpkXX3wRkMsbu3fvTt++fZk0aVKZxw8NDSU6Opq9\ne/fSrVs3APbt20ejRo28dAb/DMq8Im/atOm+V155ZZogCNd8Iz/88MOfiKKoWbt2rQq3rq/EHRFI\n2KkUVWNKksSyZSKDhwhoVcpwrUl0kZAt8t5dvhcTAMWiyMMns3mqchAdg9WJ+Ycrj4/tZ3jNVJtY\nje9jSkh8zxFOkcVI2qhizW8Xi9lhW0uENpbbDO1U6U/LS16O6C4hrNYo3ws1eyGsmwZ3PAANVRio\n/c3HkJcNy3ZATgacOwPnU+FcKvzxM+RlwQvzwOSFbOmuXdCnD8TGyq6O3bpBr17QowfExMCRIzB5\nMmzbBgb1ypSvxmM3SCVjvXSyhi1xSZh1nr+mrVoNeS6RIA+z+N7oWVOaWRMEAYNgwinZ0Aqezw2U\nTUYU/FHMwZCb6vn+AAGBUKhArGm1YLVCdrZcEunHj5+/NZUrVyYxMfFSz9rFssXrkZ+fT48ePejQ\noQPTp08vd/vhw4czbdo0WrRoQVpaGgsWLGDJkiWK1/5PosxvyN69e397tVATRVGTn58fDKDRaMTe\nvXt/6+sFXk1JlTAsqVmqxty/X/7+6thRHaGWVSIxeZuDeV1NmBRcCN0okiTxfHIudc06HqukwpBi\nYL+rgHftKbxsqkmc1vd9TG5EvmU/p8lhhEpCrUQsZHvJaqK0NdQTaikrcDvyCKs1EkHj494/t1Oe\nmVbtdmjUy7exAPb+CuuXwQtvgzkAYuLg9g7QYxAMfwaenwvTFkN1L/Sz5ufLA60/+EA2DTl4UBZq\nGzZAo0by7LTeveV5avXqKY+nAE/KIE0mcNjB7fYsOyYIAlajQJ7SUkitoMgR0lvW/UoMRsCb9v0K\njmG2gk2pwYjCzBr4SyH9+LmFmDRpEtOmTSM0NLTMvrOrWblyJbt27WLRokUEBQURFBREcHAwZ86c\nAWDZsmVXZM6mTp1KrVq1qF69Ol26dGHixIl0797dJ+fzv0q5tzOHDBnyRX5+fnBRUVFAo0aNDjZo\n0ODIrFmzrrWDUYnsuKrozqvbmLh6lUjffupl1V7eamdgPR13VFanjOSj84WcsLmYXS3U54IC4Ji7\niNn2JF4wxVFP63tx6MDFl+yiEDvDaY0Z3xuYFIn5bC9ZRVV9feoZW6og1CTyz6zGZUsntNbDvnd5\nvGjFrzdB25G+jQWQcRbemgjPzoXwSr6NJUnwxBOyc+PAC2MGYmJg1ChYvhzOn4f582HqVHjsMd+u\n5QbwxA1SoxEwmUCJq7pX7Pt1GvI8FIzgnZ41IzqcuBDxfB0GLwzG9kpmTWkZpNI5a3CFWEtNTWXW\nrFnKjufHjx+f0bt3b5KTk8nJyeGZZ565oX1GjBiBKIoUFhZSUFBAQUEB+fn5VKlSBYChQ4dy8ODB\nS9sbDAYWLlxIXl4e6enpTJgwwSfn8r9MuWLt8OHDtwUHB+evWrWqb69evb5LSkqKW7p06TA1Flca\n5xo0R8hVaHF8E6SkSCQmQufO6gi19SddHMp082xLdcqqfsm3Mf9cIQtrhWHW+P4ck9wlTLOdZLyx\nGo21vm8wLcLOEnYQhInBtMCgggFqqvM420r+j1qGZtQ23O7zeJIkUZC6FmdRMmG1H1VnbtqeFbLL\nY7dnfNObdjlOB7w5AfqOgsatfBsLYMkS2LcP5s0r/ec6HbRrBw8+qM4YgnLwxA0SvOAIaUSxfb9V\nq2wwdsiFMsibHep6OQICBnQ4lJiM4K3MmoI/iFd61gK9KtZyc3P985T8+PHjRyHlijWXy6VzOp36\nVatW9Y2Pj1+j1+udpfWxqUVwh/uh0EFJiTrDsb9dLdHrHnXmqhU4JCZvszP7TpOiPpAbJdnu4qmk\nHD6qEUYVgwoiRrQxxXaCMcYqtNT53j4+myIWsp3aRBJPY7Q+ngHvlOzstv1IgmMXrU33Eqf3fQOt\n6LZRkLoGe0ECYbVHo1GhpJQT2+DQRrjnZTmz5msWzIDwKOj3sO9jHT0Kzz8vZ9As6g2DV4InZZAA\nZrM3Zq0pH4yd5/JcrBkFDToESlA2r02pyYhBMONA+WBs0ZM/5EXMIcrdII1mcLvkGySeEhl5adaa\nfyi2Hz9+/Cin3KvXMWPGfBQXF5dUWFgY2KlTpy1JSUlxISEhCm/feU6DxreDTsPBrat9His3V2L7\ndolevdS5ez77dwedq2ppE+P78kfZUCSLp6OCaBPk+0zMedHBqyUnGGqIoYPu2sGJ3iaVXBbxG+2o\nSRfqIeDbv2GmO5Vfir9CLxjpaBmAVevb5nq3M5/81PWcPzgdtzNfFmo6FcRF+lHY9l9ZqAWoMFNs\n82rY9xuMf8P3WSybDQYNgunToWFD38byIp64QYLyzFqoSSDHK2WQygdjK5+1pmwwtsEbg7F1Cssg\n9WaQ3OBUkO4UhAv2/eWbDJTJZZk1k8mE3a4w/erHjx8//3DKTKds3769Xdu2bX8bP378u+PHj3/3\n4vPVq1dP3rRpU1d1llcGwSaMu36C7kN8Gmb9OokOHQVCQnwv1g5kuFl1wsXPg3x/wS1JEi+m5NHA\nrGdUpO97xnJFJ5NLTtBHX4m79eE+j3ec86xiH/E0pj5emu1VBm7JzTHHTs64jtPUeCeVdb4dwuyy\nZVB47mdsufsxhzUnov6/0Bl9+Du1FUDmSchIhPMnIPUA3DUBwuN8F/MiScdg4Ux4YwkEqDCT5bnn\nZLOQRx/1fSwvojOBw4Nra0sAKClQCPFCZs2qFchV0LMGEHKhby1GwTGM6LArzKwVS8qyWhqtCZc9\n2/MDCIJcCmnLA72Cvs7AYCjKhxAPb8ZERMjjLACj0ejPrPnx48ePQsoUa59++unwsWPHvl+3bt2E\nXr16fdezZ88NUVFR6YIgSHq9XtltTIWIYRYqHzvq0xh2u8SGDRIzZvh+MLRblHjhFzsvtTEQZva9\nMFyaWcyBYgfr6kX63PiiUHLxb1siXfSh9Db42BgCOEAqGznCYFpQFd9m8IrEPHbZNmIRgulseQCj\n4LsSRJftPAVnv8NReApLZDsib5uIVh/om2AntsHJ32RxZsuHiJoQWQtqtIa2w7033NpeAv+dLvfI\nmMxyCdbF/xrNsPErePQl77g7HjoETz8NDRrI/Wbt2kHVqn/9fOVKWLcO9uz5W/Sh3Qw6ExR7YL5n\nMQsUl0jgYdbZK4OxtRpO2JQZhIR4xb5fmSOkQTCRK55XtAbFBiPwVylkkILPWksQFCnIrEVGyg6q\n+Msg/fjx48cblCnWPvzww8cBjhw50uC7777rNXLkyMW5ubnWrl27burZs+eG9u3b/6rVat3qLfUv\nHNEhBKec82mMzZsk6taD2Cq+v3D79LATsw4G1fN939ieIgez0vL5tm4kFg9nG90odknk9ZKTNNIG\nMkjv2wwXwJ+k8AsJDKc1lfBtJibXncHvtvXU0d9BnL6hT0Wvo+g0OYkLCajchZDqg31rIHL0J/jj\nS2g9FFoOAWsM+GKItyjC2xcGabbrDnYb2IplAWcrgZxM2VDkznjlsfLz4f77YcQI2Rzkiy9g3Dgw\nGmXR1rIlzJ4Nq1fLM6JuMRSVQSoYjG01CpwtVFbC6I0ySNm+v2Jnrf0trPtBdoS0KTUZCZIza55y\nWRmk2Wxm5syZytbjx48fP/9wylUHDRo0ONKgQYMjzzzzzFvFxcWWzZs3d/nqq68eePrpp+f9+eef\nd6ixyKvJr1aZiN8TfHZ8UZRY/a3E2LG+z6qlF4nM/cPB//Wx+DzLleVy89ipbGZXs1LT5Fth6JIk\n3rSdorLGwCOGWJ+f22+cZCdJjKQtYfi2tDPDdYbd9h9pYuxMtK6GT2M5Ck+Rc3IJIdUGYrL6uI8q\ncTvs/Az6TANrrG9jLf8AstJh2hIw+FB8SpJsud+lC7z00pXPJybC9u3yY/ZsaNPGd+vwIZ4MxQYw\nKxyMbTVVvBskXByMrXTWml6hwYhysSZn1hQaZ3nDZCQgSNmstcvEmlarZdy4ccrW48ePHz//cG7o\nij0nJyf09OnTVV0uly4qKip91KhRi957772nfL24sjhfux6Vvtvrs+Pv2iU7panhMTB1u4OHbtNT\nN8y3wtAtSYw9lUO/UDO9rL51DBQlibftyWiA8cbqaHwo1CQktnCC/aQyiraE4NtzS3Ue56DjV1qY\nuhOuVdIlUz72/ARykz7HGvcgxmAvlAJej9N7YOtHcO+/fS/UtqyDn1bCnOW+FWoAb70FKSnw+edX\nPi8IULu2/Bg+3Ldr8DGeukEqNhgxemHOmlZQNGcN5FlrqQqFkgnd3yOzpsQNEsAU4gX7foWz1vxD\nsf348ePHq5Qr1iZPnvz64sWLR9asWfOkRqO5dAt08+bNXXy7tLIpuL0b5H/qs+OvXiXSp4/g82zQ\nzyku9p5389advjcVmZtWgEuSmBgT7NM4kiTxseMMWaKTKeZa6Hws1H7kKCfIYBRtCMS3NvInHftJ\ndO6lrSmeYK1vjVJsuYfIS/ma0JojMAT6NntH+lH46W3o8SJE1vRtrGP74ONpMG0xWCN8G2vLFjlj\ntnOnXPL4P4onQ7FBFmuZGZ7HtZoEchQbjCiz7ge5DPKQqHwwtvLMmvKh2KLinrW/wWDsy6z7/fjx\n4+fvxMiRI6latSqvv/76Te+7bNkyPv30UzZu3KhoDRqNhhMnTlCz5o1fb5Wbzlm+fPmgxMTEWr/8\n8kvnzZs3d7n4ULRShTTtdC+43BxP2O31Y584IZGeDu3b+1aolbgkXtpqZ3pHI2a9b2P9mGdjeVYx\n82uE+VQ8AXzuSOeou4hXzDUx+qLX6QISEus5SDLZjPSxUJMkiSP2nSQ5D9Le3NfnQq0kZ68s1Go9\n4nuhlnkKNsyArhMguoFvY2WkwYxxMH46xNXzbay0NBgyRB5wXd23Dp0VTcUNxfbCnDWdhlylZZAa\nHbmKxZoy634teiRE3Ap65zQ6k3cMRmxeKINUItYCA8HphBKF5+LHjx+fExcXx6ZNm256v4SEBPr0\n6UOlSpUIDw+nZ8+eJCSU3Z5kt9t5+OGHCQkJITo6mnnz5ilZtscIwo0lYpKSktBoNIjiX99PQ4cO\nVSzUPKXcq+mGDRseysnJ8f1grJsgIDgYAg3k/bzS68devUrivngBnY+HUv9nt4PGkVq6VPNt71iS\n3cXTyTl8WCOUSL1v57etcpxjmyuHKaZaBAi+i+XCzUr2kkEhw2iNGYPPYrklF/vsP5PpPkN7Sz8s\nGt9mJouz/iD/zLeE1RmNIaBq+TsoITcV1r0GHcdAtdt9G6ukCN54EvqMhFY+vtfjdMIDD8CYMdCj\nh29j/Q3wuAzSLFBc7LnYsnqhDDL4Qs+aJHl+nBAv9KwpLYMUBEEejK2gFFLQGJFEJ5KkwLfL7KUy\nSCU9a4Igl0JmZSlbhx8/fnyOIAgeff7m5eXRt29fEhISOHfuHK1ataJPnz5lbj9lyhQSExNJSUlh\n8+bNzJo1q8KEz82cr5LvJm9Srlh76aWXpt9+++17unfv/n18fPya+Pj4Nb179/5WjcVdD8lqJvzQ\nHq8eMyNDYvduie7dfSvUDma6+fSQk6ntfScyQDYUeehEFs9HB9My0LdlYCsc5/jOmclr5tpYNXqf\nxSnGwVJ24kJkKK0w3ljbpUfkuTPYUvINLpy0Nff2qTW/sySdnFOfUZi2kfA6j6M3+7Afzu2Cs4dh\n7VRoNRRqtfNdLJCdH+dNhJoNZIdHpSQnww8/QHq6bBRyNS++CEFB8MorymPdAnjqBmlWmFkLMkCJ\nC5wKes5MGgEtUCIqEI2CXrF1v1KDEQC9wsHYgqBB0BqRPHGLuYjJC2WQAcHKMmsgl0Je6FubOXMm\nZ8+eVXY8P378eJ1hw4aRkpJCfHw8QUFBzJkz54b3bdmyJaNGjcJqtaLT6ZgwYQLHjh0jJyen1O0/\n/fRTJk+eTEhICPXr12f06NEsXry41G1zc3O57777qFSpEmFhYcTHx5N6YXYjwJ133smrr75Khw4d\nCA4OpkePHmRddnNo4MCBREdHY7Va6dy5M4cPH77i+Bcza40aNWLt2rWXnnc6nURERLB37146deoE\ngNVqJTg4mB07drB48WI6dux4aftDhw5x9913Ex4eTlRUFDNmzADg999/p23btoSGhhITE8O4ceNw\nOpV9v5R7pTt8+PBPX3zxxZmNGjU6eLFnTRCECpearsggwk+lePWYa9dIdL1LICDAd2Kt0CHx+Pc2\npnUwEhXguzLBElFiZGI2vawmhvt48PVXjnQ2ObOZbq5DuMZ3AjSTQj7nDxoSTVfqIXg4H6o8JEnk\nhHMvJ537aWhoR6yujs/6F50lZylM+xFH4UkCKnUmpNoANFovl3RKolzumHoAUvdD2hEIiYI7BkKD\nbt6JcToRNnwJTge4XOByyqLQ5YTcLNBo/p+9+46zq6z2P/559t7n7FNm5pxJmZACKRDDtQU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+RfAynhYuysb+gqCc+buYZnLKRBSs6sgTxkJC5cig3hmTVRGiT0n1mT7lpr7U+EHB/t4181BqmU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\neQs+dkPX9xNZBtnSAnffHZ9VU6p+Efk7oGBNRET6LDXV4PdD7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