{ "metadata": { "name": "", "signature": "sha256:0f2cf0d33c1f8e6443920bdcc5f1d78c0696561a7862843384098288d4760bc9" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "raw", "metadata": {}, "source": [ "Content provided under a Creative Commons Attribution license, CC-BY 4.0; code under MIT license. (c)2014 Lorena A. Barba, Gilbert Forsyth. Acknowledgement: NSF for support via CAREER award #1149784 and PASI award #1242245." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Sod's Test Problems\n", "\n", "Sod, 1978, J.Comp.Phys. Vol 27: 1-31\n", "\n", "C. Laney, 1998, Computational Gas Dynamics, Cambridge University Press\n", "\n", "You can read more about the [Sod Shock Tube](http://en.wikipedia.org/wiki/Sod_shock_tube) on Wikipedia.\n", "\n", "The shock tube is a common test for computational solvers and it has an analytical solution for comparison of results. \n", "\n", "The shock tube problem set up is as follows. Imagine a tube divided by a massless, rigid membrane separating areas of different pressure and density. If the membrane is instantaneously removed, what is the reaction within the tube? \n", "\n", "###Test 1: \n", "####Find the pressure, velocity, speed of sound, density, entropy and Mach number at t = 0.01 s, where\n", "\n", "$$\\underline{w}_L = \\left[ \\begin{array}{c}\n", "\\rho_L \\\\ u_L \\\\ p_L \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "1\\ kg/m^3 \\\\ 0\\ m/s \\\\ 100\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "$$\\underline{w}_R = \\left[ \\begin{array}{c}\n", "\\rho_R \\\\ u_R \\\\ p_R \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "0.125\\ kg/m^3 \\\\ 0\\ m/s \\\\ 10\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "###Test 2: \n", "####Find the pressure, velocity, speed of sound, density, entropy and Mach number at t = 0.01 s, where\n", "\n", "$$\\underline{w}_L = \\left[ \\begin{array}{c}\n", "\\rho_L \\\\ u_L \\\\ p_L \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "1\\ kg/m^3 \\\\ 0\\ m/s \\\\ 100\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "$$\\underline{w}_R = \\left[ \\begin{array}{c}\n", "\\rho_R \\\\ u_R \\\\ p_R \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "0.010\\ kg/m^3 \\\\ 0\\ m/s \\\\ 1\\ kN/m^2 \\\\ \\end{array}\\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##The Conserved Euler Equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The conservative formulation of the Euler equations is required when solutions contain shocks. As you might expect, the Sod's Shock Tube solutions do contain shocks. The conserved variables $\\underline{\\mathbf{u}}$ are" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\underline{\\mathbf{u}} = \\left[ \\begin{array}{c}\n", "\\rho \\\\\n", "\\rho u \\\\\n", "\\rho e_T \\\\ \n", "\\end{array} \\right]$$\n", "\n", "where $e_T = e + \\frac{u^2}{2}$ is the specific total energy.\n", "\n", "The vector form of the Euler equations is:\n", "\n", "$$\\frac{\\partial }{\\partial t} \\underline{\\mathbf{u}} + \\frac{\\partial }{\\partial t} \\underline{\\mathbf{f}} = 0$$\n", "\n", "where $\\underline{\\mathbf{f}}$ is the flux vector:\n", "\n", "$$\\underline{\\mathbf{f}} = \\left[ \\begin{array}{c}\n", "\\rho u \\\\\n", "\\rho u^2 + p \\\\\n", "(\\rho e_T + p) u \\\\ \\end{array} \\right]\n", "= \n", "\\left[ \\begin{array}{c}\n", "\\rho u \\\\\n", "\\rho u^2 + p \\\\\n", "\\rho h_T u \\\\ \\end{array}\n", "\\right]\n", "$$\n", "\n", "and where $h_T$ is the total enthalpy:\n", "\n", "$$h_T = e_T + \\frac{p}{\\rho} = h + \\frac{u^2}{2}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the Jacobian matrix, the Euler equations are written in quasi-linear form:\n", "\n", "$$\\frac{\\partial}{\\partial t} \\underline{\\mathbf{u}} + A \\frac{\\partial}{\\partial x}\\underline{\\mathbf{u}} = 0$$\n", "\n", "where" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$A(\\underline{\\mathbf{u}}) = \\frac{\\partial \\underline{\\mathbf{F}}}{\\partial \\underline{\\mathbf{u}}} = \n", "\\left[ \\begin{array}{ccc}\n", "\\frac{\\partial f_1}{\\partial u_1} & \\frac{\\partial f_1}{\\partial u_2} & \\frac{\\partial f_1}{\\partial u_3}\\\\\n", "\\frac{\\partial f_2}{\\partial u_1} & \\frac{\\partial f_2}{\\partial u_2} & \\frac{\\partial f_2}{\\partial u_3}\\\\\n", "\\frac{\\partial f_3}{\\partial u_1} & \\frac{\\partial f_3}{\\partial u_2} & \\frac{\\partial f_3}{\\partial u_3}\\\\\n", "\\end{array} \\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Euler Jacobian Matrix\n", "\n", "The flux is given as:\n", "\n", "$$\\underline{\\mathbf{F}} = \\left[ \\begin{array}{c}\n", "\\rho u \\\\\n", "\\rho u^2 + p \\\\\n", "(\\rho e_T + p) u \\\\ \\end{array} \\right]\n", "= \n", "\\left[ \\begin{array}{c}\n", "f_1 \\\\\n", "f_2 \\\\\n", "f_3 \\\\ \\end{array} \\right]$$ \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To calculate the Jacobian, $\\underline{\\mathbf{A}}$, we need $\\underline{\\mathbf{F}}$ in terms of $u_1$, $u_2$ and $u_3$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Recalling that $\\underline{\\mathbf{u}} = \\left[ \\begin{array}{c}\n", "\\rho \\\\\n", "\\rho u \\\\\n", "\\rho e_T \\\\ \n", "\\end{array} \\right] =\n", "\\left[ \\begin{array}{c}\n", "u_1 \\\\\n", "u_2 \\\\\n", "u_3 \\\\ \n", "\\end{array} \\right]$ we note that $f_1 = \\rho u = u_2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For $f_2$ and $f_3$, however, we must first represent the pressure $p$ in terms of conserved variables. We can relate the pressure to the conserved variables using an equation of state. \n", "\n", "###Relating pressure to conserved variables\n", "\n", "For an ideal gas, the equation of state is\n", "\n", "$$e = e(\\rho, p) = \\frac{p}{(\\gamma -1) \\rho}, \\gamma=1.4$$\n", "\n", "$$\\therefore p = (\\gamma -1)\\rho e $$ \n", "\n", "$$e_T = e+\\frac{1}{2} u^2$$\n", "\n", "$$\\therefore e = e_T - \\frac{1}{2}u^2$$\n", "\n", "$$\\therefore p = (\\gamma -1)\\left(\\rho e_T - \\frac{\\rho u^2}{2}\\right) = (\\gamma -1)\\left(u_3 - \\frac{1}{2} \\frac{u^2_2}{u_1} \\right)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Substituting for the pressure in terms of $\\underline{\\mathbf{u}}$ yields" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\underline{\\mathbf{F}} = \\left[ \\begin{array}{c}\n", "f_1 \\\\\n", "f_2 \\\\\n", "f_3 \\\\ \\end{array} \\right] =\n", "\\left[ \\begin{array}{c}\n", "u_2\\\\\n", "\\frac{u^2_2}{u_1} + (\\gamma -1)\\left(u_3 - \\frac{1}{2} \\frac{u^2_2}{u_1} \\right) \\\\\n", "\\left(u_3 + (\\gamma -1)\\left(u_3 - \\frac{1}{2} \\frac{u^2_2}{u_1}\\right) \\right) \\frac{u_2}{u_1}\\\\ \\end{array}\n", "\\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Which can be simplied further to" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\underline{\\mathbf{F}} = \\left[ \\begin{array}{c}\n", "f_1 \\\\\n", "f_2 \\\\\n", "f_3 \\\\ \\end{array} \\right] =\n", "\\left[ \\begin{array}{c}\n", "u_2\\\\\n", "(3-\\gamma) \\frac{u^2_2}{2u_1} + (\\gamma - 1)u_3 \\\\\n", "\\gamma \\frac{u_2}{u_1}u_3 - \\frac{\\gamma -1}{2} \\frac{u^3_2}{u^2_1}\n", "\\\\ \\end{array}\n", "\\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Calculating the Jacobian\n", "\n", "Recalling that the Jacobian $\\underline{\\mathbf{A}}$ is of the form:\n", "\n", "$$A(\\underline{\\mathbf{u}}) = \\frac{\\partial \\underline{\\mathbf{F}}}{\\partial \\underline{\\mathbf{u}}} = \n", "\\left[ \\begin{array}{ccc}\n", "\\frac{\\partial f_1}{\\partial u_1} & \\frac{\\partial f_1}{\\partial u_2} & \\frac{\\partial f_1}{\\partial u_3}\\\\\n", "\\frac{\\partial f_2}{\\partial u_1} & \\frac{\\partial f_2}{\\partial u_2} & \\frac{\\partial f_2}{\\partial u_3}\\\\\n", "\\frac{\\partial f_3}{\\partial u_1} & \\frac{\\partial f_3}{\\partial u_2} & \\frac{\\partial f_3}{\\partial u_3}\\\\\n", "\\end{array} \\right]$$\n", "\n", "Calculate all partial derivatives to determine that the Jacobian matrix is\n", "\n", "$$A(\\underline{\\mathbf{u}}) = \\left[ \\begin{array}{ccc}\n", "0 & 1 & 0 \\\\ \n", "\\frac{1}{2} (\\gamma - 3) \\left(\\frac{u_2}{u_1}\\right)^2 & (3- \\gamma)\\frac{u_2}{u_1} & \\gamma - 1 \\\\\n", "-\\gamma \\frac{u_2 u_3}{u_1^2} + (\\gamma -1)\\left(\\frac{u_2}{u_1}\\right)^3 & \n", "\\gamma \\frac{u_3}{u_1} - \\frac{3}{2}(\\gamma -1)\\left(\\frac{u_2}{u_1}\\right)^2 & \n", "\\gamma \\frac{u_2}{u_1} \\\\\n", "\\end{array} \\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Expressing the Jacobian in terms of the velocity, $u$ and the speed of sound (for an ideal gas) $$a = \\sqrt{\\gamma \\frac{p}{\\rho}}$$\n", "yields\n", "\n", "$$A(\\underline{\\mathbf{u}}) = \\left[ \\begin{array}{ccc}\n", "0 & 1 & 0 \\\\ \n", "\\frac{1}{2} (\\gamma - 3) u^2 & (3 - \\gamma)u & \\gamma - 1 \\\\\n", "\\frac{1}{2}(\\gamma -2)u^3 - \\frac{a^2 u}{\\gamma -1} & \n", "\\frac{3-2 \\gamma}{2}u^2+\\frac{a^2}{\\gamma -1} & \\gamma u\\\\\n", "\\end{array} \\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Laying the groundwork\n", "\n", "There's a lot to keep track of in the Sod tests, so it is a good idea to build several functions which can take care several common operations. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initial Conditions\n", "----\n", "\n", "The initial conditions for both Sod tests are below. \n", "\n", "###Test1\n", "$$\\underline{w}_L = \\left[ \\begin{array}{c}\n", "\\rho_L \\\\ u_L \\\\ p_L \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "1\\ kg/m^3 \\\\ 0\\ m/s \\\\ 100\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "$$\\underline{w}_R = \\left[ \\begin{array}{c}\n", "\\rho_R \\\\ u_R \\\\ p_R \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "0.125\\ kg/m^3 \\\\ 0\\ m/s \\\\ 10\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "###Test 2\n", "$$\\underline{w}_L = \\left[ \\begin{array}{c}\n", "\\rho_L \\\\ u_L \\\\ p_L \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "1\\ kg/m^3 \\\\ 0\\ m/s \\\\ 100\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "$$\\underline{w}_R = \\left[ \\begin{array}{c}\n", "\\rho_R \\\\ u_R \\\\ p_R \\\\ \\end{array}\\right] = \n", "\\left[ \\begin{array}{c}\n", "0.010\\ kg/m^3 \\\\ 0\\ m/s \\\\ 1\\ kN/m^2 \\\\ \\end{array}\\right]$$\n", "\n", "Instead of writing all of this out for every test, we can create functions to \"reset\" all of our initial conditions. \n", "\n", "We're also using a standard discretization throughout, so we can roll that into our reset functions.\n", "\n", "###Discretization\n", "\n", "###Test 1\n", "* N = 50 points in [-10m, 10m]\n", "* $\\Delta x$ = 20m / 50 = 0.4 m\n", "* initial CFL = 0.4\n", "\n", "###Test 2\n", "* N = 50 points in [-10m, 15m]\n", "* $\\Delta x$ = 25m / 50 = 0.5 m\n", "* initial CFL = 0.3\n", "\n", "\n", "\n", "Initial maximum wave speed = 374.17 m/s\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "def sodIC1():\n", " nx = 50\n", " dx = 20./50\n", " CFL = 0.4\n", " c_initial = 374.17\n", " dt = CFL*(dx/c_initial)\n", " x = np.linspace(-10,10,50)\n", " \n", " nt = np.ceil(.01/dt)\n", " \n", " #initial conditions\n", " wl = np.array([1., 0, 100000.])\n", " wr = np.array([0.125, 0, 10000.])\n", " \n", " U = np.ones((3,nx))\n", " \n", " U[:,:25] = build_U(wl[0],wl[1],wl[2])\n", " U[:,25:] = build_U(wr[0],wr[1],wr[2])\n", " \n", " return U, dx, dt, nx, x, int(nt)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "def sodIC2():\n", " nx = 50\n", " dx = 25./50\n", " CFL = 0.3\n", " c_initial = 374.17\n", " dt = CFL*(dx/c_initial)\n", " x = np.linspace(-10,15,50)\n", " \n", " nt = np.ceil(.01/dt)\n", " \n", " #initial conditions\n", " wl = np.array([1., 0, 100000.])\n", " wr = np.array([0.01, 0, 1000.])\n", " \n", " U = np.ones((3,nx))\n", " \n", " U[:,:25] = build_U(wl[0],wl[1],wl[2])\n", " U[:,25:] = build_U(wr[0],wr[1],wr[2])\n", " \n", " return U, dx, dt, nx, x, int(nt)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Conserved Variables Vector\n", "\n", "Recall that \n", "\n", "$$\\underline{\\mathbf{u}} = \\left[ \\begin{array}{c}\n", "\\rho \\\\\n", "\\rho u \\\\\n", "\\rho e_T \\\\ \n", "\\end{array} \\right]$$\n", "\n", "where $e_T = e + \\frac{u^2}{2}$ is the specific total energy and\n", "\n", "$$e = e(\\rho, p) = \\frac{p}{(\\gamma -1) \\rho}, \\gamma=1.4$$\n" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def build_U(rho, u, p):\n", " gamma = 1.4\n", " e = p / ((gamma-1)*rho)\n", " e_T = e + u**2/2\n", " \n", " U = np.array([[rho],[rho*u],[rho*e_T]])\n", " \n", " return U" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###The Flux Vector" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def build_flux(U_in):\n", " '''Takes a 3x1 vector U and generates the flux vector for Conserved Euler Eqs'''\n", " gamma = 1.4\n", " u1, u2, u3 = U_in[0], U_in[1], U_in[2]\n", " F = np.array([u2,\\\n", " u2**2/u1+(gamma-1)*(u3-u2**2/(2*u1)),\\\n", " u2/u1*(u3+(gamma-1)*(u3-u2**2/(2*u1)))])\n", " return F" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###The Jacobian" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def build_jacobian(U):\n", " rho = U[0,:]\n", " u = U[1,:]/U[0,:]\n", " gamma = 1.4\n", " p = (gamma-1)*(U[2,:]-.5*U[1,:]**2/U[0,:])\n", " c = np.sqrt(gamma*p/rho)\n", " [row, col] = U.shape\n", " A = np.zeros((row,row,col))\n", " A[0,:,:] = np.zeros(col), np.ones(col), np.zeros(col)\n", " A[1,:,:] = .5*(gamma-3)*u**2, (3-gamma)*u, gamma*np.ones(col)-1\n", " A[2,:,:] = .5*(gamma-2)*u**3-c**2*u/(gamma-1), (3-2*gamma)/2*u**2 + c**2/(gamma-1)\n", " \n", " return A" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Discretizing the Euler Equations\n" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Lax Friedrichs scheme (1st order)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\underline{u}^{n+1}_i = \\frac{1}{2} \\left(\\underline{u}^n_{i+1} + \\underline{u}^n_{i-1} \\right)\n", "- \\frac{\\Delta t}{2 \\Delta x}\\left[ \\underline{f}\\left(\\underline{u}^n_{i+1}\\right) - \n", "\\underline{f}\\left(\\underline{u}^n_{i-1} \\right) \\right]$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def laxfriedrichs(U, dx, dt, nx, nt):\n", " UN = np.ones((3,nx))\n", " for i in range(nt):\n", " UN[:,1:-1] = .5*(U[:,2:]+U[:,:-2])-\\\n", " dt/(2*dx)*(build_flux(U[:,2:]) - build_flux(U[:,:-2]))\n", " UN[:,0]=UN[:,1]\n", " UN[:,-1]=UN[:,-2]\n", " \n", " U[:]=UN[:]\n", " \n", " return U" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC1()\n", "U = laxfriedrichs(U, dx, dt, nx, nt)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Making sense of the results\n", "\n", "We've solved for the vector $\\underline{\\mathbf{u}}$ using the conditions specified, but the goal is solve for pressure, velocity, sound speed, density, entropy and Mach number. \n", "\n", "$\\underline{\\mathbf{u}}$ needs to be decomposed into those elements in order to compare results with the analytical solution." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def decompose_U(U_in):\n", " '''Extract pressure, velocity, sound speed, density, entropy and Mach number from U'''\n", " gamma = 1.4\n", " \n", " vel = U_in[1,:]/U_in[0,:]\n", " pres = (gamma - 1)*(U_in[2,:] - .5 * U_in[1,:]**2 / U_in[0,:])\n", " rho = U_in[0,:]\n", " c = np.sqrt(gamma * pres / rho)\n", " S = pres/rho**gamma\n", " \n", " return vel, pres, rho, c, S" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "vel, pres, rho, c, S = decompose_U(U)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "def plot_shock_tube(vel, pres, rho, c, S, x):\n", " plt.figure(figsize=(14,7))\n", " \n", " plt.subplot(2,3,1)\n", " plt.plot(x,vel)\n", " plt.title('Velocity')\n", " \n", " plt.subplot(2,3,2)\n", " plt.plot(x,pres)\n", " plt.title('Pressure')\n", " \n", " plt.subplot(2,3,3)\n", " plt.plot(x,rho)\n", " plt.title('Density')\n", " \n", " plt.subplot(2,3,4)\n", " plt.plot(x,vel/c)\n", " plt.title('Mach Number')\n", " \n", " plt.subplot(2,3,5)\n", " plt.plot(x,c)\n", " plt.title('Speed of sound')\n", " \n", " plt.subplot(2,3,6)\n", " plt.plot(x,S)\n", " plt.title('Entropy')" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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k7ly4+mqrmpbfujGRRONgxCYDWAFcgnW2zME6UuYGnTMay1MvYvnkKiB0GX3K5pJgCxdC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c0WvwPcRKwoyfXAv7A9shY651Ll2ItIJXw4Y1ORB7FA5LUUr6fKMKko8yTt96iwkUSNHg133ln5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\neNIpj7ZB2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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC2()\n", "U = laxfriedrichs(U, dx, dt, nx, nt)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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t77l/AjdgZeUbAqd5x8/C9s/aE7gJeDCjX41USI8e8M47sHAhLF4cu61Z4zoy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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Richtmyer method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2-step method\n", "\n", "$$\\underline{\\mathbf{u}}^{n+\\frac{1}{2}}_{i+\\frac{1}{2}} = \\frac{1}{2} \\left( \\underline{\\mathbf{u}}^n_{i+1} + \\underline{\\mathbf{u}}^n_i \\right) - \n", "\\frac{\\Delta t}{2 \\Delta x} \\left( \\underline{\\mathbf{f}}^n_{i+1} - \\underline{\\mathbf{f}}^n_i\\right)$$\n", "\n", "$$\\underline{\\mathbf{u}}^{n+1}_i = \\underline{\\mathbf{u}}^n_i - \\frac{\\Delta t}{\\Delta x} \\left(\\underline{\\mathbf{f}}^{n+\\frac{1}{2}}_{i+\\frac{1}{2}} - \\underline{\\mathbf{f}}^{n+\\frac{1}{2}}_{i-\\frac{1}{2}} \\right)$$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "def richtmyer(U, dx, dt, nx, nt, damp=0):\n", " UN = np.ones((3,nx))\n", " UN_plus = np.ones((3,nx))\n", " UN_minus = np.ones((3,nx))\n", " \n", " for i in range(nt):\n", " UN_plus[:,:-1] = .5*(U[:,1:]+U[:,:-1]) -\\\n", " dt/(2*dx)*(build_flux(U[:,1:]) - build_flux(U[:,:-1]))\n", " \n", " UN_minus[:,1:] = UN_plus[:,:-1] \n", " UN[:,1:-1] = U[:,1:-1] - dt/dx *\\\n", " (build_flux(UN_plus[:,1:-1]) - build_flux(UN_minus[:,1:-1])) +\\\n", " damp * (U[:,2:] - 2*U[:,1:-1] + U[:,:-2])\n", " \n", " UN[:,0] = UN[:,1]\n", " UN[:,-1] = UN[:,-2]\n", " \n", " U[:,:] = UN[:,:]\n", " \n", " return U" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 15 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Richtmyer, Test 1\n", "\n", "Using the values for test 1, let's see how the Richtmyer scheme handles the shock tube. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC1()\n", "U = richtmyer(U, dx, dt, nx, nt)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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luZD4ckNHoBbQHAhsPzme4KhO95D3mgW0Aaqk5dt4UOfOsHUrfPSR25GIpF0bYAuwFNgP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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Damping\n", "\n", "Some schemes are prone to overshoots, which produce the sharp spikes in the plots above. One way to smooth out these overshoots is to provide a damping term. \n", "\n", "For the Richtmyer scheme, the damping term is added when the $\\underline{\\mathbf{u}}^{n+1}_i$ term is calculated.\n", "\n", "The damping term is simply added on to the existing equation, with the level of damping controlled by a damping coefficient $\\epsilon$. \n", "\n", "The full damping term is defined as:\n", "\n", "$$\\epsilon (\\underline{\\mathbf{u}}^{n}_{i+1} - 2\\underline{\\mathbf{u}}^{n}_{i} + \\underline{\\mathbf{u}}^{n}_{i-1})$$\n", "\n", "You can see that this is implemented in the Richtmyer function above with the line\n", "\n", " damp * (U[:,2:] - 2*U[:,1:-1] + U[:,:-2])\n", " \n", "where `damp` is another parameter passed to the function. `damp` is given a default value of 0, so to add damping, simply pass a non-zero value of `damp` to the same function. \n", "\n", "Try experimenting with different values of $\\epsilon$ and see what happens. Below, a value of $\\epsilon = 0.1$ is used. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC1()\n", "U = richtmyer(U, dx, dt, nx, nt, damp=0.1)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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wfAzjlQTIy7PyjFK06tVthivD84aPBTYCK4iubTgBqIXN/rzmnTeR4GxOj5D3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\nJ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+WtbBskLSVrDZveQInzvAQb8h3jXXWyqr1J8vxO8ST4FE+CT/EkWMIaSyAa8STMsQQC\nFE+mYXMdDwFfAWtcPwtrEr5XsWRku7AbEEta3zxQ0iVrDZuzgc+x3p4dJBPRBl2mSfL8SPFE8SRo\nFE/8K2rxJMyxBMIfT8IaSyAc8URERERERERERERERERERERERERERERERERERERERERERERERERE\nRERERERERERERERERDz0f0npvufsZsPvAAAAAElFTkSuQmCC\n", "text": [ "" ] } ], "prompt_number": 17 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look at the difference! Just a small damping value and all of the spikes smooth out nicely. " ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Richtmyer, Test 2" ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC2()\n", "U = richtmyer(U, dx, dt, nx, nt)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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SYswYqFsXTjjBdSTpQeWeJQi0n42IJNMll8D8+bBggetIxC/UsJGUGDDAqpyI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"text": [ "" ] } ], "prompt_number": 18 }, { "cell_type": "markdown", "metadata": {}, "source": [ "As with the first set of conditions, there are some spikes formed by overshoots. Applying damping with $\\epsilon = 0.125$, yields a similar smoothing effect. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC2()\n", "U = richtmyer(U, dx, dt, nx, nt, damp=0.125)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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C4MHQrZvraCRIEtGwmQJ8DtwH7AmUxxovFYBbsEbMoUAfoDHwFnA4UB2YCzQDtuV7TSUO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"text": [ "" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "MacCormack Method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This method is also called the 'predictor-corrector' method, where we predict the next value of $\\underline{\\mathbf{u}}$, $\\underline{\\mathbf{u}}^*_i$, and then update it. \n", "\n", "$$\\underline{\\mathbf{u}}^*_i = \\underline{\\mathbf{u}}^n_i - \\frac{\\Delta t}{\\Delta x} \\left( \\underline{\\mathbf{f}}^n_{i+1} - \\underline{\\mathbf{f}}^n_i \\right)$$\n", "\n", "$$\\underline{\\mathbf{u}}^{n+1}_i = \\frac{1}{2}\\left(\\underline{\\mathbf{u}}^n_i + \n", "\\underline{\\mathbf{u}}^*_i \\right) - \\frac{\\Delta t}{2 \\Delta x} \\left(\\underline{\\mathbf{f}}^*_i - \\underline{\\mathbf{f}}^*_{i-1} \\right) $$\n", "\n", "###Damping\n", "\n", "Damping can also be used to control overshoots in the MacCormack method. Unlike the Richtmyer damping, however, the damping used with the MacCormack method is applied to the 'predictor' step of the scheme. Again, the default value of `damp` is 0, so the undamped behavior can also be observed. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def maccormack(U, dx, dt, nx, nt, damp=0):\n", " UN = np.ones((3,nx))\n", " UN_star = np.ones((3,nx))\n", " BC = np.array([U[:,0], U[:,-1]])\n", " \n", " for i in range(nt):\n", " UN_star[:,1:-1] = U[:,1:-1] - dt/dx *\\\n", " (build_flux(U[:,2:]) - build_flux(U[:,1:-1])) +\\\n", " damp * (U[:,2:] - 2* U[:,1:-1] + U[:,:-2])\n", " \n", " UN_star[:,0] = UN_star[:,1]\n", " UN_star[:,-1] = UN_star[:,-2]\n", " \n", " UN[:,1:-1] = .5 * (U[:,1:-1] + UN_star[:,1:-1]) - dt / (2*dx) *\\\n", " (build_flux(UN_star[:,1:-1]) - build_flux(UN_star[:,:-2]))\n", " \n", " UN[:,0] = UN[:,1]\n", " UN[:,-1] = UN[:,-2]\n", " \n", " U[:,:] = UN[:,:]\n", " \n", " return U" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 20 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "MacCormack, Test 1" ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC1()\n", "U = maccormack(U, dx, dt, nx, nt, damp=0)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:8: RuntimeWarning: invalid value encountered in sqrt\n", "-c:9: RuntimeWarning: invalid value encountered in power\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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Q1FSd9kltKZBJgBUrlFomkbcAGAnMAFLAUGxWZj3eQEbqm19qWf/+sKRQEqKELncAYdKk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\nTnspefD31aSldUYzMiIiIhmakakCzchIguTmwf8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"text": [ "" ] } ], "prompt_number": 21 }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Catastrophic negative overshoots\n", "\n", "What happened? If the overshoots are very large, the value of $\\underline{\\mathbf{u}}$ can become negative which will introduce some large errors into the calculation. It will also create some complex numbers when we try to calculate anything involving square roots. \n", "\n", "Remember that the Sod tests are very restrictive, in the sense that the initial conditions we are using are very 'coarse.' There are a few ways to mitigate negative overshoots available to us. \n", "\n", "1. Check and 'correct' negative velocity, density and pressure values at each time iteration.\n", "\n", "2. Introduce damping and see if it can overcome the negative overshoots.\n", "\n", "3. Cheat. Or rather, try out a third set of test values with a much finer mesh and see if the problem persists. \n", "\n", "4. Cheat a different way. Instead of using a fixed timestep, introduce an adaptive timestep. Remember that we define out timestep `nt` in terms of the *initial* sound speed. More on this later. \n", "\n", "For now, let's try introducing some damping, with $\\epsilon = .125$, and see what happens. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC1()\n", "U = maccormack(U, dx, dt, nx, nt, damp=0.125)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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qr34AdiYuNAE7rLNOHXjrLdeRiJ9p/l3ytHAh7NsHzZu7jiR5BFds0jh1ZzmH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"text": [ "" ] } ], "prompt_number": 22 }, { "cell_type": "markdown", "metadata": {}, "source": [ "That worked much better. How does Test 2 fare with damping added?" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "MacCormack, Test 2" ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC2()\n", "U = maccormack(U, dx, dt, nx, nt, damp=0.125)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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9u4eB64AmQBbwD+/4WUB57/itwANJ/W4kLvXqQYsWMG+e60hECGENlV5AM+Ak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"text": [ "" ] } ], "prompt_number": 23 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###MacCormack, 'Test 3'\n", "\n", "What about the first 'cheat'? If we change the problem and give it a much finer mesh to work with, will the overshoots still cause trouble? Below is a third set of initial conditions, with the same physical parameters as test 2, but with `nx = 400`." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def sodIC3():\n", " nx = 400\n", " dx = 25./nx\n", " CFL = 0.3\n", " c_initial = 374.17\n", " dt = CFL*(dx/c_initial)\n", " x = np.linspace(-10,15,nx)\n", " \n", " nt = np.ceil(.01/dt)\n", " \n", " #initial conditions\n", " wl = np.array([1., 0, 100000.])\n", " wr = np.array([0.01, 0, 1000.])\n", " \n", " U = np.ones((3,nx))\n", " \n", " U[:,:nx/2] = build_U(wl[0],wl[1],wl[2])\n", " U[:,nx/2:] = build_U(wr[0],wr[1],wr[2])\n", " \n", " return U, dx, dt, nx, x, int(nt)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 24 }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC3()\n", "U = maccormack(U, dx, dt, nx, nt, damp=0)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stderr", "text": [ "-c:5: RuntimeWarning: overflow encountered in square\n", "-c:5: RuntimeWarning: invalid value encountered in add\n", "-c:7: RuntimeWarning: invalid value encountered in subtract\n", "-c:12: RuntimeWarning: invalid value encountered in subtract\n", "-c:7: RuntimeWarning: invalid value encountered in multiply\n" ] }, { "metadata": {}, "output_type": "display_data", "png": 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JwKh0rIkIUmekbUk901bAn4B/AO8RV6APBo4jennfSuVeSH+OBG4DFgPzgUeB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\nmcAJaftUKo2mCcDP6hi7pAGiPD34UqKR8+FUPoZIUmXHU5n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"text": [ "" ] } ], "prompt_number": 25 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even with a much finer mesh, the overshoots have apparently caused some trouble. But maybe we can get away with a much smaller damping coefficient?" ] }, { "cell_type": "code", "collapsed": false, "input": [ "U, dx, dt, nx, x, nt = sodIC3()\n", "U = maccormack(U, dx, dt, nx, nt, damp=0.05)\n", "vel, pres, rho, c, S = decompose_U(U)\n", "plot_shock_tube(vel, pres, rho, c, S, x)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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kU1mFTSXgKKA/NqxsOOHeGL8coldTJf4JDxo06H/3CwoKKCgoKCMUkd3985/w1FO2mlMQ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"text": [ "" ] } ], "prompt_number": 26 }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "The cell below executes the style of this notebook." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"../styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ], "language": "python", "metadata": {}, "outputs": [ { "html": [ "\n", "\n", "\n", "\n", "\n" ], "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ "" ] } ], "prompt_number": 1 } ], "metadata": {} } ] }