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      "***\n",
      "# Understand the Problem\n",
      "\n",
      "## Question\n",
      "\n",
      "* What is the 3D velocity **and** pressure field for the **3D Navier Stokes Equation** for flow over a cavity?\n",
      "\n",
      "## Initial Conditions\n",
      "\n",
      "* The velocity and pressure fields are zero everywhere\n",
      "\n",
      "## Boundary Conditions\n",
      "\n",
      "Dimensionless form:\n",
      "\n",
      "* The u-boundary condition at y=1 is 1 (the lid) \n",
      "\n",
      "* The other velocity boundary conditions are zero (no slip). \n",
      "\n",
      "* The p-boundary condition at y=1 is 0 (atmospheric pressure)\n",
      "\n",
      "* The gradient of pressure at y=0, x=0, x=1, z=0 and z=1 is zero (Neumann)\n",
      "\n",
      "* Density = 1\n",
      "\n",
      "* Viscosity = 1/Re = 1/100\n",
      "\n",
      "## Governing Equations\n",
      "\n",
      "* The Navier Stokes Momentum Equation is described as follows:\n",
      "\n",
      "$$ {\\partial u \\over \\partial t} + u {\\partial u \\over \\partial x} + v {\\partial u \\over \\partial y} + w {\\partial u \\over \\partial y} = -{1 \\over \\rho} {{\\partial p} \\over {\\partial x}} + \\nu \\left ( {\\partial^2 u \\over \\partial x^2}+  {\\partial^2 u \\over \\partial y^2} + {\\partial^2 w \\over \\partial z^2} \\right ) $$\n",
      "\n",
      "$$ {\\partial v \\over \\partial t} + u {\\partial v \\over \\partial x} + v {\\partial v \\over \\partial y} + w {\\partial v \\over \\partial z} = -{1 \\over \\rho} {{\\partial p} \\over {\\partial y}} + \\nu \\left ( {\\partial^2 v \\over \\partial x^2}+  {\\partial^2 v \\over \\partial y^2} + {\\partial^2 w \\over \\partial z^2} \\right ) $$\n",
      "\n",
      "$$ {\\partial w \\over \\partial t} + u {\\partial w \\over \\partial x} + v {\\partial w \\over \\partial y} + w {\\partial w \\over \\partial z} = -{1 \\over \\rho} {{\\partial p} \\over {\\partial z}} + \\nu \\left ( {\\partial^2 w \\over \\partial x^2} + {\\partial^2 w \\over \\partial y^2} + {\\partial^2 w \\over \\partial z^2} \\right ) $$\n",
      "\n",
      "* The Poisson Equation to link pressure and velocity is:\n",
      "\n",
      "$$ \\nabla^2 p^{n+1} = \\rho {{\\nabla \\cdot \\mathbf{u}^n} \\over {\\Delta t}}-\n",
      "   \\rho \\nabla \\cdot (\\mathbf{u}^n \\cdot \\nabla \\mathbf{u}^n)+\n",
      "   \\mu \\nabla^2 (\\nabla \\cdot \\mathbf{u}^n)\n",
      "$$\n",
      "\n",
      "* **Assuming viscosity is small**, the Poisson Equation to link pressure and velocity is as follows:\n",
      "\n",
      "$$ {{{\\partial^2 p} \\over {\\partial x^2}} + {{\\partial^2 p} \\over {\\partial y^2}} + {{\\partial^2 p} \\over {\\partial z^2}} =\n",
      "{\\rho \\over \\Delta t} \\left( {{\\partial u} \\over {\\partial x}} + {{\\partial v} \\over {\\partial y}} + {{\\partial w} \\over {\\partial z}} \\right)\n",
      "- \\rho \\left[ \\left( {{\\partial u} \\over {\\partial x}} \\right)^2 + \n",
      "\\left( {{\\partial v} \\over {\\partial y}} \\right)^2 +\n",
      "\\left( {{\\partial w} \\over {\\partial z}} \\right)^2 +\n",
      "2 \\left( {{\\partial u} \\over {\\partial y}} {{\\partial v} \\over {\\partial x}} +  \n",
      "{{\\partial w} \\over {\\partial x}} {{\\partial u} \\over {\\partial z}} +\n",
      "{{\\partial w} \\over {\\partial y}} {{\\partial v} \\over {\\partial z}}\n",
      "\\right) \\right]} $$\n",
      "\n",
      "(this equation applies in the discrete domain)\n",
      "\n",
      "***\n",
      "\n",
      "# Formulate the Problem\n",
      "\n",
      "## Input Data:\n",
      "\n",
      "The Poisson Equation has **no temporal component**, so we use a number of iterations `niter`\n",
      "\n",
      "The Navier Stokes Momentum Equation **does have a temporal component**, so we use `nt`\n",
      "\n",
      "* `niter` = 51 (maximum number of iterations - for Poisson Equation)\n",
      "* `nt` = 51 (number of temporal points)\n",
      "* `nx` = 129 (number of x spatial points - maybe initially try 21)\n",
      "* `ny` = 129 (number of y spatial points - maybe initially try 21)\n",
      "* `nz` = 129 (number of z spatial points - maybe initially try 21)\n",
      "* `tmax` = 6 (maybe initially try 0.1)\n",
      "* `xmax` = 1\n",
      "* `ymax` = 1\n",
      "* `zmax` = 1\n",
      "* `nu` = 1/100\n",
      "* `rho` = 1\n",
      "\n",
      "## Initial Conditions:\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad n = 0 \\rightarrow u = 0 \\land v = 0 \\land w = 0 \\land p = 0$\n",
      "\n",
      "## Velocity Boundary Conditions:\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad y = 1 \\rightarrow u = 1$\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad x = 0 \\lor x = 1 \\lor y = 0 \\lor z = 0 \\lor z = 1 \\rightarrow u = 0$\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad x = 0 \\lor x = 1 \\lor y = 0 \\lor y = 1 \\lor z = 0 \\lor z = 1  \\rightarrow v = 0$\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad x = 0 \\lor x = 1 \\lor y = 0 \\lor y = 1 \\lor z = 0 \\lor z = 1  \\rightarrow w = 0$\n",
      "\n",
      "## Pressure Boundary Conditions:\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad y = 1 \\rightarrow p = 0$\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad y = 0 \\rightarrow {{\\partial p} \\over {\\partial y}} = 0$\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad x = 0 \\lor x = 1 \\lor z = 0 \\lor z = 1 \\rightarrow {{\\partial p} \\over {\\partial x}} = 0$\n",
      "\n",
      "* $\\forall (n, x, y, z) \\quad x = 0 \\lor x = 1 \\lor z = 0 \\lor z = 1 \\rightarrow {{\\partial p} \\over {\\partial z}} = 0$\n",
      "\n",
      "## Output Data:\n",
      "\n",
      "* $\\forall (n,x,y,z) \\quad \\ p = ? \\land u = ? \\land v = ? \\land w = ?$\n",
      "\n",
      "***\n",
      "\n",
      "# Design Algorithm to Solve Problem\n",
      "\n",
      "## Space-time discretisation:\n",
      "\n",
      "* i $\\rightarrow$ index of grid in x\n",
      "* j $\\rightarrow$ index of grid in y\n",
      "* k $\\rightarrow$ index of grid in z\n",
      "* n $\\rightarrow$ index of time\n",
      "* m $\\rightarrow$ index of iterations\n",
      "\n",
      "## Numerical schemes for each Momentum Equation\n",
      "\n",
      "* For the **one** first derivative of velocity in time: 1st order FD in time\n",
      "* For the **three** first derivatives of velocity in space: 1st order BD in space\n",
      "* For the **one** first derivative of pressure in space: 2nd order CD in space\n",
      "* For the **three** second derivatives of velocity in space: 2nd order CD in space\n",
      "\n",
      "## Numerical schemes for the Poisson Equation\n",
      "\n",
      "* For the **two** second derivatives of pressure in space: 2nd order CD in space\n",
      "* The the **three** first derivatives of velocity in space: 2nd order CD in space\n",
      "\n",
      "## Discrete equation for u-Momentum Equation\n",
      "\n",
      "$$ {{u_{i,j,k}^{n+1} - u_{i,j,k}^n} \\over {\\Delta t}} + \n",
      "   u_{i,j,k}^n {{u_{i,j,k}^n - u_{i-1,j,k}^n} \\over \\Delta x} + \n",
      "   v_{i,j,k}^n {{u_{i,j,k}^n - u_{i,j-1,k}^n} \\over \\Delta y} +\n",
      "   w_{i,j,k}^n {{u_{i,j,k}^n - u_{i,j,k-1}^n} \\over \\Delta z}\n",
      "   = \\\\\n",
      "   -{1 \\over \\rho} {{p_{i+1,j,k}^n - p_{i-1,j,k}^n} \\over {2 \\Delta x}} +\n",
      "   \\nu {{u_{i-1,j,k}^n - 2u_{i,j,k}^n + u_{i+1,j,k}^n} \\over \\Delta x^2} + \n",
      "   \\nu {{u_{i,j-1,k}^n - 2u_{i,j,k}^n + u_{i,j+1,k}^n} \\over \\Delta y^2} +\n",
      "   \\nu {{u_{i,j,k-1}^n - 2u_{i,j,k}^n + u_{i,j,k+1}^n} \\over \\Delta z^2}\n",
      "$$\n",
      "\n",
      "## Transpose\n",
      "\n",
      "Assume $ \\Delta x = \\Delta y = h$\n",
      "\n",
      "$$ u_{i,j,k}^{n+1} = u_{i,j,k}^n - \\\\\n",
      "{{\\Delta t} \\over h} \\left[ u_{i,j,k}^n(u_{i,j,k}^n - u_{i-1,j,k}^n) + v_{i,j,k}^n(u_{i,j,k}^n - u_{i,j-1,k}^n) + w_{i,j,k}^n(u_{i,j,k}^n - u_{i,j,k-1}^n) \\right] - \\\\\n",
      "{{\\Delta t} \\over {2 \\rho h}} (p_{i+1,j,k}^n - p_{i-1,j,k}^n) + {{\\Delta t \\nu} \\over {h^2}}\n",
      "(u_{i-1,j,k}^n + u_{i+1,j,k}^n + u_{i,j-1,k}^n + u_{i,j+1,k}^n + u_{i,j,k-1}^n + u_{i,j,k+1}^n - 6 u_{i,j,k}^n )\n",
      "$$\n",
      "\n",
      "## Discrete equation for v-Momentum Equation\n",
      "\n",
      "Similarly for v-momentum:\n",
      "\n",
      "$$ v_{i,j,k}^{n+1} = v_{i,j,k}^n - \\\\\n",
      "{{\\Delta t} \\over h} \\left[ u_{i,j,k}^n(v_{i,j,k}^n - v_{i-1,j,k}^n) + v_{i,j,k}^n(v_{i,j,k}^n - v_{i,j-1,k}^n) + w_{i,j,k}^n(v_{i,j,k}^n - v_{i,j,k-1}^n) \\right] - \\\\\n",
      "{{\\Delta t} \\over {2 \\rho h}} (p_{i,j+1,k}^n - p_{i,j-1,k}^n) + {{\\Delta t \\nu} \\over {h^2}}\n",
      "(v_{i-1,j,k}^n + v_{i+1,j,k}^n + v_{i,j-1,k}^n + v_{i,j+1,k}^n + v_{i,j,k-1}^n + v_{i,j,k+1}^n - 6 v_{i,j,k}^n )\n",
      "$$\n",
      "\n",
      "## Discrete equation for w-Momentum Equation\n",
      "\n",
      "Similarly for w-momentum:\n",
      "\n",
      "$$ w_{i,j,k}^{n+1} = w_{i,j,k}^n - \\\\\n",
      "{{\\Delta t} \\over h} \\left[ u_{i,j,k}^n(w_{i,j,k}^n - w_{i-1,j,k}^n) + v_{i,j,k}^n(w_{i,j,k}^n - w_{i,j-1,k}^n) + w_{i,j,k}^n(w_{i,j,k}^n - w_{i,j,k-1}^n) \\right] - \\\\\n",
      "{{\\Delta t} \\over {2 \\rho h}} (p_{i,j,k+1}^n - p_{i,j,k-1}^n) + {{\\Delta t \\nu} \\over {h^2}}\n",
      "(w_{i-1,j,k}^n + w_{i+1,j,k}^n + w_{i,j-1,k}^n + w_{i,j+1,k}^n + w_{i,j,k-1}^n + w_{i,j,k+1}^n - 6 w_{i,j,k}^n )\n",
      "$$\n",
      "\n",
      "## Discrete equation for Poisson Equation must be Divergence Free\n",
      "\n",
      "Since no terms have a differential temporal component - bring source term to other side and equate to forward differencing (as we did for Laplace Equation). Then take steady state after a certain number of iterations.\n",
      "\n",
      "$$ {{{\\partial^2 p} \\over {\\partial x^2}} + {{\\partial^2 p} \\over {\\partial y^2}} + {{\\partial^2 p} \\over {\\partial z^2}} =\n",
      "{\\rho \\over \\Delta t} \\left( {{\\partial u} \\over {\\partial x}} + {{\\partial v} \\over {\\partial y}} + {{\\partial w} \\over {\\partial z}} \\right)\n",
      "- \\rho \\left[ \\left( {{\\partial u} \\over {\\partial x}} \\right)^2 + \n",
      "\\left( {{\\partial v} \\over {\\partial y}} \\right)^2 +\n",
      "\\left( {{\\partial w} \\over {\\partial z}} \\right)^2 + \n",
      "2 \\left( {{\\partial u} \\over {\\partial y}} {{\\partial v} \\over {\\partial x}} +  \n",
      "{{\\partial w} \\over {\\partial x}} {{\\partial u} \\over {\\partial z}} +\n",
      "{{\\partial w} \\over {\\partial y}} {{\\partial v} \\over {\\partial z}}\n",
      "\\right) \\right]} $$\n",
      "\n",
      "\n",
      "$$ {{{\\partial p} \\over {\\partial t}} = {{\\partial^2 p} \\over {\\partial x^2}} + {{\\partial^2 p} \\over {\\partial y^2}} + {{\\partial^2 p} \\over {\\partial z^2}} \\\\ -  \n",
      "\\left[ {\\rho \\over \\Delta t} \\left( {{\\partial u} \\over {\\partial x}} + {{\\partial v} \\over {\\partial y}} + {{\\partial w} \\over {\\partial z}} \\right) \n",
      "- \\rho \\left[ \\left( {{\\partial u} \\over {\\partial x}} \\right)^2 + \n",
      "\\left( {{\\partial v} \\over {\\partial y}} \\right)^2 +\n",
      "\\left( {{\\partial w} \\over {\\partial z}} \\right)^2 + \n",
      "2 \\left( {{\\partial u} \\over {\\partial y}} {{\\partial v} \\over {\\partial x}} +  \n",
      "{{\\partial w} \\over {\\partial x}} {{\\partial u} \\over {\\partial z}} +\n",
      "{{\\partial w} \\over {\\partial y}} {{\\partial v} \\over {\\partial z}}\n",
      "\\right) \\right] \\right]} $$\n",
      "\n",
      "$$ {{\\partial p} \\over {\\partial t}} = {{\\partial^2 p} \\over {\\partial x^2}} + {{\\partial^2 p} \\over {\\partial y^2}} + {{\\partial^2 p} \\over {\\partial z^2}} - \n",
      "b $$\n",
      "\n",
      "$$ {{p_{i,j,k}^{m+1}-p_{i,j,k}^m} \\over {\\Delta \\tau}} = {{p_{i+1,j,k}^m -2p_{i,j,k}^m + p_{i-1,j,k}^m} \\over \\Delta x^2} + {{p_{i,j+1,k}^m -2p_{i,j,k}^m + p_{i,j-1,k}^m} \\over \\Delta y^2} + {{p_{i,j,k+1}^m -2p_{i,j,k}^m + p_{i,j,k-1}^m} \\over \\Delta z^2}- b_{i,j,k}^m $$\n",
      "\n",
      "Assume that $ \\Delta x = \\Delta y = \\Delta z = h $\n",
      "\n",
      "$$ {{p_{i,j,k}^{m+1}-p_{i,j,k}^m} \\over {\\Delta \\tau}} = {{p_{i+1,j,k}^m -2p_{i,j,k}^m + p_{i-1,j,k}^m} \\over h^2} + {{p_{i,j+1,k}^m -2p_{i,j,k}^m + p_{i,j-1,k}^m} \\over h^2} + {{p_{i,j,k+1}^m -2p_{i,j,k}^m + p_{i,j,k-1}^m} \\over h^2}- b_{i,j,k}^m $$\n",
      "\n",
      "\n",
      "$$ p_{i,j,k}^{m+1} = p_{i,j,k}^m + {{\\Delta \\tau} \\over {h^2}} \\left( \n",
      "p_{i+1,j,k}^m + p_{i-1,j,k}^m + p_{i,j+1,k}^m + p_{i,j-1,k}^m + p_{i,j,k+1}^m + p_{i,j,k-1}^m - 6p_{i,j,k}^m \\right) - b_{i,j,k}^m \\Delta \\tau $$\n",
      "\n",
      "Based on Point Jacobi intuition: $ r = {{\\Delta \\tau} \\over {h^2}} = {1 \\over 6} $ and $ \\Delta \\tau = {{h^2} \\over 6} $\n",
      "\n",
      "Hence:\n",
      "\n",
      "$$ p_{i,j,k}^{m+1} = {1 \\over 6} \\left( p_{i+1,j,k}^m + p_{i-1,j,k}^m + p_{i,j+1,k}^m + p_{i,j-1,k}^m + p_{i,j,k+1}^m + p_{i,j,k-1}^m - b_{i,j,k}^m h^2 \\right) $$\n",
      "\n",
      "So now we need to define $ b_{i,j,k}^m $\n",
      "\n",
      "$$\n",
      "b = \\left[ {\\rho \\over \\Delta t} \\left( {{\\partial u} \\over {\\partial x}} + {{\\partial v} \\over {\\partial y}} + {{\\partial w} \\over {\\partial z}} \\right) \n",
      "- \\rho \\left[ \\left( {{\\partial u} \\over {\\partial x}} \\right)^2 + \n",
      "\\left( {{\\partial v} \\over {\\partial y}} \\right)^2 +\n",
      "\\left( {{\\partial w} \\over {\\partial z}} \\right)^2 + \n",
      "2 \\left( {{\\partial u} \\over {\\partial y}} {{\\partial v} \\over {\\partial x}} +  \n",
      "{{\\partial w} \\over {\\partial x}} {{\\partial u} \\over {\\partial z}} +\n",
      "{{\\partial w} \\over {\\partial y}} {{\\partial v} \\over {\\partial z}}\n",
      "\\right) \\right] \\right]\n",
      "$$\n",
      "\n",
      "\n",
      "\n",
      "$$ b_{i,j,k}^{m} = \n",
      "{\\rho \\over \\Delta t} \\left( {{u_{i+1,j,k}^n - u_{i-1,j,k}^n} \\over {2 \\Delta x}} + {{v_{i,j+1,k}^n - v_{i,j-1,k}^n} \\over {2 \\Delta y}} +  {{w_{i,j,k+1}^n - w_{i,j,k-1}^n} \\over {2 \\Delta z}}  \\right) -\n",
      "\\rho \\left[ \\left( {{u_{i+1,j,k}^n - u_{i-1,j,k}^n} \\over {2 \\Delta x}} \\right)^2 + \n",
      "\\left( {{v_{i,j+1,k}^n - v_{i,j-1,k}^n} \\over {2 \\Delta y}} \\right)^2 +\n",
      "\\left( {{w_{i,j,k+1}^n - w_{i,j,k-1}^n} \\over {2 \\Delta z}} \\right)^2 + \\\\\n",
      "2 \\left( \n",
      "{{u_{i,j+1,k}^n - u_{i,j-1,k}^n} \\over {2 \\Delta y}} {{v_{i+1,j,k}^n - v_{i-1,j,k}^n} \\over {2 \\Delta x}} +\n",
      "{{w_{i+1,j,k}^n - w_{i-1,j,k}^n} \\over {2 \\Delta x}} {{u_{i,j,k+1}^n - u_{i,j,k-1}^n} \\over {2 \\Delta z}} +\n",
      "{{w_{i,j+1,k}^n - w_{i,j-1,k}^n} \\over {2 \\Delta y}} {{v_{i,j,k+1}^n - v_{i,j,k-1}^n} \\over {2 \\Delta z}}\n",
      "\\right) \\right] $$\n",
      "\n",
      "Also assume that $ \\Delta x = \\Delta y = \\Delta z = h $\n",
      "\n",
      "\n",
      "$$ b_{i,j,k}^{m} = \n",
      "{\\rho \\over {2 h \\Delta t}} ( {{u_{i+1,j,k}^n - u_{i-1,j,k}^n}} + {{v_{i,j+1,k}^n - v_{i,j-1,k}^n}} + {{w_{i,j,k+1}^n - w_{i,j,k-1}^n}} ) -\n",
      "{\\rho \\over {4h^2}} \\left[ (u_{i+1,j,k}^n - u_{i-1,j,k}^n)^2 + (v_{i,j+1,k}^n - v_{i,j-1,k}^n)^2 + (w_{i,j,k+1}^n - w_{i,j,k-1}^n)^2 \\\\\n",
      "+ 2 \\left(( u_{i,j+1,k}^n - u_{i,j-1,k}^n) (v_{i+1,j,k}^n - v_{i-1,j,k}^n) +\n",
      "( w_{i+1,j,k}^n - w_{i-1,j,k}^n) (u_{i,j,k+1}^n - u_{i,j,k-1}^n) +\n",
      "( w_{i,j+1,k}^n - w_{i,j-1,k}^n) (v_{i,j,k+1}^n - v_{i,j,k-1}^n)\n",
      "\\right) \\right] $$"
     ]
    },
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     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Navier Stokes Equations - slice notation"
     ]
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      "def navier_stokes_initialisation_3d(niter, r, nx_or_ny_or_nz, tmax, xmax_or_ymax_or_zmax):\n",
      "    \"\"\"\n",
      "    Returns the velocity field and distance for 2D linear convection\n",
      "    \"\"\"\n",
      "    # Increments:\n",
      "    nx = ny = nz = nx_or_ny_or_nz\n",
      "    xmax = ymax = zmax = xmax_or_ymax_or_zmax\n",
      "    dx = xmax/(nx-1)\n",
      "    dy = ymax/(ny-1)\n",
      "    dz = zmax/(nz-1)\n",
      "    nt = int((tmax / (r*(dx)**2))+1)\n",
      "    dt = tmax/(nt-1)\n",
      "    \n",
      "    # Initialise data structures:\n",
      "    import numpy as np\n",
      "    p = np.zeros((nx,ny,nz))\n",
      "    u = np.zeros((nx,ny,nz))\n",
      "    v = np.zeros((nx,ny,nz))\n",
      "    w = np.zeros((nx,ny,nz))\n",
      "    \n",
      "    # linspace is SIMPLER than list comprehensions:\n",
      "    x = np.linspace(0.0,1.0,nx)\n",
      "    y = np.linspace(0.0,1.0,ny)\n",
      "    z = np.linspace(0.0,1.0,nz)\n",
      "    \n",
      "    # Pressure Boundary Conditions:\n",
      "    p[:,ny-1,:] = 0.0\n",
      "    \n",
      "    # Velocity Boundary Conditions:\n",
      "    u[:,ny-1,:] = 1.0\n",
      "        \n",
      "    return p, x, y, z, u, v, w, nx, ny, nz, nt, dx, dy, dz, dt, niter, r"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def navier_stokes_3d(rho, nu, niter, r, nx, tmax, xmax):\n",
      "                  \n",
      "    (p, x, y, z, u, v, w, nx, ny, nz, \n",
      "     nt, dx, dy, dz, dt, niter, r) = navier_stokes_initialisation_3d(niter, r, nx, tmax, xmax)\n",
      "    \n",
      "    # Increments\n",
      "    h = dx\n",
      "    error_target = 1.0e-2\n",
      "    import numpy as np\n",
      "    \n",
      "    # Intermediate copies:\n",
      "    un = np.zeros((nx, ny, nz))\n",
      "    vn = np.zeros((nx, ny, nz))\n",
      "    wn = np.zeros((nx, ny, nz))\n",
      "    pm = np.zeros((nx, ny, nz))\n",
      "    bm = np.zeros((nx, ny, nz)) # bm needs to be exactly zero at the boundaries\n",
      "        \n",
      "    # Loop - use decimal points for all floating point numbers\n",
      "    for n in range(nt):    \n",
      "        \n",
      "        # We know the velocity at i=0, j=0, k=0, i=nx-1, j=ny-1, k=nz-1. b is zero at the boundaries.  \n",
      "        bm[1:-1, 1:-1, 1:-1] =  ( (rho / (2.0 * h * dt)) * ( u[2:, 1:-1, 1:-1] - u[0:-2, 1:-1, 1:-1] \n",
      "                                                    + v[1:-1, 2:, 1:-1] - v[1:-1, 0:-2, 1:-1] \n",
      "                                                    + w[1:-1, 1:-1, 2:] - w[1:-1, 1:-1, 0:-2]) -\n",
      "            (rho / (4.0*h**2)) * ( (u[2:, 1:-1, 1:-1] - u[0:-2, 1:-1, 1:-1])**2.0 +\n",
      "                                   (v[1:-1, 2:, 1:-1] - v[1:-1, 0:-2, 1:-1])**2.0 +\n",
      "                                   (w[1:-1, 1:-1, 2:] - w[1:-1, 1:-1, 0:-2])**2.0 +\n",
      "                               2.0*((u[1:-1, 2:, 1:-1] - u[1:-1, 0:-2, 1:-1])*(v[2:, 1:-1, 1:-1] - v[0:-2, 1:-1, 1:-1]) +\n",
      "                                    (w[2:, 1:-1, 1:-1] - w[0:-2, 1:-1, 1:-1])*(u[1:-1, 1:-1, 2:] - u[1:-1, 1:-1, 0:-2]) +\n",
      "                                    (w[1:-1, 2:, 1:-1] - w[1:-1, 0:-2, 1:-1])*(v[1:-1, 1:-1, 2:] - v[1:-1, 1:-1, 0:-2])) ))\n",
      "        \n",
      "        # First points for p. We don't know the pressure at i=0, j=0 and i=nx-1. We DO know the pressure at j=ny-1        \n",
      "        while True: \n",
      "            for m in range(niter):\n",
      "                pm = np.copy(p)\n",
      "                p[1:-1, 1:-1, 1:-1] = (1.0/6.0)*( pm[2:, 1:-1, 1:-1] + pm[0:-2, 1:-1, 1:-1] + \n",
      "                                                  pm[1:-1, 2:, 1:-1] + pm[1:-1, 0:-2, 1:-1] +\n",
      "                                                  pm[1:-1, 1:-1, 2:] + pm[1:-1, 1:-1, 0:-2] - \n",
      "                                                  bm[1:-1, 1:-1, 1:-1]*h**2.0 )\n",
      "            \n",
      "                # Set zero gradient boundary conditions:\n",
      "                p[0, :, :] = p[1, :, :]\n",
      "                p[-1, :, :] = p[-2, :, :]\n",
      "                p[:, 0, :] = p[:, 1, :]\n",
      "                p[:, :, 0] = p[:, :, 1]\n",
      "                p[:, :, -1] = p[:, :, -2]\n",
      "            \n",
      "                error = np.abs(np.sum(np.abs(p[1:-1, 1:-1, 1:-1])-np.abs(pm[1:-1, 1:-1, 1:-1])))\n",
      "        \n",
      "                if(error < error_target):\n",
      "                    #print \"n = \" + str(m) + \" completed\"\n",
      "                    break\n",
      "            break\n",
      "        \n",
      "        # First points for u and v. We know the velocity at i=0, j=0, i=nx-1 and j=ny-1.\n",
      "        # We are simply using the value of pressure here\n",
      "        un = np.copy(u)\n",
      "        vn = np.copy(v)\n",
      "        wn = np.copy(w)\n",
      "        \n",
      "        u[1:-1, 1:-1, 1:-1] = ( un[1:-1, 1:-1, 1:-1] - \n",
      "                 (dt / h) * ( un[1:-1, 1:-1, 1:-1] * ( un[1:-1, 1:-1, 1:-1] - un[0:-2, 1:-1, 1:-1] ) + \n",
      "                              vn[1:-1, 1:-1, 1:-1] * ( un[1:-1, 1:-1, 1:-1] - un[1:-1, 0:-2, 1:-1] ) +\n",
      "                              wn[1:-1, 1:-1, 1:-1] * ( un[1:-1, 1:-1, 1:-1] - un[1:-1, 1:-1, 0:-2] ) ) - \n",
      "        (dt / (2.0 * rho * h)) * ( p[2:, 1:-1, 1:-1] - p[0:-2, 1:-1, 1:-1] ) + \n",
      "        (dt * nu / h**2.0) * ( un[0:-2, 1:-1, 1:-1] + un[2:, 1:-1, 1:-1] + \n",
      "                               un[1:-1, 0:-2, 1:-1] + un[1:-1, 2:, 1:-1] +\n",
      "                               un[1:-1, 1:-1, 0:-2] + un[1:-1, 1:-1, 2:] ) )\n",
      "        \n",
      "        v[1:-1, 1:-1, 1:-1] = ( vn[1:-1, 1:-1, 1:-1] - \n",
      "                 (dt / h) * ( un[1:-1, 1:-1, 1:-1] * ( vn[1:-1, 1:-1, 1:-1] - vn[0:-2, 1:-1, 1:-1] ) + \n",
      "                              vn[1:-1, 1:-1, 1:-1] * ( vn[1:-1, 1:-1, 1:-1] - vn[1:-1, 0:-2, 1:-1] ) +\n",
      "                              wn[1:-1, 1:-1, 1:-1] * ( vn[1:-1, 1:-1, 1:-1] - vn[1:-1, 1:-1, 0:-2] ) ) - \n",
      "        (dt / (2.0 * rho * h)) * ( p[1:-1, 2:, 1:-1] - p[1:-1, 0:-2, 1:-1] ) + \n",
      "        (dt * nu / h**2.0) * ( vn[0:-2, 1:-1, 1:-1] + vn[2:, 1:-1, 1:-1] + \n",
      "                               vn[1:-1, 0:-2, 1:-1] + vn[1:-1, 2:, 1:-1] +\n",
      "                               vn[1:-1, 1:-1, 0:-2] + vn[1:-1, 1:-1, 2:] ) )\n",
      "        \n",
      "        w[1:-1, 1:-1, 1:-1] = ( wn[1:-1, 1:-1, 1:-1] - \n",
      "                 (dt / h) * ( un[1:-1, 1:-1, 1:-1] * ( wn[1:-1, 1:-1, 1:-1] - wn[0:-2, 1:-1, 1:-1] ) + \n",
      "                              vn[1:-1, 1:-1, 1:-1] * ( wn[1:-1, 1:-1, 1:-1] - wn[1:-1, 0:-2, 1:-1] ) +\n",
      "                              wn[1:-1, 1:-1, 1:-1] * ( wn[1:-1, 1:-1, 1:-1] - wn[1:-1, 1:-1, 0:-2] ) ) - \n",
      "        (dt / (2.0 * rho * h)) * ( p[1:-1, 1:-1, 2:] - p[1:-1, 1:-1, 0:-2] ) + \n",
      "        (dt * nu / h**2.0) * ( wn[0:-2, 1:-1, 1:-1] + wn[2:, 1:-1, 1:-1] + \n",
      "                               wn[1:-1, 0:-2, 1:-1] + wn[1:-1, 2:, 1:-1] +\n",
      "                               wn[1:-1, 1:-1, 0:-2] + wn[1:-1, 1:-1, 2:] ) )             \n",
      "    \n",
      "    return u, v, w, p, x, y, z"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "def navier_stokes_initialisation_2d(niter, r, nx_or_ny, tmax, xmax_or_ymax):\n",
      "    \"\"\"\n",
      "    Returns the velocity field and distance for 2D linear convection\n",
      "    \"\"\"\n",
      "    # Increments:\n",
      "    nx = ny = nx_or_ny\n",
      "    xmax = ymax = xmax_or_ymax\n",
      "    dx = xmax/(nx-1)\n",
      "    dy = ymax/(ny-1)\n",
      "    nt = int((tmax / (r*(dx)**2))+1)\n",
      "    dt = tmax/(nt-1)\n",
      "    \n",
      "    # Initialise data structures:\n",
      "    import numpy as np\n",
      "    p = np.zeros((nx,ny))\n",
      "    u = np.zeros((nx,ny))\n",
      "    v = np.zeros((nx,ny))\n",
      "    \n",
      "    # linspace is SIMPLER than list comprehensions:\n",
      "    x = np.linspace(0.0,1.0,nx)\n",
      "    y = np.linspace(0.0,1.0,ny)\n",
      "    \n",
      "    # Pressure Boundary Conditions:\n",
      "    p[:, ny-1] = 0.0\n",
      "    \n",
      "    # Velocity Boundary Conditions:\n",
      "    u[:,ny-1] = 1.0\n",
      "        \n",
      "    return p, x, y, u, v, nx, ny, nt, dx, dy, dt, niter, r"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "def navier_stokes_2d(rho, nu, niter, r, nx, tmax, xmax):\n",
      "                  \n",
      "    (p, x, y, u, v, nx, ny, nt, \n",
      "    dx, dy, dt, niter, r) = navier_stokes_initialisation_2d(niter, r, nx, tmax, xmax)\n",
      "    \n",
      "    # Increments\n",
      "    h = dx\n",
      "    error_target = 1.0e-2\n",
      "    import numpy as np\n",
      "    \n",
      "    # Intermediate copies:\n",
      "    un = np.zeros((nx, ny))\n",
      "    vn = np.zeros((nx, ny))\n",
      "    pm = np.zeros((nx, ny))\n",
      "    bm = np.zeros((nx, ny)) # bm needs to be exactly zero at the boundaries\n",
      "        \n",
      "    # Loop - use decimal points for all floating point numbers\n",
      "    for n in range(nt):    \n",
      "        \n",
      "        # We know the velocity at i=0, j=0, i=nx-1 and j=ny-1. b is zero at the boundaries.  \n",
      "        bm[1:-1, 1:-1] = ( (rho / (2.0 * h * dt)) * ( u[2:, 1:-1] - u[0:-2, 1:-1] \n",
      "                                                    + v[1:-1, 2:] - v[1:-1, 0:-2] ) -\n",
      "            (rho / (4.0*h**2)) * ( (u[2:, 1:-1] - u[0:-2, 1:-1])**2.0 + \n",
      "                             2.0*(u[1:-1, 2:] - u[1:-1, 0:-2])*(v[2:, 1:-1] - v[0:-2, 1:-1]) + \n",
      "                                   (v[1:-1, 2:] - v[1:-1, 0:-2])**2.0 ) )\n",
      "        \n",
      "        # First points for p. We don't know the pressure at i=0, j=0 and i=nx-1. We DO know the pressure at j=ny-1\n",
      "    \n",
      "        while True: \n",
      "            for m in range(niter):\n",
      "                pm = np.copy(p)\n",
      "                p[1:-1, 1:-1] = 0.25*( pm[2:, 1:-1] + pm[0:-2, 1:-1] + pm[1:-1, 2:] + pm[1:-1, 0:-2]\n",
      "                                 - bm[1:-1, 1:-1]*h**2.0 )\n",
      "            \n",
      "                # Set zero gradient boundary conditions:\n",
      "                p[0, :] = p[1, :]\n",
      "                p[:, 0] = p[:, 1]\n",
      "                p[-1, :] = p[-2, :]\n",
      "            \n",
      "                error = np.abs(np.sum(np.abs(p[1:-1, 1:-1])-np.abs(pm[1:-1, 1:-1])))\n",
      "        \n",
      "                if(error < error_target):\n",
      "                    #print \"n = \" + str(m) + \" completed\"\n",
      "                    break\n",
      "            break\n",
      "            \n",
      "        # First points for u and v. We know the velocity at i=0, j=0, i=nx-1 and j=ny-1.\n",
      "        # We are simply using the value of pressure here\n",
      "        un = np.copy(u)\n",
      "        vn = np.copy(v)\n",
      "              \n",
      "        u[1:-1, 1:-1] = ( un[1:-1, 1:-1] - \n",
      "                 (dt / h) * ( un[1:-1, 1:-1] * ( un[1:-1, 1:-1] - un[0:-2, 1:-1] ) + \n",
      "                              vn[1:-1, 1:-1] * ( un[1:-1, 1:-1] - un[1:-1, 0:-2] ) ) - \n",
      "        (dt / (2.0 * rho * h)) * ( p[2:, 1:-1] - p[0:-2, 1:-1] ) + \n",
      "        (dt * nu / h**2.0) * ( un[0:-2, 1:-1] + un[2:, 1:-1] + un[1:-1, 0:-2] + un[1:-1, 2:] - \n",
      "                         4.0 * un[1:-1, 1:-1] ) ) \n",
      "\n",
      "        v[1:-1, 1:-1] = ( vn[1:-1, 1:-1] - \n",
      "                 (dt / h) * ( un[1:-1, 1:-1] * ( vn[1:-1, 1:-1] - vn[0:-2, 1:-1] ) + \n",
      "                              vn[1:-1, 1:-1] * ( vn[1:-1, 1:-1] - vn[1:-1, 0:-2] ) ) - \n",
      "        (dt / (2.0 * rho * h)) * ( p[1:-1, 2:] - p[1:-1, 0:-2] ) + \n",
      "        (dt * nu / h**2.0) * ( vn[0:-2, 1:-1] + vn[2:, 1:-1] + vn[1:-1, 0:-2] + vn[1:-1, 2:] -\n",
      "                         4.0 * vn[1:-1, 1:-1] ) )          \n",
      "    \n",
      "    return u, v, p, x, y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%timeit navier_stokes(1, 0.01, 50, 0.1, 21, 0.1, 1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": null
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u00, v00, w00, p00, x00, y00, z00 = navier_stokes_3d(1, 0.01, 50, 0.1, 21, 0.1, 1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u01, v01, p01, x01, y01 = navier_stokes_2d(1, 0.01, 50, 0.1, 21, 0.1, 1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def vector_contour_3d(u, v, p, x, y):\n",
      "    import matplotlib.pyplot as plt\n",
      "    from mpl_toolkits.mplot3d import Axes3D\n",
      "    import numpy as np\n",
      "    fig = plt.figure(figsize=(11,7), dpi=100)\n",
      "    Y,X=np.meshgrid(y,x) #note meshgrid uses y,x not x,y!!!\n",
      "    plt.contourf(X,Y,p[:,:,10],alpha=0.5)    ###plotting the pressure field as a contour\n",
      "    plt.colorbar()\n",
      "    plt.contour(X,Y,p[:,:,10])               ###plotting the pressure field outlines\n",
      "    plt.quiver(X[::2,::2],Y[::2,::2],u[::2,::2,10],v[::2,::2,10]) ##plotting velocity\n",
      "    plt.xlabel('X')\n",
      "    plt.ylabel('Y')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "def vector_contour_2d(u, v, p, x, y):\n",
      "    import matplotlib.pyplot as plt\n",
      "    from mpl_toolkits.mplot3d import Axes3D\n",
      "    import numpy as np\n",
      "    fig = plt.figure(figsize=(11,7), dpi=100)\n",
      "    Y,X=np.meshgrid(y,x) #note meshgrid uses y,x not x,y!!!\n",
      "    plt.contourf(X,Y,p[:,:],alpha=0.5)    ###plotting the pressure field as a contour\n",
      "    plt.colorbar()\n",
      "    plt.contour(X,Y,p[:,:])               ###plotting the pressure field outlines\n",
      "    plt.quiver(X[::2,::2],Y[::2,::2],u[::2,::2],v[::2,::2]) ##plotting velocity\n",
      "    plt.xlabel('X')\n",
      "    plt.ylabel('Y')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 48
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Results"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "3D centreline 21 spatial intervals tmax = 0.1 seconds"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "vector_contour_3d(u00, v00, p00, x00, y00)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+lmh7NO+z2hZPK6q55fVFz5wo9+5w5HgQdY/AnpFTeeMZBM4BkAUgxqBgPncs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\n+qMdUX+sK+aPdyd8iZ64PxG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sFh0eR7gNAORyMU2Zuo1XrZyBYFcOv/F6MV18actQ23Uo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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f26f38f80d0>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "2D Centreline 21 spatial intervals tmax = 0.1 seconds"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "vector_contour_2d(u01, v01, p01, x01, y01)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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RM185+JDgJGqnI1E7VRN0cvGGzOBSy1CvYsQ1KLjOQS2UMbyVWi1kNpwKVRPc\nLl/wp38t17EJhFCYM6nj3DhZk13w8r9/NzCvsfDcqttvGg1ui++87Se7Pv+L6wp7+70cEuSk9Pzv\nc82vf+yum+yhTAwAmt914Sava5KmnyxCQwTCTSDeVINEj9f1SFI1EISKYS2aHNaiSQB7tkTw59HH\nGHdYxMmESdmncdr4ifIeXwKqKLhV2xyVRlv9wZYo88BgPQAoESM988NXdjTcuPr7/X/Y2ORddRPD\nHZe8/uHvndf506fWwuUUAFjQl5v5sXV7jvfcSsMdl2Q2dYTSr7THstu64oW9fTGzcyhunNHcd/aP\nPraeampFT5UjOIfgglCFVXSdx+NkTaYEfUf9sqTCGuxE61U1SPx4CsuaENfhhFAiKJXtglJlc6ni\nJrRYdY5RJ71J1QS3auWk88waSNcAgK8l3g8AekPUmnHr2n3eVnbiXr/tznN7/ve5C0dDGwDEL1q0\nmfm0qmoX77rnqdatt935Hl6w/GO311yx9KVqCG0AQCjFS2u/dE126/7ZWl14WG+MJX0zaoeNeY3D\nwUWtw5FV84b9M2orvjdx7682tOz83M+vjayet6v++lW7mt9z0QFm6Af/P+3CGY/Pxt6bvKzxeDgH\n/n7ZhpvPvaF+8zs+P+d13WBV9fsw6pdfbT+zbUlwePUN9X1e13IqdryQjCw4L5ryug5JKjd6/F0q\ng2taVVPrWImn36gBFxQA/LMbqnLy7CU//JsX5n7+pt+P3TbjI1dW3WnS5pvf0qk3RgcPbiBA6wcv\nf3jVQ59/sBpC2yjfjJqkNZCuyb7ROW/oiS0ru37y5BW7vvCLd2z/1E+u6bvvhVZRBTOOWUMZ3U7m\nIv2/37hm619/95bHaj5w+3Orbr9p+6d/ujTz+oFAArEDHNSXRSDsda1H8+pDg/W5YSf463/d+7Zb\nmp/+5B23bL1g8ICpe13XRPR1FHxbn0rM/rebNt3648/sXOp1PSdr18ZU+Hsf23bVk/d0t3pdy6ng\nvGo+hg6TS9rKX7U8fZvXdZwuqqbFLf3q3nDs/AXVNYI1gJorzh5c+eDnv5N8fkd9aGnbkNf1nKy2\nv79uV/rV9qd50VZSG9vnNtywquq+nRNKYcxr6in2JmuF7Whzv/D2++Z/8R3lmwKmTIqdiSgoEeCl\n61UCC5r3tv3D9c/MuHVtB6HV8f1m+Nk3ZnHTPhhyuGnr6Y17FlsD6WixLxlc8K/v3UhaeDEPIxpE\nLu1lrUdXfONQAAAgAElEQVSz4Td98xLdxUYAyKec8BM/6b7imXt7Ll56Wc3L7/ry3BfPWB2p+Naf\n+762d8mmxxKrAeD+r3f8xa6XUjM+d/+yhwJRtWouTfnGB7aseeYXvZcILuh9X+9QLn1f8/94XdNE\nPH9fX+Ov/3XvhT27861vu73twZs+O2eH1zVN1BvPJuOJntLvglR+VRPcqjG0AQDzabxu3fKBunXL\nB7yu5VQwn8aX//JTTzlZk3Xc8cdOr+s5Wasf+eKD65f+Q2T2P9zwXLWOP7fiT5978PGaWxb55zR0\nzbn9xmda3ndJ1f08Ft7xofWDj24+R1iOFjizZW/NpWdtb/3Q2p3hZW0ZADCQiwhQvQZDFfverv7o\njK3P3tt7sWMJFQB0gxaijfpAMe/qj93dtaB+lu+1aINueV3nsbQuDCRK44CX7m99anjFJ5ZsaP70\nvUt/uXBNtKI/czkX2PpUombflmyLawsFAPZvzc5//r6+xvPf1lA1PfatAme7N6YXA8COF1KtAKou\nuK26vq7/XV+c+6t7v7Ln7V7XcjogQlR+0ywhRFwtfvMVr+uQpofC/gFfNQ9jkt3RZWS37I803nR+\n1fa47L3/xcbMpo74jNuu3O1rir0p3FyA597rQgksx2t3elHfifjDHfvm9uzOR9uWhgYXXxQbaFkQ\nyHtd00TYFid3fWL7qqEuM5JPO/582jEKGddfzLl+IUDe/k+zH7r+b2dVbAck2+Lkzo9tW/3UPT2X\n2kV+sPV2zvLQtv//lfN/6WVtE5FPO+zm+BOf5S5Y03yj43s7L/yJbXGy/blkbMml8YTX9U3EjeSR\nL4my91w9MkKIWA9MSk64EPDsfZyIqmlxk6TJUs2hDQCCC1rywQUtVRUSxmt867m9jW8996itIhb0\nuhZ0/XEqa5qo6z9ZuaHmRKgaFX9z56KXjvZ4pV9vpWpUfPyuxS/e8Heztn7ntjfWbnsuuQwA2l/N\nLHz5gYG6FdfUVcVZDiOsuLWtvp7+fWbrwL5CS8/uvP///sVrbz3r4tjOagtu0tSojgtiJEk6bfhQ\nCHJQox797V7XcjqrlmFOZi4O5v5t/erf/d1Pz/phTaveAwD3/nP7RV7XdTztr6ZDX7ry5at/+S/t\nC+MtviEAcCyh/v05z//N/tez80O1alXOrCOVnwxukiRVlBV45QYFdoKBT+qg2NL0dun7mjvv3HPR\nXdd+fMYf923Nzt3yZCLudU3HMmd5OJNL2cbPv7D7Hds3JA/26C1k3CAAxBr1qm5Vl8pHBjdJkiqK\nBa2uAf1Pel2HVH1UjYoP//fCl+947fxv9ezOh7yu53hu/caZj1OGI35BiTfJ4FZJCCHrCCHbCSG7\nCCGfOcZ+qwghDiHkL8ds6yCEbCaEvEoIOerlCSdKXuMmSVLF0GEaDpRQPfqr+voxyVtN84xC0zyj\n4gc5P/P8aHLF1bUv/vmPgxeMf6xulm/ygpsQ0LilUVTuBfeVjBDCAHwLwFoAXQD+TAj5vRBi2xH2\n+xqAh8YdQgC4RAgxKdcsVk1we7H9wg+W69gEQvh0c4emFHM+pZD1qYWcoeZyhp7NK9SVp2skaYqs\nxMYbbWgJFY7tdS2SNBVu+/bCZzc9/txyq8APm9GlYbb/hK9xo8KlYTsbCjnZSMDJR5pTfcsZcX2U\ncJ0R7qNwdQIQcXDgl3KY1plwNYDdQogOACCE3AvgRgDbxu33CQC/BrDqCMeYtH+gqgluiWR92ca2\nqYv1zC2YxsKMCGsOV1RXKKNLlRLuMuLYCnWs0tK2FOpYhi/3uq4Uc7pSyBlaPmdo2ZxPKZhkWv/f\nlaTysqDXNqDvCa/rkKSpUjfTb17y3qanH7mra93oNkUj9thBkDXXUiN2OhpycxHDyUcaMoNnM4wN\nZlzjIDYXzHRBiy5hpr9YfBUcKThIwUESHMXy/nkSAPClsr6Ed1oAjB33sxPAuWN3IIS0oBTmLkMp\nuI0NyQLAY4QQF8CdQoi7TqWYqgluyOK5ch16INt0tGMTTpmPMxawqR4AQxAEgdpY76J0PnqOwxXV\n4YrmCkV1uaJxEKoQ12bUsRTiWIyWgp5fL2xXmG1Swl1KOCel5Zib6zJaWlLCOaNuaRtxXUpdl1HX\nVajjUuLy0vPL9S8hSd5RYfkcKJF69O/yuhZJmnRCgEAQJlzGBKdMuIwKTik4/dS/N+5y23sviPrc\n8KxWYOF8Qa/qevLjFKVgRiCoC1rkgpmuoEVXMNNXtDbARQouUnCQZkK4DA5Ur9+nh2pm4JKTed7j\nBURfMBE9uCH7pl1OpKXyGwD+UQghCCEEh7ewrRFC9BBC6gA8SgjZLoR49mRqBaopuHlDgKMAjgKA\ng3NcDuYaj3xxIYHiMBpwqBooUgRAEaiv6V5SMI2FrmCKACFCECJA6Mg6FSAER9gmQKgQhGDcttLL\nCAEITogQBIITCEGI4Bq1Cjoz86FA6tWILzkQDwwM+NVCVY9ZJp0+6jB4hgo7qcGu6NkGpNOAEIjZ\nqWhdcahpRqr7PEZcP4GgQOkDGwAlAEFpnRACAoiRbaXtI+uUjNlnZLx7UXoFwktLCICI5f8N8cwG\nYH8XMDCAnJ63Hx8JZSm4yCngACp/HmIvnXkhnjqp5wH42Jj7P/vFm1oOuwDMGHN/BkqtbmOtAHBv\nKbOhFsDVhBBbCPF7IUQPAAghBggh96N06lUGt4og4MBBCsDBOQr7882vTfKrEFG6AJIKAoZDN9VW\n9HigNnPucDa+ui/VbBRd3aCEuzor5nVm5kJG6rWwLzkQNwYHAnpO9liSKkorOt9Si8GT/jCTpJNB\nBCe11nBNTTHR1JruWa0QJ6gQNyhAXEewrA0l6ytYT0PAgQAH4I5bcohx62O3jdmXjGm5IePOpMU5\n8Okv46/aOzFz4WwMfPbdb7p+SvLORgDzCSFtALoBvBPAu8fuIISYM7pOCPkRgD8IIX5PCDEAMCFE\nhhASAHAlTnGGBxncqo+AgDOydjgbg/0HmneO2UJchYXziloXqk+dl8rFVvSnmwyL6wECwTVWzOus\nkAsZ6U1hPTUQM4YGgno6K0/FSlNNga3ZUKMN6Ku6eRql6kGFS+uLQ3Vxa7ipOd23UiVOiBEnIEBt\nWygZRyhZLe/8ERZ64YocA4eOqeknQynwz3+DR977OdwaCkAOvltBhBAOIeTjAB4GwAD8UAixjRBy\n28jjx5qarxHAfSMtcQqAnwshHjmVemRwm97EyIWpqb79LbsPe4QhVFCVunD98PmZfGTZYKbBKLp6\nACDQqJnXmZnzKWY+Hhp8PmYMDYR9ybQMdFK51GJwvgInrcOSp/alSaFyW6kvDjbErWRTY6b/HIU4\nIYW4hgtqOlzJ2kLNGDnzMVjoBecmgwXA27P0N1+Drjt+jq2RIOQZkQojhHgQwIPjth0xsAkh/mrM\nejuAZZNZiwxupysXGbjI9O1vPXxaIYaAqQbqTBaoI9HBZR1Dc6/b2b84wAWhGrNMRlyLEccpdbxw\nbL8v/4bGinldKeZ1xcz71Xze0HJ5ldnOUV5Zkt5kJg5crMKqirklpcrjc029vjjYOHdo34UqcUIK\ndYIMrt8VLG8LJWsLJePPFR9AEX2K4LYCCz6PQ9rR3HE7Hv/uL7HY6zqkyiWDm3Q4Fzm4yAHoSOZq\n/3xwO4W/qPijoDBGb7XR3oWZfHipOzJ0iiMU1eVMdQVTCSBYqYetzYhjM+raCnFsdnjYK+hKIe9X\nC3lDy+ZV5siwdxpicBQbanwhtv3Y61okjwkBjduq3y34/bzo17nl11zLr3HLrwnbH88mF1BwhRCh\nUHCVQiiECJWCq45gOZsoGV+x+BJs9MBCvyJcV4ELP4pev7MTdv5SJFvq8bLXdUiVSwY36cRwFGAd\nft3FYLbxxaPtLgg0h1HDoaoBCv+hsNe3MJMPL3P5aNBTVFeMhj3BfYqZNZRsqj7S+0xTpPOArhQr\n82uxNGlqMTRPgZPxw5Snh6YZlVtqXXGoTueWX+eWX+WOvy49tIgSrhAIlRKuUAh1JIgpBEIFIDiI\nI0BtLogjQGwuqMNBbCGo47eKmyBgHuzx76IAB2kVLlePPHtU1ZnZhMm9ZKAfAexDDbic5nI6qJ7g\n9jn8Q9mOTSAQgokI8piBP2MGhjAPQwhAtgCdLAELDiwAybGbB7MNRw97FL6CFmg2arMXdwzNu357\n35KQzsycoWZTteH+9U3hzv2GlpcX7U4zs9BxiQpHniadBqhwaXOhr/mMofbLNWrFVOKEHMHyAtTm\nIA4XxBaEOoZlvgExErzGBjAOEwIOgwCmSQibUg4I2lGDvWjEVqxCAUEUEAQHhQ/5cV1ZJ1s5jy2N\nUT3BzcX/lu3YAgz9iCOAc7AB65BAaXLiAEzUI4XP4Htle23pEA4TJtqHOhtK190RKKZmtITqU5fs\nHZx/487+s/waNXOLm1/9WWO4p9fjaqVJIWBDq12AnT/3uhLp1KztfOZDPmo2AYBJfL1azvkjTOxX\nhWvJEFZmu1GDn+EDMBGAAIUfGUQwBAePwEAvGFJTNCPVdJ05oaJUT3CrwXVlO7YLigz82AEDDBx1\nSCGCPKLIYyGeKdvrSkenIA4dbeHI8LnDZm1EACSsDfcH1EwyZiQmZaJeqRIQUHCrCD0QQD7jdTXS\nydtWM/+hM4d2XaUTO+6jxYZiQLuq6NeGw9ns4+DIw0V+ZIwzabK1IIXz8ChexyrkR1rZBtAKP9ZB\nRxYZ/BkMgyDy3386qJ7gNgdHPcV2yig4mjCMuRhEvRw/Z0oQMFAYYIc6OzTUdi4rOIFwzg5GCQBD\nzSZjwaEXF4a2dMSMwYQcjmR6UmEnOtF6RRzD93hdi3TyuvxNXV2tTXcDQMjOBlsL3XNmpHsucCLs\n/RRcJRAKAMFBbSGIw0HsQ+vUDliF7eNOn+bhjpxClVMGHJsfDtZhC9ZhC4DSv1YfgtiNRryCC+DD\nhTDhxzSfCf50UT3B7SZM9gwE0uQhYAc7IARGg1hdvGfx+E4Ioz1PBShlxLFHe54qxLGLrs+OBwdf\nWBja3BEzhoZlUDs9tGPOM7Ow72qv65AmT0YNZrepZ2zeFj5j88GNQkDnluZ3C36/WzT00V6j3PbX\npYcW5zXfolJHhdEOCyO9RiFUAbiHdVYALV0vNxr4HAzCQs9Ij3iJAmhCFk3YjYuw+7j7T5bfyVOl\nU6F6gpvkDQo/VNRBQV081n9o6A/OVFeUwhgXTKHEdRhxbUYcW6GOxYhjc0Ftvy/3hqZYeY0V8z7V\nzPuU0jhvumIWZTCTACCBWEcLukI2FE2FI3sRT1eEoMh0q8h0KzlmWkAAQAQbj/o0wYnOLc1wC4bP\nLfrHBD6jNp1YmNd8Zym6E1CCblAA3BFKxhZKNlgobICFHjiQp+ClaUUGN6mEwhgNaLHo4DLT9QUs\n1xfggtDRuU4ZcQuhYPq1QyGskPerubxfyxfo6PTJkjRBDlRLgZMZQF1bM3p2Hv8Z0ulEECpM5iua\nzFcEMHzYgxG8dGjHwyeGtwx1nRJwggAwOp1VoFB4fiTMHR4cJamKyOB2umEwoKAOCuqj0cFlRddn\nWK4vIAShGivmdGbmNVbMNUa7npRTXUlTRYWd6Ef9W2Rwk04aIRjWoslhLZrcGZpbmqBdCETsdLjO\nGmqalew6v2ioVygBJ0gAOtoyFygUXoCNHtjjQqEkVSgZ3MrlpYdrsfKKQVCPxjtkCEBFHRjqSgHN\nH7Bc3RAgVKNmTmdmTmfFfFO064m4Mdgf8qUyMqBJXnkdix6dhz3v97oOaZohBCktkk5pkfTu4Jwd\no5tDdiZYXxxqmjXceUHRUC9TiBskEMwRLOsIJWuY5ouw0AMbCcjxyaQKI4NbuTz1q3nYsr4RH/r/\nth5nTwZy8EZBwA7bdqR1jNuvtFSjkaGziq4vMDpZvE7NnK6UJoxvjnU+HjOGBkK6DGhS5Ukh0idA\nlAyC0RCyyeM/Q5JOXkYNZTNqaNeeYNuu0W1BJxuoKw41zk4cWFP0axcrhhMk4KojlKwrWF6AcAFw\ngAgBiKBdaB8Z3sQFwEfWxy9dCPA3Lcc+Nrq/iwKEHPRdOj4Z3E4VhQ6KABgCIz0qA3XxnrMyt9wc\nL/Ymg77a1FqX6ioXjAkQKkCIEKUlQAggBIEQhAhOSuscZGQbBCdk3BL80L6HPca5zor55tiBx+LG\n4EBQT2dlQJOqBxEK7EQH2q5Zgq3/43U10uknqwRzWSW4Z29g1p7RbX6n4GsoDjSFnFwtFZxRcEaE\noNFcam5O9c8FBCGlPpyEQJCRJQU5eJ8SgIzsRwBR2peU1kvbSs8hEIoAcbmgRRe0yAUtuoIVg1Z+\nM1yk4SINBxnwSZ4OS6o6Mri9GQODMRLEgqNhLB7tP9PhiuZyVXWEoo0Mb6EBgivUtRlxLIU6NiO2\nxQW1Wf/efvHgo2Gl/ameRV9555OaUiwy6jiMuJxR12XUcRlxXRmuJKnkAGZsmIHOi7yuQ5JGFRS/\n2aHM3Atg72EPxPDsZL8WEZwE3LwRsnPhgJsP+V0zXJ8ZXFLQ9XMZcTVKuE7BdQKQ0WBXCnmsGCgW\ntoIjDRcZOEiPDIsiT/FOU1UT3PyNub8r17GFIKQ00bmickHZyJAWB8OYQhxLIY4VDqZe0RUz51ML\nOUPN5Qwtl9cUyz7SMV9+6Ltrcw9snJd5kCzgF2jPRG86X/ZikqRjSCC+pxF9N7iglIHLAVel04og\nVIy0+uUA9AA44jApPtfUQ042FHTyYb9bCDemBpYWdH3ZaLBjhOsEQuGg1tjWO8Myt0MOZDwtVE1w\nm1u3/f5yHZsQCJ9SyBtaNudTC+ZkDG3Bi3bp31YIsu3//Pi6+htW/oBqatV8A+KOS6y+lOZriRe9\nrkU6PRThyzG4hSHUtNZjYL/X9UhSJRodGmVAxyAAvBFe8KbB6RXusFK4y4UNtxD2u2aoJptYSMo+\nc4I8izsVqia4zYjt2+d1DRPBi446um7uH2ze9vc/XrH423991EEmKw1VmHjlbV+7bvmvP/1H/4xa\nGd6kKaHCTvSg6fJ6DPzI61okqVo5VHFHh0Y5uDGK58v/yo/ImROmgEdjVUx/3LIPC8Wddz++NvP6\ngYBX9ZwULsgLF/7T+wv7B3xelyKdHnZi/pM21JjXdUiSJFUqGdzKhFvOYcGNm7a+9dbvXOlVPScj\ndHZbp7l/sPmFNf/0/nx7n9/reqTpbxixAy6YYUI3vK5FkiSpEpU1uBFC1hFCthNCdhFCPnOEx2sJ\nIQ8RQl4jhGwlhNxSznqm0vjgBgDJF3aevf+7D8/2op6TEbtoYRcAmJ1DTS9c9Pn353b3Vl142/Nv\n9y/IbN4X9LoO6cRwMFeBnRxA3Ryva5EkSapEZQtuhBAG4FsA1gFYBODdhJCF43b7OIBXhRDLAFwC\n4D8JIVVz3d2xiCMENwDY9aV7r3XSeTbV9ZyM+utW9IISAQDF7kTjixd//gO5Xd1V1RISPntWYsPq\n2z/xytu+flnhwKDudT3S8WmwE4OoXeN1HZIkSZWonC1uqwHsFkJ0CCFsAPcCuHHcPj0AwiPrYQBD\nQohpMXI0t903BbfAmS3tTq5obP3InRd4UdNEabVhW2+M9Y3eL3YPN7x48Rc/kN3RVTXhre6acwYi\nq+e/3nf/ixc9c+bffnLLB799vp3MVdWXg/Sr7aFdX/7fRb33vdBo9gxrXtdTbpuw9CEbarxqumBL\nkiRNoXIGtxYAB8bc7xzZNtZdABYTQroBbALwyaMdjDtuVQ1VKyxHpX6tEDizpX1029zPve3JKzM/\n+/rcf3zbq17WNhGBM5q6Rtf9s+sPrHrki/foDVHLy5omauF/3fIUUZjD80V/Zsu+FmsgVVXhJ7x8\nTsbsSoRevenfb3uy+dbPvnbzN6pykFo7kVU6vvmnuRuv/eqVXfc81Xq0/bIIJAgETyJaP5X1TcQ9\nn9u1ZGB/oao77dzzuV1LXIdX1efqWHf/nx3L8mmH2Vb1vYd82mF7Xk6HAYDz6v+KUsy79CPz19/i\ndR2ni3K2PJzI/8bPAXhNCHEJIWQugEcJIUuFEJnxO2689qtXqRHDBICatWd3zPzwlR2TW+7kUmKB\nzJK7P3af1Z/SBx5+rb3++pXtDTeu6iWUInT2rKzX9Z2o8PI5XRAgWl04M+O2K7eEzppZNbWPiqyc\nl667evmLhQODNfO+/M5nAvOb817XNFFL7vroi/6Ztem9//n7dTWXnlV1Y5zZyZzyxt/ffe7Qo5vP\nLvYM1wcXtvbjfeg88t4EFLyQhxGPIdk/tZUem2W69N/etmntyw8Onr93U+b5L/7pnEe8rulk/P4b\n++bd/x8dNzz3q74V39mx5seUVl32wYbf9K186Q8DSwtpJ3Dbtxbef8FNDT1e13SiXEeQz1++8UOf\n+p8lP3vgOweWdWzJts1bEd5z27cXro836VXzxfjh73e2bXpsqC09YAV6dudneV3P6YKIUx9r9sgH\nJuQ8AF8WQqwbuf9ZAFwI8bUx+zwA4KtCiOdG7j8O4DNCiI3jjiWuFr/5SlkKLZNif0rV6yNHnFWh\nmqRe3hP2tdaY1dbKNl6+o98HLogxp6HgdS2nIrF+Wyx+4cJhr+s4FYOPba5Rgj4net4ZR5xNRIGt\nLcHW25fhtf/QYVXMiJ65pK38581bLuvbW6gPxpTsrCWh7o98Z+FL1RZ6inmX/vXsZz+a6rdqFZ1Y\n7/2X+b9+66cOTbZeDTIJW3l//ZOf5W7prNGii6KvLlwT7XjvV+dvroafh21xcpP+2Bc1HzWZRuxC\n2g2pOi3+PHHp13e+mIqaWVdZdX1dRX1pOZ4f/N32c/5wx/7rhRCe/AAIIUK8G5OSE8gv8CWv3seJ\nKGeL20YA8wkhbQC6AbwTwLvH7bMdwFoAzxFCGgAsANCOaWA6hDYAiKyYm/a6hslgtNVXTAA4FdUe\n2gCgdu3ZQ8d8HEPzFDjpSgptABCIqk61trCNddffbl+d6rdq284O7njH5+c8vebtjVXTUjXqhfv7\nm0dDGwDs3ZSZ984vzN1QDaENAFSNCkIhLJP7YMIHANwV7Ob4k7c7Nle/8Ifl3/O6xom69RtnvvKH\nO/Zf73Udp4OyBTchhEMI+TiAhwEwAD8UQmwjhNw28vidAP4vgB8RQjahdL3d7UKIRLlqkiSp8s3E\nvotVOINe1zEdde/KGQe25Ro/86ul36+mU4vjbX06MWN0PRhTkv/0++U/XXRhrKq+1FBGHJeLgzPs\nuI5QXEco595Yt37FNXUDXtYmVbay9q4TQjwI4MFx2+4csz4IQCZ0SZIAABQuc6DGz8SOe7yuZTqq\nm+UvfO251b/1uo5Ttfe1zEwACNepQ19+cMVP564IV92ZAcaI69qHghsABOPq8Md/sPgZr2qSqkNV\nDYsgSdL0VoNEGwXPGyhUXSeYaqBqtOq7MHIu0LsnPyPWpPX/86MrfzpzcTDndU0ngyrEHb/tXV+c\n86dwrTYtLrORykcGN0mSKsYc7LmMgcvTpNJRbXkiUROq1Ya/+uTKnzXOMaq2sxFTyGFjls5bGX79\n+k/O2uNVPVL1kHOVSpJUIQSxodW2oeNPXlciVS7H4vTrG1b/tJpDGwBQdqjFTfXR4id+uPghL+uR\nqodscZMkqSLEMNxCIJwwMrKDknRU0+XCfTbmVOkVH2x5rO3skLw8QDohMrhJklQRFmDHlQSQp0ml\n0wJTS6dK62b5um69Y8HLXtcjVQ95qlSSpAogYEOrbUWnPF0knRYYIy6hEB/+5pl/YEr1dxqRpo4M\nbpIkeS6MTJ0AoXEkqnZsMUmaCKZSd8XVtc+vvqG+z+tapOoiT5VKkuS5xdh6jQAdrI5x7yXp1NW0\n6EN/e/dZT3ldh1R9ZHCTJMlzNrTaGTjwG6/rkKSp8rG7Fj0eqS/PmG2aa6lBJxcMuPmg3zWDOi8G\nNW4bBCjbdyMByNO9U6Rqgttj26+9vVzHJoCgxHUYdWxGHEcpLW3Dn9+qsWJBV8y8TzHzPi2fN9R8\ngVGXl6sWSTrdGMhFOKheh4H9XtciSVOleX4gP5H9qXBp0MkHAk4uaLhm0MfNYENqcAklXKOEawyl\nJQHXCEA4qMUFtTjIyJLaAbvQUaa3I02hqglu9rD+wzIenoLCBwoDFAYI/DXR/jOT2fgqVzDF5Yrq\nCqa6QlFdwRRKOGfEtRlxbEZceyTw2Qp1bL8v/4amFPM6K+Z9aiHvUwsFQ83lFea8aZRsSZKAZXjt\nOhfKEIWQX4ik6U0IKMJlinAUhTuKIhxFEa6iCEfVXcvvd82gjxeDNdnEwlIQExolXKPgGoFQBIg9\nEsIsV1CLE2oZlrkFHFm4Y24cRQYOhin/lbpkql/wdFQ1wQ02hqby5Yay9RuO8hDhlOmcMsNmmgEK\nP0gp8NVE+85M56PnOFwphTzOVFcwxRWK+v/au/PwqMq7feD395yZ7IQkBAIEMIKAoCIiggsILiho\nFa1t3Vq72Gpbbf317WKttlb7ttUu1vpq3bW2tdq6IVaRxR03CCL7FiCQBAiQBbJnZs7390cGDGmA\nmZM58+SE+3NdXMzynMwdh0xun3POcwSqIuoIHMeK/i3iRCyoI3LAY44lGrH233aclJTWDZYVCdkS\nCdtWJGxJJGRbkbaZQSsctq1wOGiFWnun1+7hbCD5TQgp+QOwnWeTUreTGW7I6NtSVdAr3NDH1kjQ\nUieQ27DnGIFaACyBtv0RWNh3G9Hb0u52dCzaTghUBRxAHIU4+247KmEHVoujbaUss6V5SYdC1ihQ\ntRABwHmAZBOR6QDuBWADeExV7+7w/EwAdwJwon9+rKpvxrJtvPxT3LoPhYNmOGhGGAcsFFpVX/Dh\nQTcSCaggCLEDEUEAgiA6+xsHPtand+WwpuaMUQ7EUrUsRy1bYVmOirX/b7VsB5YdcQLBoNXanGo3\nN6QGmhtzMmsW56RX78zN3F0dsCL8SaduJwUt6WEEevXDTl7qh4wRdSS3dU9Ofmt1/8F7tk0MSDgr\nIHPE800AACAASURBVJEsgQbCatdH1G5USEQhjqo4maGmdQDC0HZ/DrwfOuA5RRjO/nHadqCZgoeF\n+YOI2ADuB3AugAoAi0VktqquaTdsgaq+HB1/AoCXABwT47ZxYXFLls9+uONSVVfwbsyDBYHWYFqf\n1kBav5S8yvE79gycuqV6aGbYCaYFrdamFLulMc1uauidVbM4J71mV17G7iruwiWTJmDxzFak1AQQ\niftng8iNgBMK9G2p6psXqu0/YO/Ok4MSzrIlnKWwwmG160MI1Kc2hhYghB0IoTYl2snoiDYBQImq\nlgKAiDwLYCaA/eVLVRvajc/CZ4uJH3bbeLG49SSKMFpRiVZUVjUWrNj/+GeFrm9aXvP4yj2FZ23a\nPSJHYdlBq7UpzW6qO3XYO49wVo6SrRUpffKx+z3TOajnO7v8va+lWa35NiKZCgm1OsHqkAbrMxqa\nF6AVlXCcJhsOUuHJiZ6UDCM9O8auEEBZu/vlACZ2HCQilwD4LYABAM6LZ9t4sLj1bIIgchFAv775\n2ye0RNIy60LZGa2R1AzbCremWg17UgPNDblZ1YsscXhsHBmgDjxcooBon425Re8cU1M6NSDhloCE\ns1KsUB9LndTGzLRzMuzmYoSwA63YBST/iH5KkEvwtpvNHnkeRQs+RtEhhsS0T1tVZwGYJSKTAfxd\nRI51k+dwWNz8y4J1wPFxKQggr2/+9gnNkfTM1khqZmskNd22wq2pdnNjRO2GPr12fdA7rWZXXubu\n3amBllbT3wBRAOG6auRNGIKyZaazUM+2JXPw5i2Zgzfvu58Vqs/s21rVv6i67PTm9JTTAxnhLBtO\nWljtxrAG6kMaqM9ubHivbTYOLSazk7eu+wJKr/sCSvfdl7GY0mFIBYDB7e4PRtvMWadU9T0RCQDI\ni46LedtYsLh5RRCEjfR2S4ykHnAiAhDIz90xvO2EA7EctaInG1i2qlgOLEvVshRiO2pZ2v5kBFh2\n20uoY4kT2fd30G5piqjdmN9rZ7Sg7dqVGmjlvD91W2sx6p2h2PRF0znoyFMfzGqoD2Zt3Jx51P4T\nY1IircG+rVX9cltr+w+o23lyKMv+QkAimQ4krJAItO0sUIVEzwqFo5CIqjiIPr7vBIasUOMGdDyB\nQRHq5LEwHITgoNnNcdCUFMUAhotIEYBtAC4HcGX7ASIyDMAmVVURGQcAqlolInsOt228WNxiIUiB\njbalP/YVMQsZ+Tk7RoU1EIzsW/6j3ZpvAMSWSMiyIqGAhEOWRMKWOI7sX/7DiUDhpKY2r7ckErbF\nCVnWvkWA25b9sK1wKNC23EcoYIXDATsUClqhcNAOhSyJOMIdTORze5C9IwI7MwLLtuHwGEsyqtVO\nCVWkD6ioSB9QsbL3qCVA2xmnvUN12UENB+3oumu2EwnYGgnY6gRsjQRtOAGr7XYgumTIsMaUtFE4\nxJIhArUg+2/b0XXanHYL5rb9rVZrVmvjyg5LgzRAuSZIsqhqWERuBDAXbUt6PK6qa0Tk+ujzDwO4\nDMA1IhICUA/gikNt25U8/iluWV07mO8wrD45lcdGNBCIOIFgWO3gZ4vu2kEB9LOFdqML71rhMASh\nXml7l6UEWhtT7JamtGBTY1qgqTE9paExxW4NsVgRHVoEgZCFSFMNcvvno6rCdB6ijlQsrU3pvSeu\njXIR/wk3qkiPNKdlRaJXRog0Z6VFWjLz66tHN6WmnrJvId62vzWokEj7qyK0K3kroovwtpW8MBrA\n4/a6TFXnAJjT4bGH293+HYDfxbptV/imuOX23nWCh19eRTScnb7n06Dd0pgaaGlMDTQ1pQebGjNS\nGhqDdojT10QeCSCydzsGTMlH1T9NZyEyRgRNgfTmpkB6Mz5bSgLIwcf/NVQdyYg0pWeGGzMzIk1Z\naZGW6BUXakY1paZOtNtKXrDtElj7S14IEC8XjlMuDJwcvilupw577zHTGYgo8cpRWDwIFRNM5yDy\nCxVLGwKZjQ2BzEYAu/Y/kYP/WgRe1JHMSGNGerg5Qzxf8Hfpdz1+AYKPihsR9Uz16FURRqCX6RxE\nPZGKpfWBrIb6QFbD4UeTH1imAxDRkW0veu1yYKW1ICXVdBYiou6OxY2IjFJYjo1IfS1yBprOQkTU\n3bG4eaz63dW5pjMQdXcBhPdWomCy6RxERN0di5vHVn77oQudcIQLgxAdwhYc9TGPcyMiOjwWNw9F\nmluthrUVw0pu/9fxprMQdWd7eYICEVFMWNw81FiyIwMKbH3w9bPDextt03nc2HDnv0crrz9PHmtA\nZg0AuxHpWaazEBF1ZyxuHmrcVJkJAKGahpy1P/rbeNN53Kh+e9XRy66690zTOainE9iI1NUip9B0\nEiKi7ozFzUPNW3Zl7ru97el3z2yuqPbdcgcZRxdUbf/X+2et+Z+/nmQ6ixtOa0jqVpVlHn4kmRZA\neO8u9D3ddA4iou6Mxc1Dzdtr9heGSGNLxurvP+a7X0qZowqrAKD0z/+5aNMfXh5uOk+8rJSgrrzu\nwWkrv/3wBKc1xJNEurGNGPoBj3MjIjo0FjcPte6oPeB4nZ2vFJ9Wt3yLr47h6T1uaDUAwFFZ/7On\nv7jtmfd8tytryLfPKy57eN6Md4bd8K3t/3rfd2uFOeGIbH1obtGeJRuze/LxhnuRvS0Cu5fXF+Uh\nIvIz3xQ3P/7Caq3am2llpDYBQCA7va7/F057r+Lpd4eZzhWPnFNH1MBquzBxakHO7tqPNhT47b0o\n/MrU8oxhBVuby6sGrP/5M9MaSnakm84UDytgqwRs/fD0n90wL+vqn6z67iOnmM7kVs37a3NW3fjY\n+MrZiws6PteM9HoAkTr0yjMQLS4L/7VjYPX2lhTTObpi0eyd//Ue+EllaVParq1NaaZzdEXj3rAv\nT1rrKNTqyE0nfnCF6RxHCt9cq7Rm4drcvDNH15jOEY+0Qfm1p75z50NbH5w3uteYIbuKbvrcRtOZ\n4mVnpDrZJxat7T1xxOa8M0dtG3jl5ArTmdwY/O3zF1Y8+eaEYbd94e3MY/o3mc4Tr8HfPHeLnZn6\nt9U3PnZZ1ujBVabzxEsdByV3Pje67LEFk1sqqvtbKYHZBRefUtlxnAWnuREZOdmoqzaRMxYv31N6\nzN9u2fCl8Rf2/eiWF8e+aTqPG9XbW1L+dM3KqwYck1H+h0UTn7Ms/x1F8Mmc3QNe+fOWSQDw7b+M\nem3M2X1893Nx61mLL5t2beHiOQ+WnzbmrLx137rv2CWOo/Db+7F49q7+pcvrR5rOcaQQ1e6/Y0JE\ndIa+cIfpHEeqUHV9IJiXFTadoyvUcdBcXpWWPqRvs+ksXVG3fEtWrzFH1ZvO0RXVC9fkWikBJ2fC\n8D3tH7cQsU/E8lvG4tM/pKK1W75P//7fTaPmPVZ+Rk6/lJphJ2dvvf6BUYv99ksWAO758opJ7zy9\n/ZxAirRe+6eRz17w3SGbTWeK14PfWX3K6w+VXwAA/Yelb/3irUPfOPfrhVtN54rHt0cs/Or2ksYi\nKNCrT7A6Oz+4Z/IVA4qv/OWw1aazxeu+r6887Y2/bjtPVY38QIiI6qdISE+Qsbjd1PcRC9/MuJE5\nfi9tACCWBb+XNgDwe2kDgLxJozqdOc9BbaGNSFN3LW0A8KXbhq750m1D15jO0RW1lS0pH71Uefqg\nUZkbv/mnka+fdH7+btOZ3Nhe0pi/7/agYzPL/VbaACCzd6AB0bmTuqpQXjDVCn3ptqN9+e/r+08e\n/+Ebf912nukcRwIWNyLqFkZi3VkKqTWdo6eb+0j5sC/dNvTlz9989Do/zhbus7usuS8AHHt6zrKf\nzRq7wHQeNzJzAo3t73/+5qL5dsDq/rvByCgWNyLqFsII5gzEttdM5+jpvnjr0DV+Lmz71GxvzR9y\nfNaGO+efPNuvZadXXrBh3+3CkRmbLvr+Ub47DpqSzzdnlRJRz2UhEggjkJ2Hat/t7vKbnlDaqiqa\nU3v1Cdb++q3xz6Vm2P46zb2d7PyU/cXtK78ZPt9kFvIPFjciMi637fi2hlS0tpjOQt1f495w4M4F\nJz+TnZ8SMp2lK3L6txW3ERN7rzjt8wU7TOchf+CuUiIybgTWn6UAj2+jmAweldVw+FHdX97AtAbL\nRuTaP4305bIyZAZn3IjIuDACOQXY+a7pHETJ1HdIWuNJ5+UvOva0HP5PC8WMxY2IjLIRDoQR6NUH\nVTy+jY4oQ47P2vut+459z3QO8hfuKiUio3JQO8hGpD4FoVbTWYiSKW9AKv/NU9xY3IjIqBHYMBU8\nvo2IKCbcVUpERoUQzClAJY9vIyKKAYsbERljIxyMwObxbUREMWJxIyJjclEz2EakPoiwr9fjIiJK\nFh7jRkTGDEfJFPD4NiKimHHGjYiMCSGY0x873jadg4jIL1jciMiIAEIpEdhZeaguN52FiMgvWNyI\nyIhc1A62Ea7j8W1ERLHjMW5EZMQxKDkTPL6NiCgunHEjIiMUEIFGTOcgIvITFjciMqIcg5dHYKWb\nzkFE5CcsbkRkRAtSah3YaaZzEBH5CYsbERnRhPQahzNuRERxYXEjIiMakVHrwEp1IGI6CxGRX7C4\nEZERDuyIQFsbkZFtOgsRkV+wuBGRMRYizQ3IzDWdg4joUERkuoisFZENInJzJ88fKyIfikiziPyw\nw3OlIrJcRJaKyKKuZuE6bkRkjA2nuRlpuQBKTWchIuqMiNgA7gdwLoAKAItFZLaqrmk3rArA9wBc\n0smXUABTVbU6EXk440ZExliINNUiZ6zpHEREhzABQImqlqpqCMCzAGa2H6Cqu1S1GMDBrgSTsGN5\nOeNGRMZsQdHSQSg7w3QOIvK/bb0LpibmK1V2fKAQQFm7++UAJsbxBRXAAhGJAHhYVR/tSjoWNyIy\nphlpNVzLjYgSobjoxLfdbDf3kfKiZQuqig4xRF0F+swZqrpdRPoCmC8ia1X1PbdfjMWNiIxp5Fpu\nRGTY+dcNKj3/ukGl++7PlHlTOgypADC43f3BaJt1i4mqbo/+vUtEXkLbrlfXxY3HuBGRMc1Iq1eI\nHUIgxXQWIqKDKAYwXESKRCQFwOUAZh9k7AHHsolIhoj0it7OBHAegBVdCcMZN4/VrdyaZWelhTOK\n+jWbzkLU/QgsOM31yMrJRe1O02mIiDpS1bCI3AhgLgAbwOOqukZEro8+/7CI9AewGEA2AEdEbgIw\nGkA/AC9K2zrjAQBPq+q8ruRhcfNY7ccb8na9uuSYcS/+5E3TWdwK1TYEgjmZYdM5qGeyEGluQnou\nixsRdVeqOgfAnA6PPdzu9g4cuDt1n3oACT1z3tNdpYdbsC46Zmp0UbqVIvK2l3lMaCrdmb3z1SWn\n1q8pzzSdxa1Pr7znnEhzK3erkydsOE3NSMsxnYOIyA88+2XcbsG66WibLrxSREZ1GJMD4AEAF6nq\n8QC+4FUeU5rLq3ppazi45od/nWQ6i1tNW3b3Lb7g1zPUcUxHcWXv0k299hSX8LJK3ZSFSPNeZJ9g\nOgcRkR94OYty2AXrAFwF4AVVLQcAVd3tYR4jWiprswGgav6yU/Ys2ejL8pDaP6em+q2V41d+88HT\nTGdxI3PUoIYlF9911crrH5rgtIZ8eUFzv+aOxUYcUxyBxSVBiIhi4GVx62zBusIOY4YDyBORt0Sk\nWES+4mEeI0K79vYCACstpXnDL5491XQeN9IG96kFgMpZH0+onLWowHSeeNlpKU7fC09eWvbI/Bkf\nT/3FJX7c7Vu/qizr3dE3fXnh2B9evvmPs4ebzuOWOg4qZy0qqH539f7rkza1reXmqyVBqre3pFRV\nNKeaztEVu8v8nR8AWhojvvtZ7okcR3HzGR93dqkn8oCXJyfEsmBdEMA4AOcAyADwoYh8pKobOg5c\ndN6dM4I5GU0A0OfcMaVDrjuvNJFhvdJn2onr+l4wbk1qYV5D4TVTt5rO40bWyMKq/l86/e1+nzt5\nY8ElE/5rSWk/GH7nFUtr3ls9Ysj15xfbaSm+2+ebfdLQupP+/cNZxTP+9yo7I9WXJ4rUr6vIWHnd\nQ+fUvL927NH/73Ov5J05ugYAWpHSoJCg6XyxqljXkPGLaUuuHj0pZ+0P/znG9VpMpv3hquXT03sF\nmm9/bdxc01ncuvPCTy6wA+J8+y+j3h44PLPRdJ54OY7iD1csnxoJqzX+wr4lY6fl7ew7JN03KxDs\nW7h2z87WrLUf7DnRdJ4jhZfFLZYF68oA7FbVJgBNIvIugBMB/FdxmzDvF3M6PuYHI39zdZfWa+kO\nhv700rViWWtN5+iKtAG5racX//6fgay0iOksbvU6fkj9aR/d9VRaYV6L6SxuZI0sbDz1nV+90lS2\ne154T+P+opaJhnwLTpPJbLGqrWxJeewH6yYfdULWlkGjMn17aMeG4j3Zaz+oHdMrL1i7/M2q4jFn\n96kyncmN0mV1w+prwjl3Xbas990fTPh3elbAVz/fliVY/mb1mLqqUO6S13ZPmHZt4YLrHxhVbDpX\nrNovXHvXZZ82fPjizjMNRzoieFnc9i9YB2Ab2hasu7LDmJcB3B89kSEVbdf+usfDTOSCWD1jb4Sf\nS9s+fi1t7aUPzm/BYOz/Po7FujPCsOtNZopVTkFqq59nqPb5152bJpx6ab+FNzxy3Hu98oK+nMFt\nqg/bDbXh3lm5gdof/nPMK34rbftk5gTq6qpCuamZVtM1dw9fajqPWz99YexbM2Uei1sSeFbcYlmw\nTlXXisjrAJYDcAA8qqqrvcpERN1PGIHMXNR8YjrHkeSqO4Z9PPSk7DrTObqiZPHe3sE0q+XH/zrx\n6aOOz/JF8e9Mr7zg3h0bmzDtm4Pe9mv5pOTydAHewy1YF73/BwB/8DIHEXVfEdhZmWjw5bGTfuX3\n0gYA2zY0Zl/3f6OeGTutj293WQNAdn5KXe9+Kbuv/tUxy01nIX/glROIyCCVCOzMbOzlVRMoLmd/\nbeCWYIoVy0lw3VpO/5S6C28c/GZP+F4oOVjciMiYLDTkCpxQKlp9f+weJVdPKTqTvtS/ZOx5fXaZ\nzkH+weJGRMZkor7ARsS3xycRddW46fksbRQXFjciMmYoNk8E0GA6BxGRX/SMdR6IyJcisDP7oGqR\n6RxERH7B4kZExkRgZ2ahnmeUEhHFiMWNiIwIIJTiwErNxt5q01mIiPyCxY2IjOiF+r42Io0W1HfX\njiUiMoXFjYiMyEBDgY0IT0wgIooDzyolIiMGo3ycxaVAiIjiwhk3IjIiAjurH3Z9YDoHEZGfsLgR\nkQGK6KWueEYpEVEcWNyIKOnS0ZQNQDPQxGPciIjiwOJGREmXhfp+vNQVEVH8eHICESXdcJSc5sDi\nbBsRUZw440ZESaeQgMAJm85BROQ3LG5ElHTbMHC9QmzTOYiI/IbFjYiSLgK7RSE8VIOIKE4sbkSU\ndBFYrZxxIyKKH4sbESWd0zbjxuJGRBQnFjciSrow7BZwVykRUdxY3Igo6SKwuauUiMgFFjciSrow\nAtxVSkTkAosbESVdtLhxVykRUZxY3Igo6cIIcFcpEZELLG5ElHRhBFoBWA6En0FERHHghyYRGSAA\nEAkhmGI6CRGRn7C4EZERAmVxIyKKE4sbERkh0HAYgVTTOYiI/ITFjYiMEGiExY2IKD4sbklQ/e7q\nXNMZiLqbaHHjrlIi6vZEZLqIrBWRDSJy80HG3Bd9fpmInBTPtvFgcUuCVd995IJIc6tv/1tve3bh\nwIaSHemmc1DPItBwBDZn3IioWxMRG8D9AKYDGA3gShEZ1WHMBQCOUdXhAK4D8GCs28bLt2XCL9Rx\n0LC24ugNtz0zxnQW1yKOLD7vjitD1fW+XTB10+9njWD57F4EGolwVykRdX8TAJSoaqmqhgA8C2Bm\nhzEXA3gKAFT1YwA5ItI/xm3jctDiJiJzROTornxxAho37UzXiGOXPf7G1PDeRl8uOJpz2sjqps07\nB3989u2XOa0hMZ3HjbTB+fULT/yf76275R/+LdAANt710siFJ/3w8p2vFPczncWtrQ/NLXr/lJ98\noW5bvRWB5ctdpe89u33gTWM/uOLV+7cONZ3FLcdROI6ajkE9xO3nLZlhOoOHCgGUtbtfHn0sljED\nY9g2LoeaQXkCwFwReQrA76JN0Ziqt1bm9Tnr+GqTGdyI1DUGBn3jnLm9Txm2I9zQYgeyMyKmM8Ur\nY2hBU95ZxxcP/ta5n8Ly5yTtwCsmbSt7aN6arNGDfPdvqL2tD8yZ0lxeNaDssQW7+100/g3Tedwo\nve/VSQ1rKoaVFVc2FV7c15ezuHMfKR9Xuqx+5Kv3b0258MYhm0znceOFuzYfW1K8d+AtL45903QW\nt/7zf1uHrniruuj7Txz3bmZOMGw6jxvvPbt94LI3qgePPbdP2ckX5lemZwV89zti4b92DPx0ftUE\n0zk2YuhUj750rP+Hk5SJjYN+aKrqcyIyB8AvABSLyN/xWXhV1XuSEXAfP5Y2AMg+aWjdCY9/9yPT\nObpq4pt3vGo6Q1edsuD2/1gB29dTDIOvm/bejhc+GnPUjTOWmc7iVtH3L1xY/vgbzUdNGjwoDbU1\npvO4cdH3j1pcVx3KOvuagcWms7jhOIo5fymb0veotMqqiubUPoVpLaYzuVFSvGfAR7N2Tj7qhKzK\nq+44ZpXpPG7s2RVKm/9YxfTlb1SXnf7FgidM53Fj0uX9t81/vGKR6fI2H9PedrPd1kfmFVUtWF50\niCEVAAa3uz8YbTNnhxozKDomGMO2cRHVg/8eE5FUADcDuBpt+2Wdfc+p6h1deeF4iIjO0BeS9npE\n5L2TseQnw7HhyRzs2WU6y5Fm9cKa3F1bmjOmXD2gwnSWrrjlzEUXDx6VteO7D49eZDqLW8Wv7ur3\nq88t/c73njjuyXO/XrjVdJ6umCnzbldVI4fTJLInzJHLDvg+RCQAYB2AcwBsA7AIwJWquqbdmAsA\n3KiqF4jIqQDuVdVTY9k2XgedcROR6QDuAfAKgJNUtdHtixARtWchEnBgpfVCnS9n0v1u9KTcGkyC\nL2c725twcb81l/6oaIPpHF1RODKzbshxWRv8Xtp6MlUNi8iNAOYCsAE8rqprROT66PMPq+prInKB\niJQAaADw9UNt25U8hzq+5FYAX1RVX04/E1H3lYX6PAtOkw3Hd8fzUPfh99IGAAVD05u+evfwBaZz\n0KGp6hwAczo89nCH+zfGum1XHKq4namH2o9KRORSBhr72ohwFp+OeJYlGH9h352mc5B/HOrkBJY2\nIvLE0Sg9BQCLGxFRnPy5tgMR+VoEdkYeqn15RiYRkUksbkSUdBHYGZlo2G06BxGR37C4EVFSCRxx\nYKX3Qh2LGxFRnFjciCipgginCtQJImz0aixERH7E4kZESRVAKBUAlwEhInKBxY2IkirQNuPG4kZE\n5AKLGxElVQCRVIH68oLgRESmsbgRUVLZnHEjInKNxY2IksrmjBsRkWssbkSUVNHixhk3IiIXWNyI\nKKlsOJxxIyJy6VAXmSciSrhCVIwElwMhInKFM25ElFQKsXuhbp3pHEREfsTiRkRJpYBtweFVE4iI\nXGBxI6IkE+HJCURE7rC4EVFSKWCxuBERucPiRkRJJmLBYXEjInKBxY2Iko0zbkRELrG4EVFSKWfc\niIhcY3EjomTjjBsRkUssbkSUVApwxo2IyCUWNyJKMrFY3IiI3GFxI6Jk44wbEZFLLG5ElFQK4TFu\nREQusbgRUbJxxo2IyCUWNyJKKgV4jBsRkUssbkSUZFzHjYjILRY3Iko2y0aExY2IyAUWNyJKKl45\ngYjIPU+Lm4hMF5G1IrJBRG4+xLhTRCQsIp/3Mo8pkeZWFmSiz/AYNyIilzwrFCJiA7gfwHQAowFc\nKSKjDjLubgCvAxCv8pi0+obHJjitoR75vRHFRwGeVUpE5JqXM0ETAJSoaqmqhgA8C2BmJ+O+B+B5\nALs8zGLUnuKSorU//vtJpnN0xaobHxu/6Lw7Z4T3Ntqms7i1/rZ/Hv/RlJ9f1FS2O9V0Fre2PjS3\n6KPJt86senNFH9NZ3BCopQr8fOqiz330UmV/03ncWjR7Z8HNZyy65N1ntheazuJWxbqGjJ9OXjTz\n+d9uGmk6i1vV21tSfn5O8YV//fH6E01nOdLdddmnZ5nOcKTwsrgVAihrd788+th+IlKItjL3YPQh\nPdgXq35nVV6iAyZL7hnHbkwrzK03ncOt5orq1K0PzZ1RNX/ZhE2/m/Vfs6Z+UXrvf2bUvLt6XMnt\n/xpnOotbJb96/vyahWvHlt732ljTWdyw4dhOawQr36kZ99xvNk8yncet2fduHb/2g9oT/3n7xnNN\nZ3Hr77dumLhmYe3Yl+/Zcp7pLG499+tNY5a/WT3+lfu2XNBUH/bt/1Q+fOOa8Sveqvbt77j3n9sx\n4MMXd55pOseRIuDh1z5oCWvnXgA/VVUVEcEhdpVueWDOmC0PzAEA9Dl3TOmQ684rTUjKJDjuL9ct\nNp2hK9IK81oKLj7l/caNO/od9b0L1pvO49aAKye/u+fjDUMHfmXKOtNZ3Br45TM/qnzp47GDvnbW\nStNZ3LARCYogMmhUZun51w3y7c/FtGsLP91d1tx36pcH+PZ7OPuagavL1zQMHDc9f5XpLG5d/P+O\nWrXy7ZoRR4/ttTU9K+Db3e/v/GP75LyBqfUnnJVXbTpLPOY+Ul60bEFVkSqQOzClsmZba4HpTEcC\nUY2lX7n4wiKnAvilqk6P3r8FgKOqd7cbswmflbV8AI0AvqWqszt8LZ2hL9zhSVAiSpp0NGaPwtob\nJmDxb01nIeou7pix5PyfvzpurmX5+1DomTLvdlU18k0ksifMkcuMfR+x8HLGrRjAcBEpArANwOUA\nrmw/QFWH7rstIk8CeKVjaSOinsNGJMjrlBId6Ka/Hv+W30sbJY9nxU1VwyJyI4C5AGwAj6vqGhG5\nPvr8w169NhF1TzYiQUAd0zmIupOcgtRW0xnIP7yccYOqzgEwp8NjnRY2Vf26l1mIyDwLTkAA4P2R\negAAG0JJREFUFjciIpe4MCwRJY0Nh7tKiajHEJE8EZkvIutFZJ6I5Bxk3BMiUikiKzo8/ksRKReR\npdE/0w/3mixuRJQ0FpwgOONGRD3HTwHMV9URAN6I3u/Mk2i7IEFHCuAeVT0p+uf1w70gixsRJU3b\nrlIe40ZEPcbFAJ6K3n4KwCWdDVLV9wDUHORrxHVmCosbESWNxV2lRNSzFKhqZfR2JQA3a9l9T0SW\nicjjB9vV2p6nJycQEbXXtquUM25ElHjbdxVOdbPdntffzal7d/FBC5OIzAfQ2SX6bm1/J3oxgXgX\nx30QwJ3R278C8EcA1x5qAxY3IkoanlVKRF75dM3Et11teNRE4Cvt7j8mt7d/WlWnHWzT6AkH/VV1\nh4gMALAznpdW1f3jReQxAK8cbhvuKiWipBEod5USUU8yG8BXo7e/CmBWPBtHy94+lwJYcbCx+7C4\nEVHSDMS2Y7irlIh6kLsATBOR9QDOjt6HiAwUkVf3DRKRZwB8AGCEiJSJyL61a+8WkeUisgzAFAA/\nONwLclcpESWNQqxeqF9rOgcRUSKoajWAczt5fBuAC9vdv7LjmOjj18T7mpxxI6KkUcCy4IRN5yAi\n8isWNyJKIrEtOCHTKYiI/IrFjYiSRiGWjQiLGxGRSyxuRJQ03FVKRNQ1LG5ElETcVUpE1BUsbkSU\nNAqxAwi3ms5BRORXLG5ElDQKCaagtcF0DiIiv2JxI6KkcWAFU9HSaDoHEZFfsbgRUVJYiNgArBS0\ntpjOQkTkVyxuRJQUKWhNF2hITAchIvIxFjciSooUtGYIlGeUEhF1AYsbESVFEKEMLgVCRNQ1LG5E\nlBRBhDnjRkTURSxuRJQUAYQyhTNuRERdEjAdgIiODINRNhoQFjcioi7gjBsRJYXCCvZC3RrTOYiI\n/IzFjYiSwoEEgwhx8V0ioi5gcSOipFBYLG5ERF3E4kZESaGccSMi6jIWNyJKCl6nlIio61jciCgp\nFMLiRkTURSxuROQ5G+EgAAQQ5nIgRERdwOJGRJ5LRUsGLzBPRNR1LG5JsOqGR8cvu+a+M5xW//7e\nWnfLP8Z88vnfne3n72HzH2cPL/7cb6a1VNammM7i1vZ/vT+w+IJfn1fz4boc01nikdLuOqUfvVTZ\n/38v+mTa0rm7803ncmvZgqo+d8xYcn7xq7v6mc7iVmVpU9odM5acP+fBsqNNZ3GrcW/Y/vXMpec+\ne+fG0aazuNVQGwr88arlk5/80bqxprN0xX1fX3ma6QxHCt8Ut+p3V+eazuBGzftrc7b+5fULt/39\nnXO3//uDQtN53GiuqE7d/IeXL6586ePJJb96/jjTedwqufPfF+16dcnp62975iTTWdxa84MnL941\n55PTNt0962TTWeIRQChdoGEA+MdtJecs/s/u05/+eckU07ncev63m0/95PWqUx+9ae0FprO49dRP\n1k/85PWqU5+9Y+MM01nc+vvPNpy0aPauM57/7eaLm+rDtuk8brzx121F7z6z4+xZ92yZub2kMd10\nHjc+eL5ywBt/3Xae6RxHCt8Ut9xJx9aYzuBG7hnH1vaecMzKrOMGl+SfN7bSdB430grzWvKmHr8k\nY/iA0kHXnlNiOo9b+dNPWpJ+dL+ygksmbDadxa2CSyYsSS3M2zHgijN8ewWCSZf3X9rvqLTyM68a\nsMx0FrcmX9l/Zd7A1B2nXVqw1HQWt077fL8NfYekVZzyub6fmM7i1rRrC9f1H5a+ddz5fRanZwUi\npvO4MfGSfuUDR2RsPv7M3E8GHJPRZDqPG6dc3HdH0ZisdaZzHClEVU1nOCwR0Rn6wh2mcxCRO32w\nu2goNl9yMj6513QWIvLGTJl3u6oaOZxGRBTvaGJ6whQx9n3EwjczbkTkXwpxFN32c5CIyDdY3IjI\ncwpxADY3IqKuYnEjIs+xuBERJQaLGxF5jsWNiCgxWNyIyHMKUYWwuBERdRGLGxF5jjNuRESJweJG\nRJ5jcSMiSgwWNyLyHIsbEVFisLgRkeei67ixuBERdRGLGxF5jjNuRESJweJGRJ5TWCxuREQJwOJG\nRJ5zOONGRJQQLG5E5Dke40ZElBgsbkTkOe4qJaKeSETyRGS+iKwXkXkiktPJmDQR+VhEPhWR1SLy\n23i274jFjYg850AULG5E1PP8FMB8VR0B4I3o/QOoajOAs1R1LIAxAM4SkTNi3b4jFjci8hzPKiWi\nHupiAE9Fbz8F4JLOBqlqY/RmCgAbQE0827fH4kZEnmsrbgI1HYSIKLEKVLUyersSQEFng0TEEpFP\no2PeUtXV8WzfXqCLgYmIDsuCYwPK3kZE3lmFqa62W/ZyDta9cdBjy0RkPoD+nTx1a/s7qqoi0unn\nnKo6AMaKSG8Ac0Vkqqq+Hev27bG4EZHnUtGSKdAQ95USkWeew9vuNpwJyMx29//v9vbPquq0g20p\nIpUi0l9Vd4jIAAA7D/VKqrpHRF4FcDKAtwHEtT3AXaVElASpaMmy4LSazkFElGCzAXw1evurAGZ1\nHCAi+fvOFhWRdADTAHwa6/YdsbgRkedSEMoUKIsbEfU0dwGYJiLrAZwdvQ8RGRidWQOAgQDejB7j\n9jGAV1T1jUNtfyjcVUpEngsilGXBCZnOQUSUSKpaDeDcTh7fBuDC6O3lAMbFs/2hcMaNiDx3FLac\nINxVSkTUZSxuROQ5B1ZKNurWmM5BROR3LG5E5DkHVjCAcIPpHEREfsfiRkSeU0hKClrrTecgIvI7\nFjci8pwDKyUVLZxxIyLqIhY3IvKcQlJS0cIZNyKiLmJxIyJPCRxLIYE0NDcefjQRER0KixsReSoV\nLRkCDVm8VikRUZexuBGRp1LRksWrJhARJQaLGxF5KgWhTF6nlIgoMVjciMhTQYSyhJe7IiJKCM+L\nm4hMF5G1IrJBRG7u5PmrRWSZiCwXkfdFZIzXmYgoeQIIZVrcVUpElBCeFjcRsQHcD2A6gNEArhSR\nUR2GbQJwpqqOAfArAI94mYmIkmsgto3irlIiosTwesZtAoASVS1V1RCAZwHMbD9AVT9U1T3Rux8D\nGORxpqRbd8s/xqy64dHxpnN0xabfvTRi+dfuP10dx3QU1yr+8c6gT6++d3JzRXWq6SxuVc5aVPDp\nVX+avHfppl6ms8TKgRXMQe3yffeXzt2d/8erlk9evbAm12Surlj7YW3O769YfubyN6v6mM7i1vaS\nxvTfX75sykcvVfY3ncWt1uaIdc+XV0x65b4tw0xncSsSduT+b62a+OydG0ebztIVj/2/teNMZzhS\nBDz++oUAytrdLwcw8RDjrwXwWmdPVC9ck5s3aVRNArMlRfXCNbmb7p51CVQl57QROwq/PKXcdKZ4\nhfc22utvfeaLGo4E0o/K3zP8jitWmc7kxqrvPHJFpL45M5iT2XTcA98qNp3HjVU3PHJpy7aaAqep\nNTjupZvfNJ0nFgorJYjQ/jXcnvjh+vO2rqofvmNTU9/ffzTxRZPZ3Hr65yWnL3+j+pSNS/YOfWjD\npL+azuPGP28vGb/w35VTV7xVfcKplxbcbzqPG0/dvGHsO09vP+ejlyqbLrxxyO8sS0xHitur95cN\nm/9YxXTLhjP58v6lhSMzfbfe4cezdha88uetF5nOcaTwurjFvG6TiJwF4BsAzujs+dI//+fELfe9\nCgDoc+6Y0iHXnVeaiIBeyz19ZE3W6EEbI40tqfnnja00nccNKy3o9B4/bHXztuo+fWeM813x3Cdv\nynHL9iwuGdHnnBN8+z30OXfMil2vfpJS8PmJ601nicMBnwMnz8hftWdXa+4pn+u7xlSgrpo4s9/a\nTUvrjhk7rY8v/ycGAMZO61O6dG5V9Qln5a0wncWt8Rfkb/3wxcrtA4dnVpjO4taEi/tWvPzH0u29\nC1Jr/Fba5j5SXrRsQVWRE1HJzAnsaagN9zad6Ugg6uGamCJyKoBfqur06P1bADiqeneHcWMAvAhg\nuqqWdPJ1dIa+cIdnQYnIMxOw6IYCVL5ZiG2+LWpEdHgzZd7tqmpk2lNEFGdpYnrCW2Ls+4iF18e4\nFQMYLiJFIpIC4HIAs9sPEJEhaCttX+6stBGR7zkOLNt0CCKinsDTXaWqGhaRGwHMBWADeFxV14jI\n9dHnHwbwCwC5AB4UEQAIqeoEL3MRUfII1HFgeX1YBhHREcHzD1NVnQNgTofHHm53+5sAvul1DiIy\nRVUhLG5ERAnAKycQkaekbVcpixsRUQKwuBGRx7irlIgoUVjciMhTAjgNyDzGdA4iop6AxY2IPLUN\nA0uUnzVERAnBD1Mi8pRCwoB02zWRiIj8hMWNiDzlQCKccSMiSgx+mBKRpxRWGBB+1hARJQA/TInI\nUw6ssLK4ERElBD9MichTDiQMftYQESUEP0yJyFPKGTciooThhykRecqBxRk3IqIE4YcpEXmKx7gR\nESUOP0yJyFMOJAJ+1hARJQQ/TInIU5xxIyJKHH6YEpHHRE0nICLqKVjciMhTAYTTBBoxnYOIqCdg\ncSMiT9kIpwo0bDoHEVFPwOJGRJ6yEWFxIyJKEBY3IvJUtLhxVykRUQKwuBGRp2w4aZxxIyJKDBY3\nIvJUISpGCBwWNyLqcUQkT0Tmi8h6EZknIjmHGGuLyFIReaXdY78UkfLo40tFZPrhXpPFjYg8pZBA\nL9SvM52DiMgDPwUwX1VHAHgjev9gbgKwGkD7JZIUwD2qelL0z+uHe0EWNyLylEJsG5EW0zmIiDxw\nMYCnorefAnBJZ4NEZBCACwA8BkA6Ph3PCwbiDEhEFBeFBFjciMhzO3dPNfCqBapaGb1dCaDgIOP+\nBODHALI7ee57InINgGIAP1TV2kO9IIsbEXlKIYEAws2mcxBRD7dq3dvuNny5CCguOtizIjIfQP9O\nnrq1/R1VVZH/vlKMiHwOwE5VXSoiUzs8/SCAO6O3fwXgjwCuPVRaFjci8pRC7ADCnHEjom5qZmnb\nn30mTWn/rKpOO9iWIlIpIv1VdYeIDACws5NhpwO4WEQuAJAGIFtE/qaq16jqznZf6zEAr3Sy/QF4\njBsReUohgSBCLG5E1BPNBvDV6O2vApjVcYCq/kxVB6vq0QCuAPCmql4DANGyt8+lAFYc7gVZ3IjI\nU9FdpSxuRNQT3QVgmoisB3B29D5EZKCIvHqQbdrvTr1bRJaLyDIAUwD84HAvyF2lROQphdgpaOUx\nbkTU46hqNYBzO3l8G4ALO3n8HQDvtLt/TbyvyRk3IvKMhYgNwAogHDKdhYioJ2BxIyLPBBFOFWg4\nrkWKiIjooFjciMgzAYRSweuUEhElDItbEmz63Usj1t/6zxNM5+iK8r++NXjtj54aG65vtk1ncWv7\nv94fuPr7j5/cvL0mxXQWt3a99knfVd995JSGDdsyTGeJRaBtxi3S/rHVC2ty//Lt1RM2Ld3by1Su\nrtr8aV2vv3x79YSV71Tnmc7i1o5NjekP37hmfPGru/qZzuJWQ20o8Oj31578wfOVAw4/uvt64n/W\nnfTKfVuGmc7RFc/8cuNo0xmOFL45OaHmw3U5uaeNPORqwt1R3aqyzHU//ceVUCBzVGFN4ZenlJvO\nFK9wfbO94toHvgZHrZT+OQ1DfzRzg+lM8VLHwYpvPXhlpK4pCwBG33ftEtOZ3Fh5/UOXNpdXDWjZ\nXtNr3Es3v2k6z+EEEEkV4IAZt4dvWHN+6fL6kVtW1A28+/2J/3XqvB88+eN1k5ctqD5l5dvVm/+y\ndtLfTOdx49k7No5762/bz33/ucrdf6uc+oDpPG68+LvSUf/5v62fm/tIecvpXyi4y3QeN2bfu+WY\nl/+05WLLRmTy5f1/l1OQ2mo6U7wWv7Kr37N3bvyi6RxHCt/MuGWfdPRe0xncSOmb3Zpe1K8sdUDu\nzj5nnbDLdB43AllpkV7HD9kQzMuqyT6xqMZ0HjfEstB7/LB1dlZaQ97U4ypM53Er59QR6+3MtIb8\n88duMp0ldgcuJD7qjNyN6b3s+uOn5G00FKjLxpydtzEt024YeWpOieksbh0/Na8sNdNuHDEhe73p\nLG4NPyV7V2bvwN6h43qtM53FrROm5lX27peye+DwzC0p6Xbk8Ft0P6Mn51TnDUjdYTrHkUJU/+vq\nDN2OiOgMfeEO0zmOdE44IlbA7v7/YKjbyEP14KHY9IXxWPIn01moZ4qEHbEDFj+XuoGZMu92VTVy\nLlLbpaYWJqgnTDL2fcTCNzNuZB5LG8VLIQ6AbvsBSP7H0kZHGhY3IvIMixsRUWKxuBGRZxTiKITF\njYgoQVjciMgzDmfciIgSisWNiDzDXaVERInF4kZEnmnbVcriRkSUKCxuROSZthk3HuNGRJQoLG5E\n5BmFxV2lREQJxOJGRJ5xIBGwuBERJQyLGxF5hjNuRESJxeJGRJ5xuI4bEVFCsbgRkWeiy4Hwc4aI\nKEH4gUpEnnG4q5SIKKFY3IjIM9HlQMCrgBMRJQaLGxF5SAAoFMLPGiKiBOCHKRF5TR1Y/KwhIkoA\nfpgSkdeUM25ERInBD1Mi8hpn3IiIEoQfpkREREQ+weJGRERE5BMsbkREREQ+weJGRERE5BMsbkRE\nREQ+weJGRERE5BMsbkREREQ+weJGRERE5BMsbkREREQ+weJGRERE5BMsbkREREQ+weJGRERE5BMs\nbkREREQ+weJGRERE5BMsbkREREQ+4WlxE5HpIrJWRDaIyM0HGXNf9PllInKSl3moa7Y+Mq/IdAbi\n+9CdzH2kvMh0BuL7QOaISJ6IzBeR9SIyT0RyDjIuR0SeF5E1IrJaRE6NZ/v2PCtuImIDuB/AdACj\nAVwpIqM6jLkAwDGqOhzAdQAe9CoPdV3VguVFpjMQ34fuZNmCqiLTGYjvAxn1UwDzVXUEgDei9zvz\nZwCvqeooAGMArIlz+/28nHGbAKBEVUtVNQTgWQAzO4y5GMBTAKCqHwPIEZECDzMZsfXBuUdv+v2s\nEaZzdEXFP94Z1Lixsq/pHF1ROWtRwfpb/3lCpLnVt4cIVL21Mq9hw/aClsraFNNZ3Nq4ZG/2325Z\nP6ZsTX2m6Sxu7djUmP63W9aPadwbTjWdxa2G2lDg7z/bcMLSubvzTWdxKxJ25B+3bTh+z87WLNNZ\nuuLfv9507IInK4aYztEVs+/dcozpDIbs7zHRvy/pOEBEegOYrKpPAICqhlV1T6zbd+TlL7BCAGXt\n7pdHHzvcmEGdfbHaRRt6JzRdkuwpLsle/b3Hrl5389+v3P7cBwNM53GjeXtNysrrHrp67yebRvu1\ngDrhiKz4xv1XbPzNC59f9+O/+XaX/IpvPHBp3aelx6664dEzTGeJlY1wvUCdfffvv27V9BfuKr30\nL9evPsdkrq548DtrprxwV+mlJcV7ffnzAACP3rR24vO/3fz5P3991RdMZ3Hr6Z+XnPDcrzdftvbD\n2hOa6sO26TxuvP5QWdHTt5Vc/uC3V1+9vaQx3XQeN5bO3Z3/xP+su8p0DkMKVLUyersSQGeTT0cD\n2CUiT4rIJyLyqIhkxLH9AURVu5y60y8schmA6ar6rej9LwOYqKrfazfmFQB3qer70fsLAPxEVT/p\n8LW8CUlEREQJo6pi4nUT3RPafx8iMh9A/06G3QrgKVXNbTe2WlXzOmQbD+BDAKer6mIRuRfAXlX9\nhYjUHG77jgLuvqWYVAAY3O7+YLTNqB1qzKDoYwcw9Q+BiIiIuj8ve4KqTjvYcyJSKSL9VXWHiAwA\nsLOTYeUAylV1cfT+CwD2nbAZy/YH8HJXaTGA4SJSJCIpAC4HMLvDmNkArgGA6BkWte2mDImIiIi6\ns9kAvhq9/VUAszoOUNUdAMpEZN+hFecAWBXr9h15tqsUAERkBoB7AdgAHlfV34rI9QCgqg9Hx+w7\n87QBwNc77iYlIiIi6o5EJA/AvwEMAVAK4EuqWisiAwE8qqoXRsedCOAxACkANqKt7+w52PaHfE0v\nixsRERERJU63WhaBC/Z2D4d7H0Tk6uh//+Ui8r6IjDGRs6eL5echOu4UEQmLyOeTme9IEePn0lQR\nWSoiK0Xk7SRHPCLE8LmULyKvi8in0ffhawZi9ngi8kT0uK4VhxjD39Me6jbFjQv2dg+xvA8ANgE4\nU1XHAPgVgEeSm7Lni/F92DfubgCvA+BJPAkW4+dSDoAHAFykqscD8O3yGt1VjD8PNwJYqqpjAUwF\n8EcR8fIEvCPVk2h7HzrF39Pe6zbFDVywt7s47Pugqh+2WzzwYxxk7T3qklh+HgDgewCeB7ArmeGO\nILG8D1cBeEFVywFAVXcnOeORIJb3YTuA7OjtbABVqhpOYsYjgqq+B6DmEEP4e9pj3am4JXTBXnIt\nlvehvWsBvOZpoiPTYd8HESlE2y+vff9HywNWEy+Wn4fhAPJE5C0RKRaRryQt3ZEjlvfhUQDHicg2\nAMsA3JSkbHQg/p72WHeaRo71l07H3UH8ZZVYMf/3FJGzAHwDgG9W8feRWN6HewH8VFVVRATcVeqF\nWN6HIIBxaDvFPwPAhyLykapu8DTZkSWW9+FnAD5V1akiMgzAfBE5UVXrPM5G/42/pz3UnYpbwhbs\npS6J5X1A9ISER9F2dYxDTZuTO7G8DycDeLatsyEfwAwRCalqx/USyb1Y3ocyALtVtQlAk4i8C+BE\nACxuiRPL+3A6gF8DgKpuFJHNAEaibU1RSh7+nvZYd9pVygV7u4fDvg8iMgTAiwC+rKolBjIeCQ77\nPqjqUFU9WlWPRttxbt9haUu4WD6XXgYwSUTs6PUHJwJYneScPV0s78NaAOcCQPSYqpFoO5GKkou/\npz3WbWbcVDUsIjcCmIvPFuxd037BXlV9TUQuEJESRBfsNRi5R4rlfQDwCwC5AB6MzvaEVHWCqcw9\nUYzvA3ksxs+ltSLyOoDlABy0LbrJ4pZAMf48/AbAkyKyDG2TEj9R1WpjoXsoEXkGwBQA+SJSBuB2\ntB0uwN/TScIFeImIiIh8ojvtKiUiIiKiQ2BxIyIiIvIJFjciIiIin2BxIyIiIvIJFjciIiIin2Bx\nIyIiIvIJFjciSgoRGSwim0QkN3o/N3p/iOlsRER+weJGREmhqmUAHgRwV/ShuwA8rKpbzaUiIvIX\nLsBLREkjIgEASwA8CeBaAGNVNWI2FRGRf3SbS14RUc8XvXTRTwDMATCNpY2IKD7cVUpEyTYDwDYA\nJ5gOQkTkNyxuRJQ0IjIWwLkATgPwAxHpbzgSEZGvsLgRUVKIiKDt5ISboicq/B7AH8ymIiLyFxY3\nIkqWbwEoVdU3ovf/AmCUiEw2mImIyFd4VikRERGRT3DGjYiIiMgnWNyIiIiIfILFjYiIiMgnWNyI\niIiIfILFjYiIiMgnWNyIiIiIfILFjYiIiMgn/j87JU1iOS841gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f26f1fb3990>"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What does the 2D and 3D velocity profile look like?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_u_vs_y(u2d, u3d, y0):\n",
      "\n",
      "   \"\"\"\n",
      "   Plots the 1D velocity field\n",
      "   \"\"\"\n",
      "   import numpy as np\n",
      "   import matplotlib.pyplot as plt\n",
      "   import matplotlib.cm as cm\n",
      "   u_vel = np.zeros((21,2))\n",
      "   u_vel[:, 0] = u2d[10, :]\n",
      "   u_vel[:, 1] = u3d[10, :, 10]\n",
      "    \n",
      "   plt.figure()\n",
      "   ax=plt.subplot(111)\n",
      "   ax.plot(y0,u_vel[:, 0],linestyle='-',c='k', label='t= 0.1 sec, 2d')\n",
      "   ax.plot(y0,u_vel[:, 1],linestyle='-',c='r', label='t= 0.1 sec, 3d')\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=(1.0,1.0), loc=2)\n",
      "   plt.xlabel('y/L (-)')\n",
      "   plt.ylabel('u/U (-)')\n",
      "   plt.show()    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_u_vs_y(u01, u00, y00)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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7sTSQ5lz4IiJ2BpqeaytJkqTB5kLEUmWmwhfv7bJ7O+AxwKv61iNJkiQNo9am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\nwLertdNGR8QqIv6bDWvAPZjyeR8FfLK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SJKlGJlmSJEmSVCOTLEmSJEmqkUmWJEmSJNXI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\nSZIkqUYmWZIkSZJUI5MsSZIkSarR/wNJW63ydpaP6AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f26f1cf1910>"
       ]
      }
     ],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def plot_v_vs_x(u2d, u3d, y0):\n",
      "\n",
      "   \"\"\"\n",
      "   Plots the 1D velocity field\n",
      "   \"\"\"\n",
      "   import numpy as np\n",
      "   import matplotlib.pyplot as plt\n",
      "   import matplotlib.cm as cm\n",
      "   u_vel = np.zeros((21,2))\n",
      "   u_vel[:, 0] = u2d[:, 10]\n",
      "   u_vel[:, 1] = u3d[:, 10, 10]\n",
      "    \n",
      "   plt.figure()\n",
      "   ax=plt.subplot(111)\n",
      "   ax.plot(y0,u_vel[:, 0],linestyle='-',c='k', label='t= 0.1 sec, 2d')\n",
      "   ax.plot(y0,u_vel[:, 1],linestyle='-',c='r', label='t= 0.1 sec, 3d')\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=(1.0,1.0), loc=2)\n",
      "   plt.xlabel('x/L (-)')\n",
      "   plt.ylabel('v/U (-)')\n",
      "   plt.show() "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 63
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_v_vs_x(v01, v00, x00)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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xDfglEbsAH3GdnSRJmiicfqhGTkEcX5viCNj4y5xOmZK4GGU0bKOaK5IkSZIGZAAbXwaw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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f26f1a4cfd0>"
       ]
      }
     ],
     "prompt_number": 66
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "What has happened here?"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "* Although a good comparison was obtained for the 2D data, the 3D data is almost completely unstable\n",
      "* It is known that the central difference scheme can cause unstable behaviour of the non-linear advection term, whether the formulation is conservative or non-conservative.\n",
      "* Perhaps a numerical scheme which solves the Riemann problem in each computational cell in each pseudo timestep/real timestep could be expected to perform better - see Konoszy and Drikakis (2014)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": []
    }
   ],
   "metadata": {}
  }
 ]
}