{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Finite volume schemes" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pylab as plt\n", "\n", "plt.rcParams['font.size'] = 12.0\n", "plt.rcParams['figure.figsize']=[8,6]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Advection problem – constant or variable velocity\n", "\n", "We first solve the easy linear problem\n", "$$\\partial_t u + \\partial_x (a u) = 0,\\quad x\\in[0,L]$$\n", "with periodic boundary conditions. Firstly, the velocity $a>0$ is constant in space and time." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Some tools:** \n", "> The following function will be usefull to represent the discrete solutions $(U_j^n)$ as functions of space and time. \n", "> General syntax: `SHOW(data=UTX,leg='scheme')` \n", "> \n", "> `SHOW()` to draw the data stored in the 2-dimensional array `UTX`. \n", ">\n", "> `SHOW(UTX_other)` to draw the data stored in another array `UTX_other`.\n", ">\n", "> `SHOW(UTX_other,leg='truc')` to add the title `truc` to the figures." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "UTX = []\n", "def SHOW(data=UTX,leg='scheme'):\n", " fig,(ax1, ax2) = plt.subplots(1,2,figsize=(14, 6))\n", " im = ax1.imshow(data[1:,:-1],interpolation='none',\\\n", " origin=\"lower\",extent=[0,L,0,T],\\\n", " cmap=plt.get_cmap('jet'))\n", " fig.colorbar(im,ax=ax1)\n", " ax1.set_aspect('auto')\n", " ax1.set_xlabel('$x$')\n", " ax1.set_ylabel('$t$')\n", " ax2.plot(data[0,:-1],u0(data[0,:-1]),'.-',data[0,:-1],data[-1,:-1],'x-')\n", " ax2.set_aspect('auto')\n", " ax2.set_xlabel('$x$')\n", " ax2.set_ylabel('$u$')\n", " ax2.legend(['Initial','Final'])\n", " fig.suptitle(leg, fontsize=14, weight='bold')\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [], "source": [ "###############################\n", "# PDE problem\n", "T = 5 # final time\n", "L = 5 # space length\n", "\n", "def Fadv(u):\n", " a = 1\n", " return a*u, a*np.ones_like(u) # returns f(u) and f'(u) (usefull for some CFL bounds)\n", "def u0(x): # initial data\n", " return np.array([0.5-0.5*np.sign(y-1)*np.sign(y-2) for y in x])\n", "Flux = Fadv # flux function\n", "\n", "###############################\n", "\n", "# Numerical parameters\n", "J = 20 # number of points\n", "mu = 1 # cfl parameter\n", "\n", "# Discretization\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "###############################\n", "\n", "## Initialisation\n", "t = 0\n", "U = u0(x)\n", "UTX = np.concatenate([[x],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U) # compute f(U_j^0)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "## Time iterations ##\n", "while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "SHOW(UTX1,leg='Left flux for $\\mu=1$')\n", "SHOW(UTX2,leg='Left flux for $\\mu=0.9$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 1.** For the two above CFL parameters $\\mu\\in\\{0.9,1\\}$, compute the solution with $J=200$ cells to observe the convergence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Answer 1.**" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "###############################\n", "# PDE problem\n", "T = 5 # final time\n", "L = 5 # space length\n", "\n", "def Fadv(u):\n", " a = 1\n", " return a*u, a*np.ones_like(u) # returns f(u) and f'(u) (usefull for some CFL bounds)\n", "def u0(x): # initial data\n", " return np.array([0.5-0.5*np.sign(y-1)*np.sign(y-2) for y in x])\n", "Flux = Fadv # flux function\n", "\n", "###############################\n", "\n", "# Numerical parameters\n", "J = 200 # number of points\n", "\n", "\n", "# Discretization\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "###############################\n", "\n", "\n", "######## FIRST CFL NUMBER\n", "mu = 1\n", "\n", "## Initialisation\n", "t = 0\n", "U = u0(x)\n", "UTX = [x.copy()]\n", "UTX = np.concatenate([UTX,[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U) # compute f(U_j^0)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "## Time iterations ##\n", "while t *Remark.* The scheme for $\\mu=1$ is exact since it exactly reproduces the transport along characteristic lines, that are aligned with the space-time grid. For $\\mu<1$, we observe the smoothing of the discontinuity, due to the diffusion effect of the scheme (see previous work on finite difference schemes). However, the discrete profile is closer to the exact solution for a large grid." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 2.** Now implement the Lax-Friedrichs flux \n", "> $$F_{j+1/2}^n = \\dfrac{1}{2}(f(U_j^n)+f(U_{j+1}^n)) - \\dfrac{\\sigma}{2}(U_{j+1}^n-U_{j}^n),$$\n", "> with $\\sigma = \\max\\big\\{|f'(u)|,\\ u \\in[\\inf u_0,\\sup u_0]\\big\\}.$ \n", "> Compare the discrete solution with $\\mu=0.9$ to the one obtained with the previous left scheme." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Answer 2.**" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# PDE problem\n", "T = 5 # final time\n", "L = 5 # space length\n", "Flux = Fadv # flux function\n", "\n", "# Numerical data\n", "J = 200 # number of points\n", "mu = 0.9 # cfl parameter\n", "\n", "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U) # compute f(U_j^0)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "sigma = Vmax\n", "\n", "## Time iterations ##\n", "while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "SHOW(UTX2,leg='Left flux for $\\mu=0.9$ ; '+str(J)+' cells')\n", "SHOW(UTXLF,leg='Lax-Friedrichs flux for $\\mu=0.9$ ; '+str(J)+' cells')" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8386269487439237e-14" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.norm(UTX2-UTXLF)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> *Remark.* When computing the discrete solution for the Lax-Friedrichs scheme, there is no difference in the numerical solution. Namely, the numerical fluxes exactly coincide since $\\sigma=a=1>0$ and the $F_{j+1/2}^n = a U_j^n$. However the Lax-Friedrichs scheme may differ from the Left flux for equations with varying $\\sigma$ (non-constant coefficients and/or nonlinear equations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Advection with time+space-depending velocities\n", "\n", "We consider now the linear problem\n", "$$\\partial_t u + \\partial_x (a(t,x) u) = 0$$\n", "with periodic boundary conditions.\n", "\n", "For the tests, we consider the following velocity field\n", "$$ a(t,x)= 2\\cos(2\\pi t)\\sin(2\\pi x),$$\n", "varying both in time and space, for $x\\in[0,4]$. \n", "The initial data is\n", "$$u_0(x) = e^{-9(x-1)^2}.$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def FadvTX(u,t,x):\n", " a = 2*np.cos(2*np.pi*t)*np.sin(2*np.pi*x)\n", " return a*u, a\n", "\n", "def u0(x):\n", " return np.exp(-9*(x-2)**2)\n", " #return np.array([0.5-0.5*np.sign(y-1.5)*np.sign(y-2.5) for y in x])" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "T = 3 # final time\n", "L = 4 # space length\n", "\n", "x = np.linspace(0,L,21)\n", "LT = np.linspace(0,T,17)\n", "U, V = np.meshgrid(x, LT)\n", "\n", "fig, ax = plt.subplots()\n", "U = np.cos(2*np.pi*V)*np.sin(2*np.pi*U)\n", "V = np.ones_like(V)\n", "q = ax.quiver(x, LT, U, V)\n", "ax.set_xlabel('x')\n", "ax.set_ylabel('t')\n", "ax.set_title('Velocity field $a(t,x)$', fontsize=14, weight='bold')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> *Remark.* The previous figure represents the velocity field, that is concerned with the characteristic lines for the advective equation $\\partial_t u + a(t,x)\\partial_x u$ but also to understand the behavior and the properties of the conservative form $\\partial_t u + \\partial_x (a(t,x) u ) =0$. \n", "> There are some straigth lines in the $(x-t)$-plane where the velocity field vanishes, namely for $x\\in\\tfrac{1}{2}\\mathbb{Z}$ and for $t\\in \\tfrac{1}{4}+\\tfrac{1}{2}\\mathbb{Z}$. The flux along these lines therefore is zero and there is conservation of mass in any space interval of the form $[j,j+1/2]$ for $j\\in \\tfrac{1}{2}\\mathbb{Z}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We use the Lax-Friedrichs scheme with $F_{j+1/2}^n \\overset{\\rm def}{=} \\dfrac{1}{2}(f(U_j^n,t^n,x_{j+1/2})+f(U_{j+1}^n,t^n,x_{j+1/2})) - \\dfrac{\\sigma}{2}(U_{j+1}^n-U_{j}^n)$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "T = 3 # final time\n", "L = 4 # space length\n", "\n", "# PDE problem\n", "Flux = FadvTX # flux function\n", "\n", "# Numerical data\n", "J = 36 # number of points\n", "mu = 1 # cfl parameter\n", "\n", "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1]\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U,t,x) # compute f(U_j^0)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "y = np.concatenate(([-dx],x,[L])) + dx/2\n", "\n", "## Time iterations ##\n", "while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "SHOW(UTX,leg='Lax-Friedrichs flux ; $\\mu=1$ ; '+str(J)+' cells')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 3.** From the properties of the velocity field above, explain why the choice of a grid with $J=8p+4$ cells is interesting. What properties are expected to be satisfied for the exact solution to the problem and what kind of defect is however present in the numerical solution ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Answer.** The numerical flux is computed at the points $x_{j+1/2} = (j+1/2)\\Delta x = 4(j+1/2)/J$. Among them, there exists an integer $j$ such that $x_{j+1/2}$ coincides with a point in $\\tfrac{1}{2}\\mathbb{Z}$ if and only if $J\\in 4+8\\mathbb{N}$. \n", "The conservation of mass in the elementary intervals previously discussed (of the form $[j,j+1/2]$ for $j\\in \\tfrac{1}{2}\\mathbb{Z}$) is not satisfied for the discrete solution: some mass is going outside the domain $[1,3]$. The reason is that the numerical flux does not vanished at the expected points since it includes also a gradient of the discrete solution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We perform several computations with finer grids." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for J in [8*10+4,8*20+4,8*40+4,8*80+4,8*160+4]:\n", "\n", " mu = 1 # cfl parameter\n", " \n", " # Discretization parameters\n", " dx = L/J\n", " x = np.linspace(0, L, J+1)\n", " x = x[0:-1]\n", "\n", " ## Initialize\n", " U = u0(x)\n", " t = 0\n", " UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", " LT = [t,t]\n", "\n", " F,dF = Flux(U,t,x) # compute f(U_j^0)\n", " Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", " dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", " y = np.concatenate(([-dx],x,[L])) + dx/2\n", "\n", " ## Time iterations ##\n", " while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "SHOW(UTX,leg='Lax-Friedrichs flux ; $\\mu=1$ ; '+str(J)+' cells')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 4.** Did the defect disappear for large values of $J$ ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Answer.** Increasing the value of $J$ reduces the observed defect." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We consider now another scheme for the resolution of the same problem, using an upwind strategy.\n", "The numerical flux is\n", "$$F_{j+1/2}^n = \\begin{cases}f(U_j^n,t_n,x_{j+1/2}), & \\textrm{ if } a(t_n,x_{j+1/2})>0 ; \\\\ \n", "f(U_{j+1}^n,t_n,x_{j+1/2}), & \\textrm{ if } a(t_n,x_{j+1/2})<0.\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "T = 3 # final time\n", "L = 4 # space length\n", "\n", "# PDE problem\n", "Flux = FadvTX # flux function\n", "\n", "# Numerical data\n", "J = 36 # number of points\n", "mu = 1 # cfl parameter\n", "\n", "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1]\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U,t,x) # compute f(U_j^0)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "y = np.concatenate(([-dx],x,[L])) + dx/2\n", "\n", "## Time iterations ##\n", "while t0) + FR*(dFR<0)\n", " ##########################################\n", " U = U - dt/dx*(NumFlux[1:]-NumFlux[:-1])\n", " t = t + dt\n", "\n", " LT = np.append(LT,t)\n", " UTX = np.concatenate([UTX,[U]],axis=0)\n", " \n", " \n", "LT = np.resize(LT,(len(LT),1))\n", "UTX = np.concatenate([UTX,LT],axis=1)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for J in [8*10+4,8*20+4,8*40+4,8*80+4,8*160+4]:\n", "\n", " mu = 1 # cfl parameter\n", " \n", " # Discretization parameters\n", " dx = L/J\n", " x = np.linspace(0, L, J+1)\n", " x = x[0:-1]\n", "\n", " ## Initialize\n", " U = u0(x)\n", " t = 0\n", " UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", " LT = [t,t]\n", "\n", " F,dF = Flux(U,t,x) # compute f(U_j^0)\n", " Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", " dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", " y = np.concatenate(([-dx],x,[L])) + dx/2\n", "\n", " ## Time iterations ##\n", " while t0) + FR*(dFR<0)\n", " ##########################################\n", " U = U - dt/dx*(NumFlux[1:]-NumFlux[:-1])\n", " t = t + dt\n", "\n", " LT = np.append(LT,t)\n", " UTX = np.concatenate([UTX,[U]],axis=0)\n", " \n", " LT = np.resize(LT,(len(LT),1))\n", " UTX = np.concatenate([UTX,LT],axis=1)\n", " \n", " plt.plot(x,U,label='J='+str(J))\n", " \n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "SHOW(UTX,leg='Upwind flux ; $\\mu=1$ ; '+str(J)+' cells')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 5.** Does the upwind scheme provide good results ?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Answer.** Even with a very few cells, the upwind scheme strongly reduces the local conservation defect. Having common points in the grid with the $\\tfrac{1}{2}\\mathbb{Z}$ points, there the numerical flux vanished and the invariance structure is strongly preserved. \n", "> Increasing the number of cells significantly improves the quality of the result." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Nonlinear Burgers problem" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def Fburgers(u):\n", " return u**2/2, u" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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db3TzKuBg4HvANcCFVTWd5NQk4730sxgMvX9q7Pgq4HLg+8A3gRcAp1fVto7rqp6xk9guP2xGak+n6+Cr6i4GwT1+/DMMHsIbPXYNg18CxstOAyd1WS9NFvuLbXFERWqTW9WqP+wkNss5eKk9Brx645Gtau0ytiT4u5fUIgNevWO8t8VfuKQ2GfDqDYeB22XbSO0x4NU7dhglaWEGvHrDXmK7XCYntceAV++4sUpbHFGR2mTAqzfsIzbMxpGaY8Crd+wxtsX2kNpkwKs3/LCZdtkyUnsMeElPiM9ESG0y4NUb9hLb5eiK1B4DXr0xmyHO+bYl8ZcvqUUGvHrHIeG22BpSmwx49Yj9xFY5Qi+1x4BX7zhE3xY/bEZqkwGv3rCX2C6bRmqPAa/escPYFptDapMBr96wl9gul8lJ7THg1Ts+Rd8Ym0NqkgGv3rCT2C6bRmqPAa/ecQ6+LTaH1CYDXr1Rw36igdKWuJWd1CQDXr3hEH27yoSXmmPAq3ccom+LzSG1yYBXb9hHbJejK1J7DHj1kH3GljiiIrWp04BPcniSDyXZmeSOJOfMU25jkh8kmRl5HTdy/uQkn09y7/C/J3dZT/WTm6m0y6aR2tN1D/5twIPAUcC5wOVJ1s1T9v1VtXLkdTtAkicB1wPvAQ4D3gVcPzwu2WNsjBsPSW3qLOCTrADOBi6uqpmqugn4MHDeHl7qNGAZ8JaqeqCq/pjBmOxzuqqrpG75FL3Uni578CcAD1XV5pFjtwDz9eDPSHJXkukkF44cXwfcWo8ej711N9fRfsb+YlscUZHa1GXArwS2jx27B1g1R9kPAD8JTAGvBH4nyUtHrnPPIq9DkguSbEqyaevWrY+37uoB53nbZdtI7eky4GeA1WPHVgM7xgtW1Veq6ltV9XBV/Q3wVuDFe3qd4bWuqKoNVbVhamrqCd2A+iF2GSVpQV0G/GZgWZLjR46tB6YX8d7ikZHXaeCkPPqn+EmLvI4mmFvVtimJM/BSgzoL+KraCVwHXJJkRZJTgDOBq8bLJjkzyWEZeBbwagZPzgPcCDwMvDrJQUkuGh7/ZFd1VT85DNwu20ZqT9fL5F4FHAx8D7gGuLCqppOcmmRmpNxLgH9kMOz+buCNVfUugKp6EDgLeBlwN/AK4KzhccmHuhpjc0htWtblxarqLgbhPH78Mwwenpv9/qXjZcbKfxF4Zpd1U//ZS2yZjSO1xq1q1TturNIWR1SkNhnw6g37iO1ydEVqjwGv3rHH2BbbQ2qTAa/e8MNm2mXLSO0x4CU9IT4TIbXJgFdv2Etsl6MrUnsMePWOc75tsT2kNhnw6o9hJ9G96NsSHF2RWmTAqzf8zPF2OUIvtceAV+/Yf2+MIypSkwx49Ya9xHbZNFJ7DHj1jh3GttgcUpsMePWGvcR2uUxOao8Br95xY5W2OKIitcmAV2/YSZSkxTPg1Tv2GNtic0htMuDVG66Db5ejK1J7DHj1jj3GtrizoNQmA169sauXaJ40ZbBVrV14qTUGvHrDCGmXQ/RSewx49Y7L5NriCL3UJgNe/WE3sVk2jdQeA169Y4+xLY6oSG0y4NUbdhLb5UN2UnsMePWO/cXG2CBSkwx49YbzvO2ybaT2GPDqHTdWaYutIbWp04BPcniSDyXZmeSOJOfMU+41Sb6cZEeSryV5zdj5rye5L8nM8HVDl/VUP81+JKmB0pbE5yOkFi3r+HpvAx4EjgJOBj6a5Jaqmh4rF+BlwK3A04AbkvxzVb1vpMwZVfXxjusnSdJ+obMefJIVwNnAxVU1U1U3AR8GzhsvW1VvqqovVNVDVfUPwPXAKV3VRZNp1061duGbEuzCSy3qcoj+BOChqto8cuwWYN3u3pTBhOqpwHgv/+okW5PckGR9h/WUJGnidRnwK4HtY8fuAVYt8L6Nw3r82cixc4G1wDHAp4C/SnLoXG9OckGSTUk2bd26dc9rrd6YfVLbjVXaMpiDtwsvtabLgJ8BVo8dWw3smO8NSS5iMBf/i1X1wOzxqrq5qu6rqnur6jLgbga9/MeoqiuqakNVbZiamnqi96CGGSHtcpmc1J4uA34zsCzJ8SPH1vPYoXcAkrwCeC3w3KrassC1Cx+e1iz/JTTFZyKkNnUW8FW1E7gOuCTJiiSnAGcCV42XTXIu8PvAL1TV7WPn1iQ5JcmTkiwfLqE7Eri5q7qqn8puYrNsGak9XW908yrgYOB7wDXAhVU1neTUJDMj5S4FjgD+bmSt+9uH51YBlwPfB74JvAA4vaq2dVxX9ZQ9xrb4TITUpk7XwVfVXcBZcxz/DIOH8Ga/P3Y315gGTuqyXpL2LkdXpPa4Va16x/5iWxxRkdpkwKs3di2TM1GaY/9dao8BL0nSBDLg1Ruzm6nYf29LEtfBSw0y4CVJmkAGvHrjkTn4pa2HHi04By+1yIBXbxgiDXOMXmqOAa/ecWOVtjiiIrXJgFdv2Elsl00jtceAV+/YY2yLzSG1yYBXb/iZ4+1ydEVqjwEv6QlxZ0GpTQa8esNlcm0aLJOzCy+1xoCXJGkCGfDqHZfJtSVxDl5qkQEvSdIEMuDVGzXsJjoH3xo/bEZqkQGv3jBE2mXTSO0x4NU7duDb4oiK1CYDXr1hL7Fd5fCK1BwDXr3jxiptsTWkNhnw6o1dG90sbTU0xt+3pDYZ8JIkTSADXr0xux2qPca2xGVyUpMMeEmSJpABr9545MNm7MK3JPHDZqQWGfCSJE2gTgM+yeFJPpRkZ5I7kpwzT7kkeWOSbcPXGzPSLUtycpLPJ7l3+N+Tu6yn+sk+Ypv8sBmpTV334N8GPAgcBZwLXJ5k3RzlLgDOAtYDJwFnAL8GkORJwPXAe4DDgHcB1w+Pa39mijTLlpHa01nAJ1kBnA1cXFUzVXUT8GHgvDmKvxx4c1VtqapvAm8Gzh+eOw1YBrylqh6oqj9msPT5OV3VVf3l9Ht7/PheqU1d9uBPAB6qqs0jx24B5urBrxuem6vcOuDWevTel7fOcx3tR+wltsutaqX2dBnwK4HtY8fuAVbNU/aesXIrh/Pw4+d2dx2SXJBkU5JNW7dufVwVV3/YV2yQjSI1qcuAnwFWjx1bDexYRNnVwMyw174n16GqrqiqDVW1YWpq6nFVXP1Q5RK5FgVHV6QWdRnwm4FlSY4fObYemJ6j7PTw3FzlpoGT8uif5CfNcx1JkjSHzgK+qnYC1wGXJFmR5BTgTOCqOYq/G/itJE9N8hTgvwBXDs/dCDwMvDrJQUkuGh7/ZFd1VT8V5WhwgzLY6UZSY7peJvcq4GDge8A1wIVVNZ3k1CQzI+X+F/AR4EvAl4GPDo9RVQ8yWEL3MuBu4BXAWcPjkiRpEZZ1ebGquotBOI8f/wyDh+dmvy/gvw5fc13ni8Azu6yb+m8wB7/UtdA45+ClNrlVrSRJE8iAV28UbqrSosFWtfbhpdYY8OoNM6RdNo3UHgNe/WIHvjk2idQmA1694WeOt8vRFak9Brx6xd5ie9xdUGqTAa/+cJlckwbL5OzCS60x4CVJmkAGvHrDZXKNinPwUosMeEmSJpABr96oKufgGxRiD15qkAEvSdIEMuDVG1Uuk2uRoypSmwx49YajwO1yL3qpPQa8esVNVdpji0htMuDVG3YS22XTSO0x4NUr9hbb46CK1CYDXr1R+JRdi1wmJ7XJgJckaQIZ8OoNl8m1KfHDZqQWGfCSJE0gA1694jK59sQPm5GaZMBLkjSBDHj1hh8206o4Ay81yIBXbxgi7XKIXmqPAa9esQPfHkdVpDYZ8OqNKh+ya9GgRezCS63pJOCTHJ7kQ0l2JrkjyTm7KfuaJF9OsiPJ15K8Zuz815Pcl2Rm+LqhizpKkrQ/WdbRdd4GPAgcBZwMfDTJLVU1PUfZAC8DbgWeBtyQ5J+r6n0jZc6oqo93VDdNiKIcom+Qy+SkNj3hHnySFcDZwMVVNVNVNwEfBs6bq3xVvamqvlBVD1XVPwDXA6c80XpIkqRHdDFEfwLwUFVtHjl2C7BuoTdmMKF6KjDe0786ydYkNyRZ30EdNQEGc/BLXQuNi8vkpCZ1EfArge1jx+4BVi3ivRuHdfizkWPnAmuBY4BPAX+V5ND5LpDkgiSbkmzaunXr4mstSdIEWzDgk9yYpOZ53QTMAKvH3rYa2LHAdS9iMBf/i1X1wOzxqrq5qu6rqnur6jLgbga9/DlV1RVVtaGqNkxNTS10O+qxQS/RLnxrBnPw9uGl1iz4kF1Vnba788M5+GVJjq+qrw4Pr+exw+6j73kF8Frg56tqy0JVwJ/qkiTtkSc8RF9VO4HrgEuSrEhyCnAmcNVc5ZOcC/w+8AtVdfvYuTVJTknypCTLh0vojgRufqL1VP85B9+m4Cp4qUVdbXTzKuBg4HvANcCFs0vkkpyaZGak7KXAEcDfjax1f/vw3CrgcuD7wDeBFwCnV9W2juqpXjNGWuUIvdSeTtbBV9VdwFnznPsMgwfxZr8/djfXmQZO6qJOmkx24Nvj7oJSm9yqVr3hEH27fMhOao8BL0nSBDLg1RtVg01V1JbEpyOkFhnwkiRNIANevVGUc/ANCnbhpRYZ8JIkTSADXr0xmINXa5yDl9pkwEuSNIEMePVG4aYqLQqug5daZMBLkjSBDHj1hp3ENjkHL7XJgFdvuEyuTUn85UtqkAEvSdIEMuDVH37YTJMGnwdvF15qjQEvSdIEMuDVG4UfNtOk+ACk1CIDXpKkCWTAqzeqfIq+RSHOwEsNMuAlSZpABrx6YzAHr9Zk8Bi9pMYY8JIkTSADXr1R5YfNtMh18FKbDHj1hkP0bYrL5KQmGfCSJE0gA169UVV24RvkMjmpTQa8JEkTyIBXbzgH36bBHLx9eKk1BrwkSROos4BPcniSDyXZmeSOJOfspuzGJD9IMjPyOm7k/MlJPp/k3uF/T+6qnuoxl8k1yX1upDZ12YN/G/AgcBRwLnB5knW7Kf/+qlo58rodIMmTgOuB9wCHAe8Crh8elyRJi7Csi4skWQGcDfx0Vc0ANyX5MHAe8No9vNxpw3q9pQYTe3+c5LeB5wAf66K+i/HKd2/izpkH9tUfp0X42p07mVp50FJXQ+MSquCFf3LzUtdEat4rTjmWM9Y/ZZ/8WZ0EPHAC8FBVbR45dgvwb3bznjOS3AV8G/ifVXX58Pg64NZ69FM7tw6PPybgk1wAXACwZs2ax38HY1Y86QDuP6irvx514Wee+mRO+4kfXepqaMxzTvxRbt1yNw//0IF6aSEHHrDvHn3rKsFWAtvHjt0DrJqn/AeAK4DvAj8LXJvk7qq6ZnitexZ7raq6YngtNmzY0NlPmLe85OldXUqaaCf/y0O58j88a6mrIWnMon6VSHJjkprndRMwA6wee9tqYMdc16uqr1TVt6rq4ar6G+CtwIuHp/foWpIk6bEWFfBVdVpVZZ7XzwGbgWVJjh9523pgepH1GF3iPA2clEc/Ln3SHlxLkqT9XieTAVW1E7gOuCTJiiSnAGcCV81VPsmZSQ7LwLOAVzN4ch7gRuBh4NVJDkpy0fD4J7uoqyRJ+4MuZ/tfBRwMfA+4BriwqqYBkpyaZGak7EuAf2Qw7P5u4I1V9S6AqnoQOAt4GXA38ArgrOFxSZK0CJ09Jl5VdzEI5rnOfYbBw3Oz3790gWt9EXhmV3WTJGl/41a1kiRNIANekqQJZMBLkjSBDHhJkiaQAS9J0gQy4CVJmkAGvCRJE8iAlyRpAuXRn8rab0m2And0eMkjgTs7vN5SmpR7mZT7AO+lVZNyL5NyH+C97M4xVTU114mJCviuJdlUVRuWuh5dmJR7mZT7AO+lVZNyL5NyH+C9PF4O0UuSNIEMeEmSJpABv3tXLHUFOjQp9zIp9wHeS6sm5V4m5T7Ae3lcnIOXJGkC2YOXJGkCGfCSJE2g/Trgkxye5ENJdia5I8k585RLkjcm2TZ8vTFJ9nV9d2cP7mVjkh8kmRl5Hbev6zufJBcl2ZTkgSRXLlD2N5N8J8n2JO9MctA+quaiLPZekpyf5OGxNjltn1V0AUkOSvKO4b+rHUn+PsnpuynfbLvsyb203i4ASd6T5NvDv+vNSf7Tbso22y6w+HvpQ7sAJDk+yf1J3jPP+b2eK/t1wANvAx4EjgLOBS5Psm6OchcAZwHrgZOAM4Bf20d1XKzF3gvA+6tq5cjr9n1Wy4V9C7gUeOfuCiV5PvBa4LnAMcBxwO/u9drtmUXdy9DfjrXJjXu3antkGfDPwL8Bngy8HvhAkrXjBXvQLou+l6GW2wXgMmBtVa0Gfgm4NMkzxwv1oF1gkfcy1Hq7wOBn8t/t5vxez5X9NuCTrADOBi6uqpmqugn4MHDeHMVfDry5qrZU1TeBNwPn77PKLmAP76VpVXVdVf05sG2Boi8H3lFV01X1feD3aKhNYI/upWlVtbOqNlbV16vqh1X1f4CvAXP98G26XfbwXpo3/Ht+YPbb4etpcxRtul1gj+6leUleAtwNfGI3xfZ6ruy3AQ+cADxUVZtHjt0CzNXrXTc8t1C5pbIn9wJwRpK7kkwnuXDvV2+vmKtNjkpyxBLV54l6epI7h0OTFydZttQVmk+Soxj8m5ue43Sv2mWBe4EetEuSP0lyL3Ab8G3gL+Yo1ot2WeS9QMPtkmQ1cAnwWwsU3eu5sj8H/Epg+9ixe4BV85S9Z6zcyq7nS56APbmXDwA/CUwBrwR+J8lL92719oq52gTmvufW/TXw08CPMhiJeSnwmiWt0TySHAhcDbyrqm6bo0hv2mUR99KLdqmqVzH4+z0VuA54YI5ivWiXRd5L6+3yewxGS7YsUG6v58r+HPAzwOqxY6uBHYsouxqYqXY2EVj0vVTVV6rqW1X1cFX9DfBW4MX7oI5dm6tNYO72a1pV3V5VXxsOGX+JwW//zbVJkh8BrmLwrMdF8xTrRbss5l760i4Aw/+fbwKOBuYaletFu8DC99JyuyQ5GXge8N8XUXyv58r+HPCbgWVJjh85tp65h+qmh+cWKrdU9uRexhXQykjEnpirTb5bVb2e7x5qrk2GvYp3MHiI8+yq+sE8RZtvlz24l3HNtcscljH3vHXz7TKH+e5lXEvtchqwFvhGku8Avw2cneQLc5Td+7lSVfvtC3gfcA2wAjiFwRDJujnK/Trw/4CnAk8ZNsKvL3X9H+e9nAkcxuB/iGcB3wRevtT1H6nfMmA5gydqrxp+vWyOci8AvgP8FHAo8EngD5a6/o/zXk4Hjhp+fSLwZeANS13/sTq+HfgssHKBcn1ol8XeS9PtwmCI+iUMhnoPAJ4P7AR+qW/tsof30my7AIcAPzby+kPgg8DUHGX3eq4s+V/IEjfG4cCfD/8hfQM4Z3j8VAZDJbPlArwJuGv4ehPDbX5bee3BvVzD4KnuGQYPsrx6qes+dh8beeQJ2tnXRmDNsM5rRsr+FvBdBs8f/Blw0FLX//Hcy/CHwHeHbXc7gyHHA5e6/iP3ccyw7vcP6z37Ordv7bIn99KDdpkCPs3gae3twJeAVw7P9a1dFn0vrbfL2H1tBN4z/Hqf54p70UuSNIH25zl4SZImlgEvSdIEMuAlSZpABrwkSRPIgJckaQIZ8JIkTSADXpKkCWTAS5I0gQx4SZIm0P8HRV1urUwJc0oAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def u0(x):\n", " return np.array([0.5-np.sign(y-1)*np.sign(y-2) for y in x])\n", "plt.plot(x,u0(x),label='u0')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "# PDE problem\n", "T = 0.5 # final time\n", "L = 4 # space length\n", "Flux = Fburgers # flux function\n", "mu = 0.9 # cfl parameter\n", "\n", "J = 100 # number of points" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 6.** Program the Lax-Friedrichs scheme for the Burgers equation:\n", "> $$F_{j+1/2}^n = \\dfrac{1}{2}(f(U_j^n)+f(U_{j+1}^n)) - \\dfrac{\\sigma}{2}(U_{j+1}^n-U_{j}^n),$$\n", "> with $\\sigma = \\max\\big\\{|f'(u)|,\\ u \\in[\\inf u_0,\\sup u_0]\\big\\}.$ \n", "> Compare the discrete solution with $\\mu=0.9$ for several values of the grid size $J$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": false }, "outputs": [], "source": [ "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1]\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "sigma = Vmax\n", "\n", "## Time iterations ##\n", "while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "UTXRus = UTX\n", "SHOW(UTXRus,leg=\"Burgers - Lax-Friedrichs\")" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for J in [25,50,100]:\n", " dx = L/J\n", " x = np.linspace(0, L, J+1)\n", " x = x[0:-1]\n", "\n", " ## Initialize\n", " U = u0(x)\n", " t = 0\n", " UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", " LT = [t,t]\n", " \n", " F,dF = Flux(U)\n", " Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", " dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", " sigma = Vmax\n", "\n", " ## Time iterations ##\n", " while t **Question 7.** Solve the Riemann problem for the Burgers flux and then program the Godunov scheme for the Burgers problem. Compare the solution to the Lax-Friedrichs scheme." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "## Time iterations ##\n", "while tV[j+1]:\n", " if V[j]+V[j+1]>0 :\n", " FG = V[j]**2/2\n", " else :\n", " FG = V[j+1]**2/2\n", " else :\n", " if V[j]>0 :\n", " FG = V[j]**2/2\n", " elif V[j+1]<0 :\n", " FG = V[j+1]**2/2\n", " else :\n", " FG = 0\n", " NumFlux[j] = FG\n", " ##########################################\n", " U = U - dt/dx*(NumFlux[1:]-NumFlux[:-1])\n", " t = t+dt\n", "\n", " LT = np.append(LT,t)\n", " UTX = np.concatenate([UTX,[U]],axis=0)\n", " \n", "LT = np.resize(LT,(len(LT),1))\n", "UTX = np.concatenate([UTX,LT],axis=1)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "UTXGod = UTX\n", "SHOW(UTXGod,leg=\"Burgers - Godunov scheme\")" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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Xt0YdeiCc3PXd3aK3SD3ttNOS9rnyyiupra1lxYoVbN68mZNOOolhw4bxla98hXvuuYcnn3yShQsXUlZWxhlnnNH1ecV56aWXWLZsGcuXL+ewww7j9NNPZ/z48fzgBz/gtdde4+2338bMOO2007jlllv4/ve/zznnnMMjjzzCKaecAsDTTz9NdXU1Bx98cLd/frbRCF4kn02ZCdb+17zBFeJOmJmhgDpXFPBTXV7Iuthr8KBqdrsrPrl31b4LNm3aRHV1NYHAznHjkUceSVVVFSUlJbzwwgs8+uij3HrrrfTr14+xY8fy7W9/mwcffBCA2bNnc/XVVzNq1CgGDBjAjBkzuh3DTTfdRElJCRMmTGDChAksWrQIgIcffpiZM2cyePBgBg0axE033dT2c88991zmzZtHQ0MDAH/4wx8455xzdvevIytoBC+SzwbsBS4MxVW4plrWM5AnB13KpYedm+nIkhpWGbNVrkhT9J1KYWQNeNfcE8zkUDkKvvxUx/ZdMHDgQDZt2kQwGGxL8q+88goAI0eOZP369bS2tjJmzJi214wZM4aaGq/Owdq1axk1alS757pr6NChbd+XlpZSV1fXduz4n7t27VoA9t57b8aPH88TTzzBqaeeyrx581i4cGG3f3Y20gheJJ+9fpeXJL/5Dv8+9z8c0fRzRh57Yaaj6tTQyuIEU/Qawe+WKTOhIG6nREGJ154mRxxxBEVFRTz++OMJn6+urqagoIBVq1a1tX388ceMGOGt/xg2bBirV69u91yssrKytlE2wPr161OObfjw4R1+7vDhw9seR6fpH3/8cfbbbz/23nvvlI+dzZTgRfLV9rWw9C98MPK/Oep/53PhfW9gBvXN2b2veFhl8c59+RrBp8dBZ8GpP/dG7Jj356k/T2uJ4qqqKm666Sa+/vWv89hjj7Fjxw7C4TBvv/029fX1+P1+zjrrLK6//np27NjBqlWr+MlPftK2UO6ss87i5z//OWvWrGHr1q3cdlv72YmJEyfy6KOP0trayoIFC3jsscdSju2cc87hlltuYePGjWzatImbb7657ecCnH322TzzzDPcddddnHtu9s5udZem6EXyzeLZ3va42tU4YPZ/HDUtXsJ0Dm58fCkBvy9rVs7HG1ZZwvamIPXNQcq0yC59Djqrx+858J3vfIcRI0Zw++23c8EFF1BWVsaee+7Jj370I4488kgmTJjAlVdeyZ577klxcTGXXnopF198MQCXXnopy5cvZ8KECVRUVHDNNdfwz3/+s+3Y0QVx/fv359hjj+Xcc89ly5YtKcV1ww03sH37dg466CAAvvjFL3LDDTe0PT9s2DCOOOIIXnjhBWbPTv/2wUyxfCo+MHnyZLdgwYJMhyGSOdHtUDF73xtcIde1XsK88NFtbSOqSnj5uhMyEWGX5i6s4eo/vs1z3z6WvQaWws394dhr4fjvZjq0jHvvvfcYP358psOQDEj23pvZm865yYleoyl6kXySQmEbyJ7StIkMje6F39YEPh8Uqh69yK5QghfJJ50Utmn3OEtK0yays9hNzFY5LbIT6TYleJF8UtnxRjIAa93Atu+zqTRtIkMqovXoY6rZaQQv0m1K8CL5ZMpMMH+7pkZXyP+6s7OyNG0ixQV+BpYVsm57zFY5JXiRbtMqepF8MvoIcKFIUqyjsXQY126bxufOvZI7Dxja9euzxNDKYtZti52iV4KPcs5hZpkOQ3rRri6G1wheJJ8suM8rTfu1l2HWNr41/CFeKjmBE/YdnOnIuqV9Nbt+KlUbUVxczObNm3Xr1T7EOcfmzZspLi7u9ms1ghfJF61N8NYD8KmTof8YttS38Ox7G7jgiLEUBnLrs/ywymIWrIrscdYIvs3IkSNZs2YNGzduzHQo0ouKi4sZOTLx+prOpC3Bm9kVwEXAgcAjzrmLkvS7EPgGMA7YDvwB+K5zLhh5/nng00C03FaNcy57VwSJZIulc6BhMxx+GeDtJ28NOb44ufv/MWTa0MpitjW00tgSoqSoUgk+oqCggD322CPTYUiOSOcIfi1wCzAV6GwPTilwNfA6MAiYB1wDxNYlvMI5d28aYxPJXzGV6/AFmP/O+1w9O0TNtiYK/Mb763aw79CKTEfZLbFb5fYs6gctOyAc9vbFi0hK0vbb4pyb45ybC2zuot9dzrkXnXMtzrka4GHgqHTFIdKnRCvXRe8UFg5ywJs3csj2ZwFoDTlmzFnC3IU1GQyy+4ZVemOE9bVNO28401KXwYhEck82fBz+L2BpXNutZrbJzF42s+N6PySRHJGgcl1JXOW6xtYQdzy9rLcj2y07R/BNuqOcyC7KaII3s4uBycCPY5qvBfYERgB3A0+Y2V6dHOMyM1tgZgu08ET6nBQr12VzadpEhsZWs9MNZ0R2ScYSvJlNA24FTnbObYq2O+ded87tcM41O+ceAF4GPpfsOM65u51zk51zkwcNGtTjcYtklRQq10F2l6ZNpLjAz4CyQm8EX6xbxorsiowkeDP7LHAPcKpzbkkX3R2gqg4iiRx/A/G/Hg2ukNuDO28Lmu2laZMZWlEcuQYfTfCaohfpjrQleDMLmFkx4Af8ZlZsZh1W6ZvZCXgL685wzr0R91yVmU2NvtbMzsO7Rv/3dMUpklcKSwEHpdWA0dpvBNe1XsLzhcflTGnaROYurGHFxjqee/8TvvTgu16jRvAi3ZLObXI3ADfFPP4S8D0zuw94F9jPOfcxcCNQCfw1ptzii865k4ECvK12+wIh4H1gmnNueRrjFMkf8++BipFw1SLwB/jJ39/nyRc+5NVvHdt205ZcM3dhDTPmLKEpGAbgw+0+KIaF//mYSftnODiRHJK2BO+cmwXMSvJ0eUy/4zs5xkbg0HTFJJLXNi6Dlf/2bjDjD9AaCvPYm2s4Yd/BOZvcAe54ehmNraG2x3WRshovvrOCSdMyFJRIDsqGbXIisiveuAf8hXDwhQD86/1P2Lijmf936OgMB7Z74lf81+F9WAmrHr1It6gWvUiuWTwbnp0F22ugoJT5z/2Zq98dR822RnwGOxpbMh3hbhleVUJNTJJ3+NjhShha1JrBqERyj0bwIrkkWrlue6QyXWsDB7x5A4ds/wcAYQfXz12ac5XrYk2fug8lBe3vaV9PCZ8eUZihiERykxK8SC7J08p1saZNGsGtpx9IdbmX0KvLCyntV8XY8mAXrxSRWErwIrkkTyvXxZs2aQT3Xuitt739zIOoqBygbXIi3aQEL5JL8rRyXSJlhd40fX1zyKtmpwQv0i1K8CK55MgrOzTlS+W6eKVF3hrghpagV49eCV6kW5TgRXJJQ2Qqvt8wwAj1G8mM1kt4ruDYnK5cl0h5oZfg65tDSvAiu0Db5ERyRagV3rwf9j4RvvQYAPe88CGP/+19nv2fo9h7cL/MxpdmJZEpem8Eryl6ke7SCF4kV7z3BNRtgMMuBcA5x6NvfMyhY/vnXXIHKAz4KPT7qIsdwYfDmQ5LJGdoBC+S7RbP9rbH1a4G80PjVgBeXbGZjzY38I0p4zIcYM8pLfJ7I/jKCsBBS93O28eKSKeU4EWyWbSwTXTvuwvBk1eD+Xhk6TgqigN87sBhGQ2xJ5UVBnZegwdvFK8EL5ISTdGLZLMEhW1obWTdnO/yxKK1hJzj7++sz0xsvaAsOoKPTfAikhIleJFslqSwzRC3CfBWmM+YsySnS9N2prQwQH1LyFtkB0rwIt2gBC+SzVIobJPrpWk7U1bkp745dgRfm9mARHKIErxINpsyE7B2TfGFbSD3S9MmU1oY8BJ8sUbwIt2lBC+SzfoNBRyUDACM9QziutZLmBc+ul23fChNm0h5UYCGlpCuwYvsAq2iF8lmb9wDJf3hW+9CQQnPvraKeXPfadclX0rTJlJaqEV2IrtKI3iRbFVbA+8/BZPOhwJvhN7Q4t0ydXC/orwrTZtIWVGAuuYgFJZ7DUrwIinTCF4kW731ALgwHPoVwKtc98gbq5k8pj+PXX5khoPrHaWFfppaw4Tw4S8sh6btmQ5JJGcowYtkm8Wz4bnveVvkAsWw+g3oP5ZXP9zMyk31XHnC3pmOsNeUFe68o1y/ogpoVoIXSZUSvEg2ia9cF2zyHgMPv7M3lSUFeV25Ll5Z2y1jQ/TTHeVEukXX4EWySSeV655avI5gOJzXlevilRV5d5Rr2wuvBC+SMiV4kWzSxyvXxSvVPeFFdpkSvEg26eOV6+KVRe4JXx/dKqdr8CIpU4IXySb/dU2Hpr5UuS7ezmvwkWp2GsGLpEwJXiSbBJu9P8uH0Bcr18XbeQ0+csMZJXiRlKU1wZvZFWa2wMyazez+Lvp+08zWm9l2M7vPzIpinhtrZv8yswYze9/MPpPOOEWyknMw/14YcQhcsxxmbePvJ/2jQ3LP58p18Upjtsm1XYMPhzMclUhuSPcIfi1wC3BfZ53MbCpwHTAFGAPsCXwvpssjwEJgIHA98JiZDUpzrCLZZeW/YdNyOPSStqbaBq9y3ZCKvlG5Ll50H/zgj56A138NOPjpAd52QhHpVFr3wTvn5gCY2WQg8Wohz4XAb51zSyP9vw88DFxnZp8CDgZOcs41An82s6uBM4BfpzNekawy/x7vpjL7nw5AMBTm0fkfc8y4ah78yuEZDi4zSov8fMH3Eke/dx+Em7zG7TVttQE46KzkLxbp4zJ1DX5/YFHM40XAEDMbGHluhXNuR9zz+/difCK9Z/FsuHNfeO8JCLfCe/MA+NeyjayrbeK8w8dkOMDMKfD7uLZgNgXR5B7V2ujVDBCRpDJVya4cqI15HP2+X4Lnos8nnJM0s8uAywBGjx6d3ihFelp85brmHTsr1705liEVRUwZPziDAWbeMNuc+IkkNQNExJOpEXwdUBHzOPr9jgTPRZ9PuHzWOXe3c26yc27yoEG6TC85Jmnluhk8v2wjDS0hnlq8LjOxZYlPqE78RJKaASLiyVSCXwpMiHk8AdjgnNsceW5PM+sX9/zSXoxPpHckrVznjVp3NAX7VOW6RH5Xcj7NOzfZeApKYMrMzAQkkiPSvU0uYGbFgB/wm1mxmSW6DPB74Ctmtp+ZVQE3APcDOOeWA28DN0Ve/9/AQcCf0xmrSFZQ5bouvV7+GX7b/2ooi8zQlQ2GU3+uBXYiXUj3CP4GoBFvC9yXIt/fYGajzazOzEYDOOf+DtwO/Av4GFgF3BRznLOBycBW4DbgTOfcxjTHKpJ5ky/u0NSXK9clUl4U4LmC4+CLD3gNZ9yr5C6SgnRvk5sFzErydHlc358AP0lynI+A49IXmUiW2rYKLAD9hsD2taynmh+2frHPVq5LpLTQz6a6ZvAXew3h1swGJJIjdD94kUxp3Oatop94Npz2SwDmPv8B8/7efjq+L1WuS6SsKODdbMYX+e8qFMxsQCI5QrXoRTJl0SPQ2gCHXtrWtK62Cb/B0MriPlm5LpHSQj8NzaGdCT6sBC+SCo3gRTIhHPbqzo88FIZPBKC+Ocict2o4dcJwfnr2pMzGl0XKoyN4f4HXoCl6kZRoBC/S2xbPhjs/BZs/gM0fttVVn7doLTuag3zp0323cl0ipYUBmlrDhExT9CLdoRG8SG+Kr1zXuAWe+AYOeOi1Yew7tB+HjOmf0RCzTfSWsY0h81bqaopeJCUawYv0piSV69bPmcHStdtZV9vE42+vzUxsWartlrFB8xo0RS+SEiV4kd7UReW62sbWPl+5Ll50BN+W4ENK8CKpUIIX6U2ViVfDq3JdcmVtI/jIf1eaohdJiRK8SG8aN7VDkyrXda40MoKvDzqvQQleJCVaZCfSm9Yv8WqpBwqhtoZ1VHOrKtd1KjqCr9cUvUi3KMGL9Ja1b8OaN+Czt8GnLwfg/r+9x7wXVrTr1tcr18WLXoPf0apFdiLdoSl6kd4y/x4oKIUJ57Q1ffhJPeVFfoarcl1S0VX09S2RBu2DF0mJRvAivaFhCyx5DCacDSVVANRsa+Sf72/g8uP2YvrUfTMbXxYrK4ok+NYwmF/X4EVSpAQv0pMWz/b2vteu9h5X7axS98jrHwNwzmGjMxFZzigtjGyTa46Uq9UUvUhKNEUv0lOiVeuiyR3g37fD4tm0BMM8Ov9jTth3CCP7l2YuxhxQ4PdRGPBR3xICX4Gm6EVSpAQv0lOSVK1r+NtMDv/hs2yqa2Hhx1tV1CYFZYV+6puD4NMUvUiqNEUv0lOSVK0rbljP1mZvmnlzfQsz5iwB0MK6TpTF3lFOU/QiKdEIXqSnVI5M2BxbtQ5UuS4VZYWByD3hC7QPXiRFSvAiPWXKTPC1nyRLVLUOVLmuK6VF/sgIPqApepEUKcGL9JTxp4K/EAIlgEHlKH4U+HqHqnWgynVdKSsM0NAS8j4wKcGLpETX4EV6yjt/htYGuPBJ2OMYAHbMfhvear+oTpXrulZa6GdTXTMENEUvkioleJGe4By8cQ8MGg9jj440ORavqWXUgBLCYW9afnhVCdOn7qMFdl0ojy6yKyrQCF4kRUrwIj2h5k1Y9zZ8/k4wr4b6qx9u5oNP6vjxFydw5iGJF+BJYqVFfm+RXWVAI3iRFCnBi6RTu8p15l2Dj/j9q6voX1rAKQcNy1x8OaqsMDKC1zV4kZQpwYukS7RyXVtxGwd/+w4Eilk35lT+8d4GLjlmD4oL/BkNMxeVFgZoag3jfAFM++BFUqIEL5IuSSrXrZ/zXY5oKgNgcL+iDASW+6K3jA1ZgIBK1YqkRNvkRNIlSeW6wW5T2/c/fnq5StPugugd5UKoVK1IqtKa4M1sgJn9xczqzWyVmZ2bpN/fzKwu5qvFzJbEPP+RmTXGPP9MOuMU6REpVK5T1bpdE72jXND8KlUrkqJ0j+B/CbQAQ4DzgLvMbP/4Ts65k51z5dEv4BXgT3HdTo3pc1Ka4xRJvykzwdr/SiWqXKeqdd1XVuiN4IMEdDc5kRSlLcGbWRlwBnCjc67OOfcSMA84v4vXjQWOAX6frlhEMmLYRHBhKKoEjPUM4rrWSzpUrlPVuu4rjVyDDzqN4EVSlc5Fdp8Cgs655TFti4Bju3jdBcCLzrmP4tofNjMfsBCY7pxblLZIRXrC/Hu9bXFXvgnlg3htYQ1P/WkR4Nq6qGrdrimPXINvxadr8CIpSucUfTmwPa6tFujXxesuAO6PazsPGAuMAf4FPG1mVYlebGaXmdkCM1uwcePGboYskibNdbDoEdhvGpQPAuD4fQZjOEoL/RgwoqqEW08/UFXrdkFpZIq+1flV6EYkRekcwdcBFXFtFcCOZC8ws6OBocBjse3OuZdjHt5qZhfiTeM/EX8M59zdwN0AkydPdvHPi/SodoVtgAF7tj31pzdXEwzD4187gv2HV2YowPwQ3SbX6rSKXiRV6RzBLwcCZjYupm0CsLST11wIzHHO1XVxbAfYbsYnkl7RwjbR5A7wys9g8WzCYceDr61i8pj+Su5pEB3BtzhN0YukKm0jeOdcvZnNAW42s0uAicBpwJGJ+ptZCXAW8N9x7aOBUcB8vA8gVwLVwMvxxxDJqE4K23z6D15hm/8aV52BwPJPWWSbXHPYpyl6kRSle5vc14ES4BPgEeBy59xSMzvGzOJH6dOAbXjX2GP1A+4CtgI1wGeBk51zm9Mcq8juSaGwzZ/eXKPCNmkQ8PsoCvho1hS9SMrSWqrWObcFL3HHt7+Itwgvtu0RvA8B8X2XAgelMy6RHlE5sv30fERsYZum1jB3PL1MC+vSoKwooBG8SDeoVK3Irpoy07u7WQwVtuk5pYV+mkOmEbxIipTgRXbVftMgUAKBYlTYpueVFQZoCkcK3ThtmBHpiu4mJ7Kr3psHLTvgvMdg3Im8trCGvz2mwjY9pazIT1NTZDNNOAR+/fcl0hmN4EV21Rv3QP89YK8pAJw2cTiDyosI+EyFbXpAWVGAxlDkvyyVqxXpkj4Ci+yKdYth9Wtw0g/A5yWdBau2sra2iR/+94Gce/joDAeYf0oL/TSGoiN4XYcX6YoSvEh3tKtcZ1BY1vbUA698REVxgGmThmcuvjxWVhigIZrgtZJepEtK8CKpilauaytu4+DpGVBYxoaxX+Dv76znoiPHtlVdk/QqLfLTEIxO0WsEL9IV/U8kkqrOKtc1eSP5oZXFGQisbygrClAfBPwowYukQIvsRFKVQuW6O59Zrsp1PcTbJhf5L0tT9CJdUoIXSVXlyITNsZXrGltD3PH0st6KqM+Yu7CG3760wrubHPCPdxJ/2BKRnZTgRVI1ZSZY+18ZVa7reXMX1jBjzhJqG4MEI1cVf/bMe5opEemCErxIqkYeCi4MRRWocl3vuePpZTS2hgAIRv7LCgZbNVMi0gUtshNJ1YLfgvnhf16HiuG8trCGp2arcl1Pi50RCeJN0QcIaqZEpAsawYukoqUB3noQxp8CFd4+92PGVQOOskK/Ktf1oNgZkegUfQEhzZSIdEEjeJFUvPNnaNoGh13W1vTo/NWEHMz9n6MYN6Rf5mLLc9On7sOMOUtobA21TdGXBtBMiUgXlOBFOhNbuc4XgO1rAQiGwjz02iqO2nugknsPi86I/PCv7xGs8/7LuvyY0RytmRKRTmmKXiSZaOW62tXe43DQe7x4Nv94dwPrapu48IixGQ2xr5g2aQR/vvxIWiPX4I/eszLDEYlkP43gRZLppHLd5U0/w+8z6ppUUa23lBUF2hbZqZKdSNc0ghdJpovKdaGw4/q572g/di8pLfQTUoIXSZkSvEgyqlyXVYoCPoIWSfAqVSvSJSV4kWSOvwGwdk2qXJc5ZkZBQZH3QCN4kS4pwYskU1gKOCitRpXrskOgoMD7RiN4kS5pkZ1IMvPvgcpRcNUi8Pl55c01PPGnRe26qHJd7yooKIQgGsGLpEAjeJFEPnkfVv4bJl8MPu+6b1lxAAcMKCtU5boMKSiMTtFrBC/SFY3gRRKZfy/4i+DgC9qa7n/5I0ZUlfDC9OMI+PXZOBMKCwu9b0IawYt0Rf9LicRaPBt+sp83Pe/zw4f/BOD99dt5dcVmzj9ijJJ7BhVFE7ym6EW6pBG8SFS0cl20uE1rA8HHr+SWeUu5v+4wACqK9SuTSW0jeE3Ri3QprUMRMxtgZn8xs3ozW2Vm5ybpN8vMWs2sLuZrz5jnJ5rZm2bWEPlzYjrjFEkoQeW6QKiJS1oeanv8/SffU2GbDCoqKva+0Sp6kS6le67xl0ALMAQ4D7jLzPZP0vePzrnymK8VAGZWCDwOPAT0Bx4AHo+0i/ScJJXrhtvmtu9V2CazNEUvkrq0JXgzKwPOAG50ztU5514C5gHnd/NQx+FdOvipc67ZOfdzvGojJ6QrVpGEUqhcBypsk0mlRQWEnCnBi6QgnSP4TwFB59zymLZFQLIR/KlmtsXMlprZ5THt+wOLnXMupm1xJ8cRSY8j/qdDU6LKdSpskzklhQGCBHBBTdGLdCWdCb4c2B7XVgskuln2bGA8MAi4FJhpZufEHKc2xeNgZpeZ2QIzW7Bx48ZdjV0E6iP/fvoNA4yGkmF8N9i+cp0K22RWaaGfVvwEgy2ZDkUk66UzwdcBFXFtFcCO+I7OuXedc2udcyHn3CvAz4Azu3ucyLHuds5Nds5NHjRo0G6dgPRhwWZ48wHY53Pw7fdh1jY+Ov8N5oaOpqI4oMI2WaKs0E8IH0GN4EW6lM49P8uBgJmNc879J9I2AViawmsdO+/qsRT4tplZzDT9QXgL+ER6xruPQ8MmOOzStqb7X1lJSYGfF79zApWlBRkMTqJKCgO0EsDXqhG8SFfSNoJ3ztUDc4CbzazMzI4CTgMejO9rZqeZWX/zHAZ8A2/lPMDzQAj4hpkVmdkVkfZ/pitWkTaLZ8P/HgBzLgVfAOq8afot9S3MfXstpx88Qsk9i5QW+gniJ6QEL9KldFft+DpwH/AJsBm43Dm31MyOAf7mnCuP9Ds70q8IWAP8yDn3AIBzrsXMpgH3ArcB7wHTnHP6jZb0ii9sEw7Ck1eBGY9sPpiWYJiLjhyb0RClvbYEr2vwIl1Ka4J3zm0BpiVofxFv8Vz08TnxfeL6LwQOSWdsIh0kKGxDayPr5nyXO5p+RlHAx9K12xk3JOH6TsmA0sIAQecnFNQ2OZGuqKi29F1JCtsMcZsAaA6GmTFniSrXZZHoCD6sEbxIl5Tgpe9KobCNKtdll+g2ubBK1Yp0SQle+q4TbmDn5g1PosI2qlyXPUoLA4Twq9CNSAqU4KXvKukPOCgdCBjrGcR1re0L24Aq12WTkugUve4mJ9Il3ftS+q437oHyofDNd8BfwNOvrGTevHfbdVHluuwSnaInpEV2Il3RCF76pi0r4INn4ZCLwO/tc99U5y3cGlJRpMp1WarA7yNEAKdr8CJd0ghe+qb5vwWf30vwQFNriIdf/5jPjB/CvRdOzmxs0inn8+tuciIp0Ahe+pbFs+En+8OrvwBfAXz0IgDz3l7LlvoWLj56bGbjky45XwHoGrxIlzSCl74jvnJdsJHg41dyy7yl3F93GAGfsaG2KbMxSpecL4BpBC/SJY3gpe9IULkuEGrikpaHAAiGHd/9yzsqbJPtfAVK8CIpUIKXviNJ5brhtrntexW2yX6mEbxISpTgpe9IoXIdqLBN1vMH8DkleJGuKMFL33H0Nzs0Japcp8I22c38BUrwIilQgpe+o6nW+7N8KGDUFw/rULlOhW2yn5fgQ5kOQyTraRW99A3hECz4HYw9Bi56EoBHXlzBvKfeY1C/IjbtaGZ4VQnTp+6jwjZZzucvwI9G8CJdUYKXvuE/z0DtxzD1FgCCoTC/e/kjDhs7gNlfOyLDwUl3WKCAgEbwIl3SFL30DW/cA/2GwT6fB+DZ9zZQs61RhW1ykN9fSIAQraFwpkMRyWpK8JLfFs+GO/eFD5+DlnpYOgeA+176iJH9Szhxv6EZDlC6yxcI4CdEQ4tG8SKdUYKX/BWtXLdjnfe4eTvBx6/khptn8sZHW9jR1MoTi9ZmNkbptkBBIQWEaFSCF+mUErzkrySV674WfBiA2sYgM+YsUeW6HOMPFOIzR0NTc6ZDEclqSvCSv1S5Li8FAt7tfRubdN8Akc4owUv+UuW6vBQoLASgsbklw5GIZDcleMlfB5/foUmV63JfoMBL8E3NGsGLdEYJXvLX1lXgK4SKEYCxpWCIKtflgYJogtc1eJFOqdCN5KeGLfDOn2HSeXDqTwmHHWf+5AVaA2FGOMfabU2qXJejCiNT9E0tmqIX6YwSvOSnt/8AwSY49CsAPL/8E1ZsqudnZ0/ktIlK6LmsoKAIgGZN0Yt0SlP0kn/CYVjwWxh1OAw9EIB7X1zJ0IpiPnfgsAwHJ7ursMgbwTc3a4pepDNpTfBmNsDM/mJm9Wa2yszOTdJvupm9Y2Y7zGylmU2Pe/4jM2s0s7rI1zPpjFPy2OLZcOenYMsK2PQf5s/7DYf+4Fle+XAzDS1Bnlq8LtMRym6KjuBbNEUv0ql0j+B/CbQAQ4DzgLvMbP8E/Qy4AOgPfBa4wszOjutzqnOuPPJ1UprjlHwUrVxXv9F73LiFA968gSPqnwNge5MK2+QDn9+7sqgRvEjn0pbgzawMOAO40TlX55x7CZgHdNir5Jy73Tn3lnMu6JxbBjwOHJWuWKSPSlC5rsRa+E5gdttjFbbJAz6v0E1rq0bwIp1J5wj+U0DQObc8pm0RkGgE38bMDDgGWBr31MNmttHMnjGzCWmMU/JVCpXrQIVtcp5fCV4kFelM8OXA9ri2WqBfF6+bFYnjdzFt5wFjgTHAv4Cnzawq0YvN7DIzW2BmCzZu3Nj9qCV/VCZeHR9fuU6FbXKczw/oGrxIV9KZ4OuAiri2CmBHsheY2RV41+I/75xru6DmnHvZOdfonGtwzt0KbMMb5XfgnLvbOTfZOTd50KBBu3sOksvGf6FDU3zlOhW2yQORKfqgRvAinUpngl8OBMxsXEzbBDpOvQNgZhcD1wFTnHOJ51Z3cngL80SS2/QfKKqEypE4jPU2iDsKv86bFZ/BgBFVJdx6+oEqbJPr/ErwIqlIW6Eb51y9mc0BbjazS4CJwGnAkfF9zew84IfA8c65FXHPjQZGAfPxPoBcCVQDL6crVslDW1fBB8/Cf02HE67nH0vXc9mDb/KLcydx00HDMx2dpJNG8CIpSfc2ua8DJcAnwCPA5c65pWZ2jJnVxfS7BRgIzI/Z6/7ryHP9gLuArUAN3ja6k51z7VdKicR66wEwg4MvALzCNiOqSvjs/kMzHJikXeQafDDYmuFARLJbWkvVOue2ANMStL+Itwgv+niPTo6xFDgonXFJngu1wsKHYNxJzF3p4wdPPcvGumYqSwI8uXidpuTzTWSKPhTUCF6kM6pFL7lr8Wxv73vtagCWh4YyY84SGltDANQ2eoVtACX5fBKZog9ril6kU6pFL7kpWrUuktwBRn34B04MvdCumwrb5KHIFH041IpzLsPBiGQvJXjJTYmq1tG+al2UCtvkmcgUvZ8QzcFwhoMRyV5K8JKbUqxaBypsk3ciU/QBQtQ3BzMcjEj2UoKX3FQ5MmFzfNU6FbbJQ/6dCb6hJZThYESylxK85KYpM8Ff2K6pkSIeLL2AEVUlKmyTzyLX4AOE2hZUikhHWkUvuemgs+C1X8O6heAc9SVDmVH735x57teZ8SmVLM5rmqIXSYlG8JKb6jfD+sVw2FdxN23lvwt/w/LBJ3PMuOpMRyY9LTJFX0CIRk3RiySlEbzkpiV/gnArFy4cxwsv/BWA8w4fhXf3YclrPl2DF0mFRvCSk7a9+jvecXvywvadpWj//FYNcxfWZDAq6RU+Hw7DbyHqWzRFL5KMErzknnWLqKp9n0eDx7ZrbmoNq6hNX+Ev0BS9SBc0RS+5I6Y0rXPQ6jp+PlVRmz7CV6ApepEuKMFLboiWpo1UrzODmwoepLG1iHnho9u6qahNH+HzU0BQU/QindAUveSGBKVpS619aVoVtek7zF9AgYU1ghfphEbwkhs6KU1reCP36VP3UVGbvsJXQLFfCV6kM0rwkhsqR7a7c1xUqN9wVn7v8xkISDLKX0CxL0yDpuhFktIUveSGKTOhoP319WYrouCkWZmJRzLL56fI5zSCF+mEErzkhoPOYv6B3yOID+dgTbia5/a+3itZK32Pr4Ain7bJiXRGCV5ywtyFNVw4fxQh5+M3oVM5uuXnfPv9fVTYpq/yF1BkYa2iF+mEErzkhDueXkZZ6xaKLEhN5Jawja0hFbbpq3x+CjWCF+mUErzkhLXbGhlpmwCocdXt2qUP8mmbnEhXlOAlJwyvKmG4bQbaJ3gVtumj/AUUKsGLdEoJXnLC9Kn7MNK3EdiZ4FXYpg/zebXotU1OJDntg5ecMKJ/CbVsYjtl1FPKCBW26dt8fgIWol4jeJGklOAlJ9z1/IdcFNhC+eCxrPy6Ctv0eZG7ybUEw4TCDr/PMh2RSNZRgpesNXdhDXc8vYy12xpxwPcrtuKr0pS84N1NzrzRe0NLkH7FBRkOSCT76Bq8ZKW5C2uYMWcJNZHkDlDRvI4Vrf0zGpdkCX+AgPOuv2uhnUhiaU3wZjbAzP5iZvVmtsrMzk3Sz8zsR2a2OfL1IzOzmOcnmtmbZtYQ+XNiOuOU7HfH08tobN35H3cF9fSzRv66WiM1AXwBWlpbAfj0D5/jqNv+qaJHInHSPYL/JdACDAHOA+4ys/0T9LsMmAZMAA4CTgW+CmBmhcDjwENAf+AB4PFIu/QR8fvbo1vk3muozEQ4kmVW17bS2NQEgANqtjUyY84SJXmRGGlL8GZWBpwB3Oicq3POvQTMA85P0P1C4E7n3BrnXA1wJ3BR5Lnj8NYG/NQ51+yc+zlgwAnpilWyX/z+9hHmbZFrKdeqeYHF6xrw035qXpUNRdpL5wj+U0DQObc8pm0RkGgEv3/kuUT99gcWO+dczPOLkxxH8tT0qfu0Wxk9IlLF7vTjP52pkCSL7Gh2FNBxD7wqG4rslM4EXw5sj2urBfol6Vsb1688ch0+/rnOjoOZXWZmC8xswcaNG3cpcMk+x4yrxnCUFPgxYN/ibYR8hZx8+EGZDk2yQGFREX7CHdpV2VBkp3Qm+DqgIq6tAtiRQt8KoC4yau/OcXDO3e2cm+ycmzxo0KBdClyyz30vryTk4Ikrj2blbZ/n3H0Mf9Uo8Gnjh8CEMdUUxE3Rq7KhSHvp/N9yORAws3ExbROApQn6Lo08l6jfUuCg2FX1eAvxEh1H8lBtYyu/f2UVJx8wlL0Hl0caV0PVqMwGJlljryFVlAV2juBHVJVw6+kHqrKhSIy0FbpxztWb2RzgZjO7BJgInAYcmaD774Fvmdlf8RbBfhv4v8hzzwMh4Btm9mvg0kj7P9MVq2SnaGGbmsh11PHDYiZyatfAuBMzFJlkHV+AAGEG9SviM+MHc+vpunQjEi/d851fB0qAT4BHgMudc0vN7Bgzq4vp9xvgCWAJ8A7wVKQN51wL3ha6C4BtwMXAtEi75KnYwjZRv/rXh962p9YmqNsAlaMzGKFkFX8BhFsZWFbI5jr91yCSSFpL1TrntuAl5/j2F/EWz0UfO+A7ka9Ex1kIHJLO2CS7xRe2gZ3bnqaNHuM1aIpeonwF4MIMKAmwtUEJXiQRrViSrJBse9PabY2w7WPvQaUSvET4/AAMKvWxpV4JXiQRJXjJCsm2Nw2vKvEW2IFG8LKT3ytZPLDUrwQvkoQSvGSFqz8zrkNb27anbasBgwqtkJYIXzTB+9jW2Eoo7Lp4gUjfowQvWaGu2atKVl1eiBG37al2DfQb1jZqE4n+WxhQDM55WytFpD3dD14yrqk1xK9f+JDD9hjA7K8e0bGD9sBLvMg1+AGl3p9b6psZUKb7UYnEUoKXjInf937GISMTd9z2MYw8tBcjk6wXmaIfUORNQm6p1wheJJ6m6CUjEu17/91LKzve7jMcgu01GsFLe5Ep+spi79q7FtqJdKQELxmReN97uOPtPnesh3BQW+SkPZ83+VhV5FW0VoIX6UgJXjKi033vUYtnw93Hed//64feYxFoS/CVhV6CV7EbkY6U4CUjOt33Dl4yf+IbUP+J97hhk/dYSV6gbYq+yBemrFB74UUSUYKXjLhqyt4d2trd7vO5m6E1bpTf2ui1i0QW2REK0r+sUAleJAEleMmILQ3equeE+97B2/ueSLJ26Vsi2+SiN5xRghfpSNvkpNftaGrl1y98yLGfGsQDFx+WuFPlyJ0lauPbRaJFj8IawYskowQvvSZ+3/shY6qSd54yE/7yNXAxK+0LSrx2kbYp+lYGlJbznw11nfcX6YM0RS+9ItG+97ueX9Fx33vUuBMBg8Iy78/KUXDqz+Ggs3olXslyMSP4AWWFWkUvkoBG8NIrOr3f+6QEN5FZ9Ci4IHz5XzDsoF6KUnJG2zV4b4q+oSVEU2uI4gJ/ZuMSySIawUuvSGnfe5RzsOB3MOIQJXdJLHaKPlKDXtfhRdpTgpde0eW+91gfvwqblsEhX+7hqCRntU3RK8GLJKMEL73ioiPHdmhrt+8dvCI2/3sA/O5kwHotNslBkUp2hIJtCV7X4UXa0zV46RWL1myjwGcMLC9iw/YmhleVMH3qPjuvv0cr17UVt3Hwt+kQKNLCOukomuDDQfqXagQvkogSvPS4xWu28eTidVx5wt58+6R9EnfqrHKdErzEi5miH6gpepGElOClx3j73t+nZlsTPoMRVcXJO6tynXRHzCK7ipICfAZbleBF2tE1eOkRO/e9NwEQdvC9J95Lvu89WYU6Va6TRNq2yYXw+4yq0kK26Bq8SDtK8NIjOtv3ntCUmWBxC+tUuU6SiZmiBxigcrUiHSjBS4/o1r538CrVOQcl/VHlOulSzBQ9wIBSJXiReLoGLz1iaGUx62qbOrQn2w/PK/8HJQPgm0uhsLSHo5OcF1OqFqB/WQEfbWrIYEAi2UcjeOkRB46o6NDWYd971KYPYNlf4dBLlNwlNRb5ryuS4AeUFbFZI3iRdtKS4M1sgJn9xczqzWyVmZ3bSd/pZvaOme0ws5VmNj3u+Y/MrNHM6iJfz6QjRuk9NdsaeWH5Jg4eVcWIqpLE93uHnYVtfnEI4KB8SKZCllxj5k3TR6foywrY2tCCcy7DgYlkj3RN0f8SaAGGABOBp8xskXNuaYK+BlwALAb2Ap4xs9XOuUdj+pzqnHs2TbFJL4m/HeypE4fz5aP2SNy5Q2Eb4B83QHGFrrtLavwFbYvs+pcWEgo7tjcFqSwpyHBgItlht0fwZlYGnAHc6Jyrc869BMwDzk/U3zl3u3PuLedc0Dm3DHgcOGp345DMSnQ72Nv/viz5trjOCtuIpMIXgJA3RT+wXMVuROKlY4r+U0DQObc8pm0RsH9XLzQzA44B4kf6D5vZRjN7xswmpCFG6WHd3hanwjayu3yBnYvsVK5WpIN0JPhyYHtcWy3QL4XXzorE8LuYtvOAscAY4F/A02ZWlewAZnaZmS0wswUbN25MPWpJq+5vi1NhG9lNMVP0bTecUYIXadNlgjez583MJfl6CagD4pdMVwA7ujjuFXjX4j/vnGuOtjvnXnbONTrnGpxztwLb8Eb5CTnn7nbOTXbOTR40aFBXpyM9ZGhl4jK0SbfFHfudjm0qbCPd4Stom6LXLWNFOuoywTvnjnPOWZKvo4HlQMDMxsW8bAIdp93bmNnFwHXAFOdcV3OyDt07NOuNHdhxe1vSbXEADZu9P8sHo8I2skt8/phtcpEEr3K1Im12exW9c67ezOYAN5vZJXir6E8DjkzU38zOA34IHO+cWxH33GhgFDAf78PHlUA18PLuxik9562Pt/Lqii0cv081yzfUs3ZbY8fbwcZqrvMK2+w1Bc6f0/sBS36ImaIvKfBTFPBpil4kRrq2yX0duA/4BNgMXB7dImdmxwB/c86VR/reAgwE5tvO2uMPOee+hnfd/i687XNNwNvAyc65zWmKU9Jo7sIabn/6fdZG7hY3df9h/O7Lo5O/YPFsb5V87Wrv8chDeydQyU8x++DNjIFlhSp2IxIjLQneObcFmJbkuRfxFuJFHyfZGA2RDwUHpSMm6VnRbXHRlfPe3eLepbjAn3jUnmjf+ys/g4F7aVpedk3MKnqA/mWFGsGLxFCpWtkl3d4Wp33vkm7+9gl+QJluGSsSSwledkm3t8Vp37ukW8wUPXh74TWCF9lJCV52SWVp4nKgSbfFad+7pJu/oMMIXtfgRXZSgpduW1fbSGNLEF/c5sVOt8UdcUXHNu17l90Rs00OvAS/oylIayicwaBEsofuBy8p824m8z4127z7vE+bOJz5H23telscwLpFYH5v3/uO9d7IfcpMLbCTXecrgJad94DvH61m19DC4H6JCy+J9CVK8JKS+FXzAE8v3dDxFrCJrF8Cix6BI6+Ek77fw5FKnxGzDx7gw0+84pmH/+C5rj9wivQBmqKXlHR71TzsvN/7r4/27t89YK8ejlL6lJi7yc1dWMMf3vDqKzigZlsjM+YsSX43Q5E+QAleUtLtVfPRfe/RojYuDE9f57WLpEPMPvg7nl5GS7D9tfcuP4CK5DkleElJWVHiqzlJV81r37v0tJgp+m5/ABXpA3QNXhLyFtQtY+22RgaUFVLXHMTvM0Jh19an01Xz2vcuPS3mbnLDq0qoSZDMk34AFekDNIKXDqIL6mq2NeKAzfUtGHDW5JGMqCrBgBFVJZ0vsOs3NHG79r1Luvj8bSP46VP3oaTA3+7pTj+AivQBGsFLB4kW1Dng38s38fJ1J3R9AOegqAJ2rGvfrn3vkk4xhW6iHzRvfvJdttS3UF1eyA2f30+r6KVP0wheOtjl65nRVfPfq4JNy2D0kd593nW/d+kJcaVqp00awbPfOhaAi4/eQ8ld+jyN4KWDXbqemehucesWKqlLz4krVQteNbu9B5czf+UWOC4zYYlkCyV4Adovqist9Hd4vsvrmZ2tmleCl54QV6o26tCx/Xly8TpCYYc/vp6ySB+iKXrpsKiuvsW7/l5VUpDagjrQqnnpfXFT9FGHjh3AjqYgyzfsyEBQItlDI3hJuKgOvL3vb990UmoHKR8Cdes7tmvVvPQUfwG4kLeo03aO1A8dOwCA+R9tYfywikxFJ5JxGsHL7hcJaa5L3K5V89KTfJFLSXGj+JH9SxhaUcwbK7dkICiR7KERfB8Ve83dzBsExeuySMji2d419mg52n0+591YpnaN7hYnPc9X4P0ZDgKFbc1mxqF7DOCNlZtxzmGm6/DSNynB90Hxd4ZLlNy7XFSXaNX8in9p1bz0Hn80wXe8Dn/Y2P48sWgta7Y2MmpAaS8HJpIdNEXfByW75u43S31RnWrNS6ZFR/ChjivpJ0euw2uaXvoyjeD7iNgp+QQDdgDCzrHyts+ndkCtmpdMi16DT7BVbp8h/agoDrBg1RbOOEQLPaVvUoLvA+Kn5JNJ/Zr7Gkj2MUGr5qW3dDJF7/MZI/uX8KcFa3j0jdUMryph+tR9VN1O+hQl+D4g2ZR8rF265h5Pq+alN7VN0XdM8HMX1rB8Qx3ByN0Pa7Y1MmPOEgAleekzlODzVCpT8gAGqY1uEl1zBzA/uLBWzUvv88euom/vjqeXtSX3qMbWEHc8vUwJXvoMJfg8lOqU/IiqkuR3h4udju83DHasTdzPhWHWtt0LWGRXdHINfrdrO4jkASX4PBE7YvcZhDobtpNgSj42oZf0h5Y6CLV4zyVL7qBr7pI5nUzR79INk0TyjBJ8johN4MOrSjh+30H86/2NrN3WSGVJAfUtQVojWb2z5B6dkv/pfv/h0OevgccTJPTGZFuLjHaL63TNXTKpk0V206fuk3AWq745yB7XPaVFd9InpC3Bm9kA4LfAScAmYIZz7g9J+s4CrgeaY5oPcs6tiDw/MXKs8cB7wFecc2+nK9auzJ/3G0a9dQeD3UY+sUGsHHA0e2x5qccerz54OkDSn7neqtkRmsQfbSHDizaxtqGa5xZM5Gu+t73HoWqes4lMKXyb4baJta6a58ITmeJr/3hqYBFD2QTWHxalktDjOe++7qpUJ9lg1cven/dM8f49jjsJ/vMM1K5hWuVIDtzzKMpWPcdgt5F1VPNsaCJTQm+3/Q79a84k1j6+kKFuU0Z+r7PhcS7EmIsxpxLj6oOnc+gXvtqjvyLmEpUx25UDmT2CVzjnK8BE4CngSOfc0gR9ZwF7O+e+lOC5QuA/wE+BXwFfBb4NjHPOtXQWw+TJk92CBQt26zzmz/sNB7x5AyW280fF3csi7Y+bnR/DKLTgLh+ju493SeUo+OY7u3kQkTRYPBsevwJCzV33jejp36ls+L3OxxhzMeZUYmx0hbxzyC27neTN7E3n3OREz6Wlkp2ZlQFnADc65+qccy8B84Dzd+Fwx+HNLPzUOdfsnPs53txwktVg6TXqrTvaJXfomBjT/bjIQu3+IfTGz+w2TcdLNnnu5m4ld+j536ls+L3OxxhzMeZUYiyxFka9dQc9KV2laj8FBJ1zy2PaFgH7d/KaU81si5ktNbPLY9r3Bxa79lMLi5Mdy8wuM7MFZrZg48aNuxp/m8Fu94+RF3wFUDIAMG/krhrzkk1UMVHywGC3qUePn65r8OXA9ri2WqBfkv6zgbuBDcDhwJ/NbJtz7pHIsWpTPZZz7u7IsZg8efJuX2/4xAYxlD6Y5H0FUNQPGrfq+rpkv8qRO+9iKJKjPrFqhvbg8VMawZvZ82bmkny9BNQBFXEvqwB2JDqec+5d59xa51zIOfcK8DPgzMjT3TpWuq0+eDqNrrBdW/wyhXQ/bnZ+Wlyg0z4dHtP54y7Fj9Cn/QquXentaf/mO0rukt2mzPQuG3VDh9+ZbPy97uXHuRBjLsacSoyNrrBtMV5PSSnBO+eOc85Zkq+jgeVAwMzGxbxsAtBhgV2yH4F3nZ3Iaw6y9jdxPqgbx9oth37hq7xzyC2sZxBhZ6xnEK8N/O8efbz4kFtZdMgPO+2zYuzZXiKOJGSb/JVOH9PVYyV0yWUHneVdNurGv/n435EVY8/O+O91ph/nQoy5GHMqMaZjgV1X0rmK/lG8RH0J3ir6v5J8Ff1pwL+BbcChwF+A7zrnHohZRf8T4NfApcB0emkVvYiISK7o8VX0EV8HSoBPgEeAy6PJ3cyOMbO6mL5nAx/gTbv/HviRc+4BgEgSnwZcgPcB4GJgWlfJXURERHZKW6Eb59wWvMSc6LkX8RbPRR+f08WxFgKHpCs2ERGRviadI3gRERHJEkrwIiIieUgJXkREJA8pwYuIiOQhJXgREZE8pAQvIiKSh5TgRURE8pASvIiISB5KW6nabGBmG4FVaTxkNdCz9/PrPTqX7JVP56NzyU75dC6QX+ezu+cyxjk3KNETeZXg083MFiSr8ZtrdC7ZK5/OR+eSnfLpXCC/zqcnz0VT9CIiInlICV5ERCQPKcF37u5MB5BGOpfslU/no3PJTvl0LpBf59Nj56Jr8CIiInlII3gREZE8pAQvIiKSh/p0gjezAWb2FzOrN7NVZnZukn5mZj8ys82Rrx+ZmfV2vJ3pxrnMMrNWM6uL+dqzt+PtjJldYWYLzKzZzO7vou83zWy9mW03s/vMrKiXwkxJqudiZheZWSjufTmu1wJNgZkVmdlvI/++dpjZ22Z2cif9s/29Sfl8cuT9ecjM1kX+vpeb2SWd9M329yalc8mF9yXKzMaZWZOZPZTk+bTnmT6d4IFfAi3AEOA84C4z2z9Bv8uAacAE4CDgVOCrvRRjqlI9F4A/OufKY75W9FqUqVkL3ALc11knM5sKXAdMAcYAewLf6/Houielc4l4Ne59eb5nQ+u2ALAaOBaoBG4AZpvZ2PiOOfLepHw+Edn+/twKjHXOVQBfAG4xs0PiO+XIe5PSuURk+/sS9UtgfifPpz3P9NkEb2ZlwBnAjc65OufcS8A84PwE3S8E7nTOrXHO1QB3Ahf1WrBd6Oa5ZD3n3Bzn3FxgcxddLwR+65xb6pzbCnyfLHpfoFvnkvWcc/XOuVnOuY+cc2Hn3JPASiDRf7y58N5053yyXuTvujn6MPK1V4KuufDepHouOcHMzga2Ac910i3teabPJnjgU0DQObc8pm0RkGjUu3/kua76ZUp3zgXgVDPbYmZLzezyng+vxyR6X4aY2cAMxbO7JpnZpsiU5I1mFsh0QJ0xsyF4//aWJng6596bLs4HcuD9MbNfmVkD8D6wDvhrgm458d6keC6Q5e+LmVUANwPf6qJr2vNMX07w5cD2uLZaoF+SvrVx/cp39/pIGnXnXGYD44FBwKXATDM7p2fD6zGJ3hdIfN7Z7t/AAcBgvNmYc4DpGY2oE2ZWADwMPOCcez9Bl5x6b1I4n5x4f5xzX8f7Oz4GmAM0J+iWE+9NiueSC+/L9/FmTNZ00S/teaYvJ/g6oCKurQLYkULfCqDOZU8RgZTPxTn3rnNurXMu5Jx7BfgZcGYvxNgTEr0vkPg9zGrOuRXOuZWRqeIleJ/4s/J9MTMf8CDemo8rknTLmfcmlfPJpfcn8rv9EjASSDRDlzPvTVfnku3vi5lNBD4D/G8K3dOeZ/pygl8OBMxsXEzbBBJPzy2NPNdVv0zpzrnEc0C2zER0V6L3ZYNzLuevd5Ol70tkNPFbvMWcZzjnWpN0zYn3phvnEy8r3584ARJft86J9yZOsnOJl23vy3HAWOBjM1sPXAOcYWZvJeib/jzjnOuzX8CjwCNAGXAU3pTI/gn6fQ14DxgBDI/8pX8t0/Hv4rmcBvTH+yU4DKgBLsx0/HExBoBivJW0D0a+DyTo91lgPbAfUAX8E7gt0/Hv4rmcDAyJfL8v8A5wU6bjTxDnr4HXgPIu+mX9e9PN88nq9wdvivpsvGlePzAVqAe+kGvvTTfPJdvfl1JgaMzXj4HHgEEJ+qY9z2T8LyDDf/kDgLmRfzwfA+dG2o/BmxqJ9jPgdmBL5Ot2ImV+s+WrG+fyCN6K7jq8xSvfyHTsCc5lFjtXzka/ZgGjI3GPjun7LWAD3hqE3wFFmY5/V84l8ou/IfL+rcCbaizIdPxx5zImEn9TJPbo13k5+t6kfD7Z/v7gral5AW+l9nZgCXBp5Lmcem+6cy7Z/r4kOLdZwEOR73s8z6gWvYiISB7qy9fgRURE8pYSvIiISB5SghcREclDSvAiIiJ5SAleREQkDynBi4iI5CEleBERkTykBC8iIpKHlOBFRETy0P8HbxPe7Kocrr8AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x,UTXRus[-1,:-1],'-o',label=\"Lax-Friedrichs\")\n", "plt.plot(x,UTXGod[-1,:-1],'-o',label=\"Godunov\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 8.** Program the local Lax-Friedrichs scheme for the Burgers equation:\n", "> $$F_{j+1/2}^n = \\dfrac{1}{2}(f(U_j^n)+f(U_{j+1}^n)) - \\dfrac{\\sigma_j^n}{2}(U_{j+1}^n-U_{j}^n),$$\n", "> with $\\sigma_j^n = \\max\\big\\{|f'(u)|,\\ u \\in[\\min(U_j^n,U_{j+1}^n),\\max(U_j^n,U_{j+1}^n)]\\big\\}.$ \n", "> Compare the solution to the previous schemes." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "## Time iterations ##\n", "while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x,UTXRus[-1,:-1],'-o',label=\"Rusanov\")\n", "plt.plot(x,UTXGod[-1,:-1],'-o',label=\"Godunov\")\n", "plt.plot(x,UTXLocLF[-1,:-1],'-o',label=\"Local Lax-Friedrichs\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> **Question 9.** Solve a Cauchy problems for the nonlinear equations with flux $f(u)= 2 u^3 -u$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def FLUX(u):\n", " return 2*u**3-u, 6*u**2-1\n", "up = np.linspace(-1,1)\n", "plt.plot(up,FLUX(up)[0])\n", "plt.show()\n", "\n", "\n", "def u0(x):\n", " return -1*(x<1)-0.75*(x>=1)*(x<2)+0.25*(x>=2)*(x<3)-0.5*(x>=3)\n", "x = np.linspace(0,4)\n", "plt.plot(x,u0(x),label='u0')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# PDE problem\n", "T = 1.25 # final time\n", "L = 4 # space length\n", "Flux = FLUX # flux function\n", "mu = 0.9 # cfl parameter\n", "\n", "J = 1200 # number of points\n", "\n", "# Discretization parameters\n", "dx = L/J\n", "x = np.linspace(0, L, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "## Initialize\n", "U = u0(x)\n", "t = 0\n", "UTX = np.concatenate([[x.copy()],[U]],axis=0)\n", "LT = [t,t]\n", "\n", "F,dF = Flux(U)\n", "Vmax = max(np.abs(dF)) # get a bound for velocities (to adapt depending on the properties of f)\n", "dt = mu*dx/max(1,Vmax) # max(1,Vmax) to avoid very large dt (bad for accuracy)\n", "\n", "## Time iterations ##\n", "while t