{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Finite difference schemes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "The PDE problem under consideration is the linear advection equation with velocity $a=1$:\n", "$$\n", " \\begin{aligned}\n", " \\partial_t u+ a\\partial_x u = 0,\\\\\n", " u(0,x) = u_0(x).\n", " \\end{aligned}\n", "$$\n", "\n", "\n", "The discretization parameters are denoted $\\Delta t>0$ and $\\Delta x>0$. The Courant number $\\mu := a\\Delta t/\\Delta x$ is a constant parameter to choose conveniently. The discrete initial data is $U^0_j=u_0(j\\Delta x)$ for $j\\in\\mathbb{Z}$, and $U_j^n$ will be an approximation of $u(n\\Delta t,j\\Delta x)$. Several finite difference one-step schemes are successively considered (but some of them are never stable !)\n", "\\begin{align}\n", " \\tag{L1}\n", " U_j^{n+1} &= U_j^n - \\dfrac{a\\Delta t}{\\Delta x}\\Bigl[U_j^n-U_{j-1}^n\\Bigr]\\\\[0.5em]\n", " \\tag{L2}\n", " U_j^{n+1} &= U_j^n - \\dfrac{a\\Delta t}{2\\Delta x}\\Bigl[3U_j^n-4U_{j-1}^n+U_{j-2}^n\\Bigr]\\\\[0.5em]\n", " \\tag{BW2}\n", " U_j^{n+1} &= U_j^n - \\dfrac{a\\Delta t}{2\\Delta x}\\Bigl[3U_j^n-4U_{j-1}^n+U_{j-2}^n\\Bigr]+\\dfrac{a^2\\Delta t^2}{2\\Delta x^2}\\Bigl[U_j^n-2U_{j-1}^n+U_{j-2}^n\\Bigr]\\\\\n", " \\ \\notag\\\\[0.5em]\n", " \\tag{C2}\n", " U_j^{n+1} &= U_j^n - \\dfrac{a\\Delta t}{2\\Delta x}\\Bigl[U_{j+1}^n-U_{j-1}^n\\Bigr] = U_j^n - a\\Delta t\\, (\\mathrm{D}_0U^n)_j\\\\[0.5em]\n", " \\tag{LW2}\n", " U_j^{n+1} &= U_j^n - \\dfrac{a\\Delta t}{2\\Delta x}\\Bigl[U_{j+1}^n-U_{j-1}^n\\Bigr] + \\dfrac{a^2\\Delta t^2}{2\\Delta x^2}\\Bigl[U_{j+1}^n-2U_{j}^n+U_{j-1}^n\\Bigr]\\\\[0.5em]\n", " \\ \\notag\\\\[0.5em]\n", " \\tag{C2-RK3}\n", " U_j^{n+1} &= U_j^n - a\\Delta t\\, \\mathrm{D}_0(U^n)_j + \\dfrac{1}{2} (a\\Delta t\\, \\mathrm{D}_0)^2(U^n)_j - \\dfrac{1}{6} (a\\Delta t\\, \\mathrm{D}_0)^3(U^n)_j\\\\[0.5em]\n", " \\tag{C2-CN2}\n", " U_j^{n+1} &+ \\dfrac{a\\Delta t}{2}\\, \\mathrm{D}_0(U^{n+1})_j = U_j^n - \\dfrac{a\\Delta t}{2}\\, \\mathrm{D}_0(U^n)_j\n", "\\end{align}" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pylab as plt\n", "\n", "plt.rcParams['font.size'] = 14.0\n", "plt.rcParams['figure.figsize']=[8,8]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Symbolic stability study" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### i. Symbol computations\n", "\n", "Determine *on the paper* the corresponding symbol functions $g(\\xi \\Delta x)$ in terms of the CFL parameter $\\mu$. \n", "For example the symbol of (L1) is\n", "$$g(\\theta)=1-\\mu(1-\\mathsf{e}^{-\\mathsf{i}\\theta}),\\quad \\theta\\in[-\\pi,\\pi].$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ii. Representation of the symbol\n", "\n", "Draw on the same figure, the complex curves $\\theta\\mapsto g(\\theta)$ with the choice $\\mu=0.95$. Also plot the unit circle $\\theta\\mapsto\\mathsf{e}^{\\mathsf{i}\\theta}$ on the same figure." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "theta = np.linspace(-np.pi,np.pi,500)\n", "c = np.exp(1j*theta) # for the unit circle and the parameterization of exponentials in formulas\n", "\n", "mu = 0.95\n", "gL1 = 1 - mu*(1-c**(-1)) \n", "\n", "plt.plot(np.real(c),np.imag(c), linestyle=('dashed'), linewidth=1, color=\"black\")\n", "for g in [gL1]:\n", " plt.plot(np.real(g),np.imag(g))\n", "plt.legend([\"Unit circle\",\"L1\"])\n", "plt.axis('square')\n", "plt.xlim(-1.5,1.5)\n", "plt.ylim(-1.5,1.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### iii. Stability domains\n", "\n", "Using the above representation, check numerically the following CFL uniform stability conditions $\\mathsf{Stab}=\\{\\mu\\in\\mathbb{R} \\text{ s.t.} \\|g\\|_\\infty\\leq 1\\}$ *(no mathematical proof is required here)*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " - L1 stable iff $\\mu\\in[0,1]$\n", " - L2 **unstable** for any $\\mu$\n", " - BW2 stable iff $\\mu\\in[0,2]$\n", " - C2 **unstable** for any $\\mu$\n", " - LW2 stable iff $\\mu\\in[-1,1]$\n", " - C2RK3 stable iff $\\mu\\in[-\\sqrt{3},\\sqrt{3}]$ (we did the exact computation together)\n", " - C2CN2 **stable for any $\\mu$**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Numerical simulations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PDE problem $\\partial_t u + a \\partial_x u =0$ is set over the periodic space domain $\\mathbb{T}$ (that is the torus $\\mathbb{R}/\\mathbb{Z}$ identified to the interval $[0,1]$ with the appropriate boundary conditions). \n", "At the discrete level, the space points $x_j = j\\Delta x$ are considered only for indices $0\\leq j\\leq J-1$. The integer $J$ is the \"main\" parameter and $\\Delta x$ is deduced from the scaling relation $J\\Delta x = 1$ ; the (independant) space points are then $x_j\\in[0,1[$ for indices $0\\leq j\\leq J-1$. \n", "The numerical boundary conditions are obtained by the periodicity property $U_{j+J}^n = U_j^n$ for any required integer $j$. \n", "The numerical solution is computed up to the time $T>0$. \n", "\n", "In the first tests, we consider the following initial data and parameters\n", "\\begin{equation*}\n", " u_0(x) = \\sin(2\\omega \\pi x),\\qquad \\omega = 4,\\quad J=100,\\quad T=2,\\quad \\mu=0.95.\n", "\\end{equation*}\n", "\n", "The following algorithm may help for your code:\n", "```python\n", "# Physical data\n", "a = 1\n", "T = 2\n", "# Initial data\n", "omega = 4\n", "u0 = lambda x: np.sin(2*omega*np.pi*x)\n", "# Numerical parameters\n", "J = 100\n", "mu = 0.95\n", "# Discretization parameters\n", "dx = 1/J\n", "dt = mu*dx/a\n", "# Space grid\n", "x = np.linspace(0, 1, J+1)\n", "x = x[0:-1] # removes the very last point for periodicity\n", "\n", "## Initialize\n", "t = 0\n", "U = u0(x)\n", "\n", "## Iterate in time\n", "while t" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "u0 = lambda x: [1-np.sign(y-0.0001)*np.sign(y+0.0001) for y in x]\n", "\n", "J = 400\n", "T = 0.25\n", "\n", "mu = 0.95\n", "\n", "plt.rcParams['figure.figsize']=[30,10]\n", "\n", "plt.plot([T % 1, T % 1],[0,1],'k',linewidth=4)\n", "for name_iteration in [L1,BW2,LW2,C2RK3,C2CN2]:#O3]:\n", " [x,U] = SCHEME(name_iteration,a,T,u0,J,mu)\n", " plt.plot(x,U)\n", "plt.legend([\"exact\",\"L1\",\"BW2\",\"LW2\",\"C2RK3\",\"C2CN2\"])#,\"O3\"])\n", "plt.title('transport of a Dirac like data – mu='+str(mu))\n", "plt.show()\n", "\n", "######################################################################\n", "\n", "mu = 0.10\n", "\n", "plt.rcParams['figure.figsize']=[30,10]\n", "\n", "plt.plot([T % 1, T % 1],[0,1],'k',linewidth=4)\n", "for name_iteration in [L1,BW2,LW2,C2RK3,C2CN2]:#O3]:\n", " [x,U] = SCHEME(name_iteration,a,T,u0,J,mu)\n", " plt.plot(x,U)\n", "plt.legend([\"exact\",\"L1\",\"BW2\",\"LW2\",\"C2RK3\",\"C2CN2\"])#,\"O3\"])\n", "plt.title('transport of a Dirac like data – mu='+str(mu))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Back to symbolic analysis\n", "\n", "We introduce the real-valued function $\\rho$ (positive) and $\\alpha$ such that the symbol is $g(\\xi\\Delta x) = \\rho(\\xi\\Delta x)\\, \\mathsf{exp}(-\\mathsf{i}\\xi\\Delta t\\,\\alpha(\\xi\\Delta x)).$\n", "The quantity $\\alpha(\\theta)$ is called the **phase velocity** for waves of frequency $\\theta$. We observe that if $\\rho(\\xi\\Delta x)=1$ then $g(\\xi\\Delta x)^n = \\mathsf{e}^{-\\mathsf{i} \\xi n\\Delta t\\, \\alpha(\\xi\\Delta x)}$. Assuming that the exact velocity $a$ is well approximated by $\\alpha(\\xi\\Delta x)$ this last quantity is $\\simeq \\mathsf{e}^{-\\mathsf{i} \\xi t_n a}$. \n", "\n", "Draw *numerically* on the same picture the dissipation factor $\\rho(\\theta)$ as a function of $\\theta\\in[-\\pi,\\pi]$ and on a second picture the dispersion factor $\\alpha(\\theta)$ for the two parameters $\\mu=0.95$ and $\\mu=0.10$.\n", "\n", "Interpret the above results from the observed properties." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.0" }, "vscode": { "interpreter": { "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49" } } }, "nbformat": 4, "nbformat_minor": 2 }