{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Fluid Dynamics\n", "==============\n", "\n", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "This numerical tour explores fluid dynamics for image generation." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from __future__ import division\n", "\n", "import numpy as np\n", "import scipy as scp\n", "import pylab as pyl\n", "import matplotlib.pyplot as plt\n", "\n", "from nt_toolbox.general import *\n", "from nt_toolbox.signal import *\n", "\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Velocity Flow Field\n", "-------------------\n", "A velocity flow is simply a 2-D vector field $V = (V_i)_{i=1}^N \\in \\RR^{n \\times n \\times 2}$\n", "where $V_i \\in \\RR^2$ is one of the $N=n \\times n$ vectors at a position indexed by $i$.\n", "\n", "\n", "It can be generated as a realization of Gaussian process.\n", "The blurring creates correlations in the flow." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 128 # grid size" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "t = np.linspace(0,1,n)\n", "[Y,X] = np.meshgrid(t,t)\n", "gamma = .05 # blurring size\n", "xi1 = np.exp(-(X-Y)**2/gamma)\n", "xi = lambda x: np.dot(np.dot(xi1,x),xi1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from numpy import random\n", "n = 128\n", "V = np.random.randn(n, n, 2)\n", "for k in range(2):\n", " V[:,:,k] = xi(V[:,:,k])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Subsampling display operator." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from nt_toolbox.plot_vf import * \n", "myplot = lambda V: plot_vf(V[np.ix_(np.arange(0,n,6),np.arange(0,n,6),np.arange(2))])" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We can display the vector field using arrow." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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wjC2vh+LP6cb5GbYMGSG0BJm4GjgsWGZwKbB8ZCyqDMISYG4JBMcJWEbnsSJs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\n8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (7,7))\n", "myplot(V)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We can renormalize the flow, which enhances the singularities. It defines\n", "$\\tilde V$ as $\\tilde V_i = V_i/\\norm{V_i}$." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "normalize = lambda V: V/(np.repeat(np.maximum(1e-9*np.ones(np.shape(V)[:2]), np.sqrt(np.sum(V**2, 2)))[:,:,np.newaxis],2,axis=2))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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+XYjwL6BP+OePwC6eGWUikUgkjGINar9hSQiTNbKuJfQ4/BqrqRof9gVix9Mf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize = (7,7))\n", "myplot(normalize(V))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Incompressible Flows\n", "--------------------\n", "An incompressible flow has a vanishing divergence. The set of vector\n", "incompressible flow defines a sub-space of $\\RR^{n \\times n \\times 2}$\n", "$$ \\Ii = \\enscond{V}{ \\text{div}(V)=0 }\n", " \\qwhereq \\text{div}(V) = \\pd{V}{x_1} + \\pd{V}{x_2} \\in \\RR^{n \\times n}. $$\n", "Here $\\pd{}{x_s}$ for $s=1,2$ are finite differences approximation of\n", "the horizontal and vertical derivative operators (we suppose here periodic boundary conditions).\n", "\n", "\n", "\n", "The orthogonal projection $U = \\text{Proj}_{\\Ii}(V)$ on $\\Ii$ is\n", "computed by solving a Poisson equation\n", "$$ U = V-\\nabla A \\qwhereq \\Delta A = \\text{div}(V). $$\n", "\n", "\n", "This is especially simple for periodic boundary conditions since $A$ can\n", "be computed over the Fourier domain as\n", "$$ \\forall \\om \\neq 0, \\quad \\hat A(\\om) = \\frac{\\hat Y(\\om)}{\\mu(\\om)}\n", " \\qwhereq Y = \\text{div}(V) \\qandq\n", " \\mu(\\om_1,\\om_2) = -4 \\sin(\\om_1 \\pi / n)^2 -4 \\sin(\\om_2 \\pi / n)^2 $$\n", "and $\\hat A(0)=0$.\n", "\n", "\n", "\n", "Compute the kernel $\\mu(\\om)$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Y, X = np.meshgrid(np.arange(0,n),np.arange(0,n))\n", "mu = np.sin(X*np.pi/n)**2\n", "mu = -4*(mu + np.transpose(mu))\n", "mu[0,0] = 1" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a = np.hstack((np.arange(1,n),[0]))\n", "b = np.hstack(([n-1],np.arange(n-1)))\n", "Grad = lambda f: np.dstack( (f[a,:]-f, f[:,a]-f) )\n", "Div = lambda v: v[b,:,0]-v[:,:,0] + v[:,b,1]-v[:,:,1]\n", "Delta = lambda g: (g[a,:] + g[b,:] + g[:,a] + g[:,b]) - 4*g\n", "DeltaV = lambda V: np.dstack( (Delta(V[:,:,0]), Delta(V[:,:,1])) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Computation of $A$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "#from nt_toolbox.div import *\n", "#A = lambda V: np.real(pyl.ifft2(pyl.fft2(Div(V[:,:,0], V[:,:,1], bound=\"per\"))/mu))\n", "A = lambda V: np.real(pyl.ifft2(pyl.fft2(Div(V))/mu))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Projection on incompressible flows." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "ProjI = lambda V: V + Grad(A(V))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display $U=\\text{Proj}_{\\Ii}(V)$." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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+xJwTkt93nyLdCluLuSm6tdw3dhwFXJlhmzrAicCATL32h8mwrubknH7MUU/R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\nOUSra82foNHO7XOGYv5uSc7OoLO4Fcq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WloDmWoeBPl+18/E7Opthnej2QZ3+oK8Qd6Xf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\nI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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "U = ProjI(V)\n", "plt.figure(figsize=(7,7))\n", "myplot(U)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display $W=U-V$ the irrotational component of $V$." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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Njb/2+2AVVJVwh3QBFjo8ivRT9rLEBIAhrtJ/JtYAez5wS6KN2bBK2QNTFyHC9KnXFgpt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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7,7))\n", "myplot(V-U)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Note that the decomposition $V=U+W$ is called the Hoge decomposition of\n", "the vector field.\n", "\n", "\n", "Image Advection Along the Flow\n", "------------------------------\n", "A flow defines a warping operator that transport the content of an image\n", "along the streaming of the flow.\n", "\n", "\n", "We load an image $f$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "f = load_image(\"nt_toolbox/data/hibiscus.bmp\", 2*n)\n", "f = f[np.ix_(np.arange(n-n//2,n+n//2),np.arange(n-n//2,n+n//2))]" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Given some vector field $U$, the warping operator $f_1 = \\Ww_U(f)$\n", "along the flow is defined\n", "$$ f_1(x) = f(x+U(x)) $$\n", "i.e. it advects the values of $f$ by the vector field $U$ to obtain the values of $f_1$.\n", "\n", "\n", "We define $U$ as a scaled normalized incompressible flow." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "U = normalize( ProjI(V) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Helper function: enforce periodicity." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "periodic = lambda P: np.concatenate(((P[:,:,0]%n)[:,:,np.newaxis], (P[:,:,1]%n)[:,:,np.newaxis]), axis=2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Helper function: extend an image by 1 pixel to avoid boundary problems." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "extend1 = lambda f: np.hstack((f,f[:,[0]]))\n", "extend = lambda f: np.transpose(extend1(np.transpose(extend1(f))))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Helper function: bilinear interpolation on a grid." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "from scipy import interpolate\n", "\n", "def myinterp(P1,f1,Pi):\n", " return interpolate.griddata(P1, np.ravel(f1),(Pi[:,:,1],Pi[:,:,0]))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "First we compute the initial and wraped grids." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "Y, X = np.meshgrid(np.arange(0,n),np.arange(0,n))\n", "P = np.concatenate((X[:,:,np.newaxis],Y[:,:,np.newaxis]),axis=2)\n", "Y1, X1 = np.meshgrid(np.arange(0,n+1),np.arange(0,n+1))\n", "P1 = np.concatenate((np.ravel(Y1)[:,np.newaxis],np.ravel(X1)[:,np.newaxis]),axis=1)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Defines the warping operator $\\Ww_U$." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "W = lambda f, U: myinterp(P1, extend(f), periodic(P - U))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Display a warped image $\\Ww_{\\rho U}(f)$ for some scaling $\\rho$." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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GzTG8wuRWgdNmy12KZlU8CXi8ftb9HVuVS+wKL13CMLvBYHAI7ILZ2UNlRpFt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\nDs8OW3PMDYyF99maR2xbWra6BBOTakeblubKoUk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rho = 2\n", "plt.figure(figsize = (5,5))\n", "imageplot(W(f, rho*U))" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 1__\n", "\n", "Display $\\Ww_{\\rho U}(f)$ for various values of $\\rho$." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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kGCmuvtCuMku5tMhnz54d6agE3mc+08zHx7HoGE7+nv/vxq/Tg5Lt0rVkq8m2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\nVWvCmi1qhqpZcd4nyOUYcREALnqPx9HTojd+6tSp7r5UnCnTi2M+EYG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0HKZB6gLgjJPTebnfSYBWZP2tRDjHvCKHAN9EaMTdoOtClpIhbPD22Os4lZdbC+vj5oc+4Lhpdz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\nZTyKcabmYv7sJyK6WSvrNmwlO5ZPxS7COsD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/graphics_5_fluids/exo1" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 2__\n", "\n", "Define an iterative scheme via:\n", "$$ f^{(\\ell+1)} = \\Ww_{\\rho U}(f^{(\\ell)}). $$\n", "Display the result $f^{(\\ell)}$, which corresponds approximately to solving\n", "an advection equation at time $t=\\ell \\rho$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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OQJeE2M7r53mzWBLyst4u6aJDxdg5MeeImaoYqllGpxJH5xDXCm7Zi+C96CVn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\nb5SdbWoum+0iP1cVIwXk95Gyf4pVrpgpNRPUsQFLdVeAGg9Uz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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/graphics_5_fluids/exo2" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Fluid Dynamics\n", "--------------\n", "Fluid dynamics solves the incompressible Navier-Stokes equations to\n", "evolve in time the vector field.\n", "\n", "\n", "We discribe here a simple algorithm introduced in:\n", "\n", "\n", "J. Stam, _Stable Fluids,_\n", "SIGGRAPH'99, 1999, p. 121-128.\n", "\n", "\n", "It proposes a semi-implicit scheme for the resolution of the Navier\n", "Stockes equations for the movement of incompressible fluids\n", "$$\n", " \\pd{V}{t} =\n", " \\text{Proj}_{\\Ii}\\pa{\n", " -(V \\cdot \\nabla) V + \\nu \\Delta V + W\n", " }.\n", "$$\n", "Here $\\nu \\geq 0$ is the viscosity of the fluid,\n", "$W$ is a source term, $\\Delta$ is the Laplacian, and\n", "$-(V \\cdot \\nabla) V$ is the\n", "non-linear self-advection, where we have used the short-hand\n", "notation $V \\cdot \\nabla$ for the derivative operator along a flow $V$:\n", "$$ (V \\cdot \\nabla)U = ( V_1 \\pd{U_1}{x_1} + V_2 \\pd{U_1}{x_2},\n", " V_1 \\pd{U_2}{x_1} + V_2 \\pd{U_2}{x_2} ).$$\n", "\n", "\n", "In order to visualize the flow, we also advect and diffuse along the flow\n", "a density $g$ of particules, which is a scalar field. Once $V$ has\n", "been computed, it follows a linear PDE\n", "$$\n", " \\pd{g}{t} =\n", " -(V \\cdot \\nabla) g + \\mu \\Delta g + h\n", "$$\n", "with some initial condition at time $t=0$, where $h$ is a source for the density.\n", "\n", "\n", "In practice, we solve this PDE in parallel to the PDE for $V$.\n", "\n", "\n", "In the following, we use $W=0$ and $h=0$ (no sources).\n", "\n", "\n", "Set the viscosity $\\nu$ for the velocity field." ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "nu = 1/10\n", "mu = nu" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Extend the warping operator $\\Ww_U$ to work with vector fields as input.\n", "This will apply $\\Ww_U$ on each channel of the vector field (X and Y coordinates)." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "#Wt = lambda V, U: np.concatenate((W(V[:,:,0],U)[:,:,np.newaxis],W(V[:,:,1],U)[:,:,np.newaxis]),axis=2)\n", "Wt = lambda V, U: np.dstack( (W(V[:,:,0],U),W(V[:,:,1],U)) )" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We discretize the PDE's using some time step $\\tau$." ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "tau = .03" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The algorithm computes $V^{(\\ell)}$ at iteration $\\ell$\n", "which is an approximation of the PDE solution at time $\\ell \\tau$.\n", "It is computed itertatively as\n", "$$\n", " \\tilde V^{(\\ell)} = \\Ww_{\\tau V^{(\\ell)}}( V^{(\\ell)} )\n", " \\qandq\n", " V^{(\\ell+1)} = \\text{Proj}_{\\Ii}\\pa{ \\tilde V^{(\\ell)} + \\tau\\nu\\Delta \\tilde V^{(\\ell)} + \\tau W }\n", "$$\n", "\n", "\n", "It computes in parallel the evolution of the density as\n", "$$\n", " \\tilde g^{(\\ell)} = \\Ww_{\\tau V^{(\\ell)}}( g^{(\\ell)} )\n", " \\qandq\n", " g^{(\\ell+1)} = \\tilde g^{(\\ell)} + \\tau\\nu\\Delta \\tilde g^{(\\ell)} + \\tau h\n", "$$\n", "\n", "\n", "\n", "Set the initial field $V=V^{(0)}$ at time $t=0$." ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "U = ProjI(V)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "Set the initial density $g=g^{(0)}$ at time $t=0$." ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "g = np.copy(f)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The first step is to advect the vector field $V$ and $g$ along the flow $V$ itself.\n", "This corresponds to an implict discretization of the term\n", "$-(V \\cdot \\nabla) V$." ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "g = W (g, tau*U)\n", "U = Wt(U, tau*U)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We implement the Laplacian using finite difference." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The second step is to diffuse the vector field and the density." ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "U = U + tau*nu*DeltaV(U)\n", "g = g + tau*mu*Delta(g)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The last step is to ensure incompressibility of $V$ by projecting on $\\Ii$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "U = ProjI(U)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "__Exercise 3__\n", "\n", "Compute the fluid dynamic by iterating these steps." ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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srdNDnZ2d2XXJeP+ZLbrqH27tStUxl+E0b053t0uG7RcF7tlfy97N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\nsunOrlHIiA+nd+O5sh6IOjWyQfSIqEvQcWKydJxyRQnyhsR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nqM9Zq5C/15b3zrFJ5+fn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\nb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bRS1Wi+6uftllkwgDVjXDdeq1QxU0pz3B7D9uBQDFUFGYuVnbdGP5qxuoewWWamDMMw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\ntmKTUA7nJbtz586eh59F4zAybYiK1mrrx/VEmUp3lV2Tn0GP0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f3rX7/egkVne8e6PvbU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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "run -i nt_solutions/graphics_5_fluids/exo3" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "## Insert your code here." ] }, { "cell_type": "raw", "metadata": { "deletable": true, "editable": true }, "source": [ "" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.4.5" } }, "nbformat": 4, "nbformat_minor": 0 }