{ "cells": [ { "cell_type": "raw", "metadata": {}, "source": [ "Text provided under a Creative Commons Attribution license, CC-BY. All code is made available under the FSF-approved MIT license. (c) Lorena A. Barba, Gilbert F. Forsyth 2015. Thanks to NSF for support via CAREER award #1149784." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[@LorenaABarba](https://twitter.com/LorenaABarba)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "12 steps to Navier-Stokes\n", "=====\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The final two steps in this interactive module teaching beginning [CFD with Python](https://bitbucket.org/cfdpython/cfd-python-class) will both solve the Navier-Stokes equations in two dimensions, but with different boundary conditions.\n", "\n", "The momentum equation in vector form for a velocity field $\\vec{v}$ is:\n", "\n", "$$\\frac{\\partial \\vec{v}}{\\partial t}+(\\vec{v}\\cdot\\nabla)\\vec{v}=-\\frac{1}{\\rho}\\nabla p + \\nu \\nabla^2\\vec{v}$$\n", "\n", "This represents three scalar equations, one for each velocity component $(u,v,w)$. But we will solve it in two dimensions, so there will be two scalar equations.\n", "\n", "Remember the continuity equation? This is where the [Poisson equation](http://nbviewer.ipython.org/urls/github.com/barbagroup/CFDPython/blob/master/lessons/13_Step_10.ipynb) for pressure comes in!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Step 11: Cavity Flow with Navier-Stokes\n", "----\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is the system of differential equations: two equations for the velocity components $u,v$ and one equation for pressure:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\frac{\\partial u}{\\partial t}+u\\frac{\\partial u}{\\partial x}+v\\frac{\\partial u}{\\partial y} = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x}+\\nu \\left(\\frac{\\partial^2 u}{\\partial x^2}+\\frac{\\partial^2 u}{\\partial y^2} \\right) $$\n", "\n", "\n", "$$\\frac{\\partial v}{\\partial t}+u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial y} = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y}+\\nu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}\\right) $$\n", "\n", "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2} = -\\rho\\left(\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}+2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}+\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the previous steps, we already know how to discretize all these terms. Only the last equation is a little unfamiliar. But with a little patience, it will not be hard!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Discretized equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, let's discretize the $u$-momentum equation, as follows:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{eqnarray}\n", "&&\\frac{u_{i,j}^{n+1}-u_{i,j}^{n}}{\\Delta t}+u_{i,j}^{n}\\frac{u_{i,j}^{n}-u_{i-1,j}^{n}}{\\Delta x}+v_{i,j}^{n}\\frac{u_{i,j}^{n}-u_{i,j-1}^{n}}{\\Delta y}\\\\\\ \n", "&&=-\\frac{1}{\\rho}\\frac{p_{i+1,j}^{n}-p_{i-1,j}^{n}}{2\\Delta x}+\\nu\\left(\\frac{u_{i+1,j}^{n}-2u_{i,j}^{n}+u_{i-1,j}^{n}}{\\Delta x^2}+\\frac{u_{i,j+1}^{n}-2u_{i,j}^{n}+u_{i,j-1}^{n}}{\\Delta y^2}\\right)\\end{eqnarray}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly for the $v$-momentum equation:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{eqnarray}\n", "&&\\frac{v_{i,j}^{n+1}-v_{i,j}^{n}}{\\Delta t}+u_{i,j}^{n}\\frac{v_{i,j}^{n}-v_{i-1,j}^{n}}{\\Delta x}+v_{i,j}^{n}\\frac{v_{i,j}^{n}-v_{i,j-1}^{n}}{\\Delta y}\\\\\\\n", "&&=-\\frac{1}{\\rho}\\frac{p_{i,j+1}^{n}-p_{i,j-1}^{n}}{2\\Delta y}\n", "+\\nu\\left(\\frac{v_{i+1,j}^{n}-2v_{i,j}^{n}+v_{i-1,j}^{n}}{\\Delta x^2}+\\frac{v_{i,j+1}^{n}-2v_{i,j}^{n}+v_{i,j-1}^{n}}{\\Delta y^2}\\right)\\end{eqnarray}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the discretized pressure-Poisson equation can be written thus:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\frac{p_{i+1,j}^{n}-2p_{i,j}^{n}+p_{i-1,j}^{n}}{\\Delta x^2}+\\frac{p_{i,j+1}^{n}-2*p_{i,j}^{n}+p_{i,j-1}^{n}}{\\Delta y^2} \n", "=\\rho\\left[\\frac{1}{\\Delta t}\\left(\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}+\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right)\\right.$$\n", "\n", "$$-\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}\n", "- \\ 2\\frac{u_{i,j+1}-u_{i,j-1}}{2\\Delta y}\\frac{v_{i+1,j}-v_{i-1,j}}{2\\Delta x}\n", "-\\left.\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You should write these equations down on your own notes, by hand, following each term mentally as you write it.\n", "\n", "As before, let's rearrange the equations in the way that the iterations need to proceed in the code. First, the momentum equations for the velocity at the next time step.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The momentum equation in the $u$ direction:\n", "\n", "$$\n", "u_{i,j}^{n+1} = u_{i,j}^{n} - u_{i,j}^{n}\\frac{\\Delta t}{\\Delta x}(u_{i,j}^{n}-u_{i-1,j}^{n})\n", "- v_{i,j}^{n}\\frac{\\Delta t}{\\Delta y}(u_{i,j}^{n}-u_{i,j-1}^{n})$$\n", "$$-\\frac{\\Delta t}{\\rho 2\\Delta x}(p_{i+1,j}^{n}-p_{i-1,j}^{n})\n", "+\\nu\\left(\\frac{\\Delta t}{\\Delta x^2}(u_{i+1,j}^{n}-2u_{i,j}^{n}+u_{i-1,j}^{n})\\right.\n", "+\\left.\\frac{\\Delta t}{\\Delta y^2}(u_{i,j+1}^{n}-2u_{i,j}^{n}+u_{i,j-1}^{n})\\right)\n", "$$\n", "\n", "The momentum equation in the $v$ direction:\n", "\n", "$$v_{i,j}^{n+1} = v_{i,j}^{n}-u_{i,j}^{n}\\frac{\\Delta t}{\\Delta x}(v_{i,j}^{n}-v_{i-1,j}^{n})\n", "- v_{i,j}^{n}\\frac{\\Delta t}{\\Delta y}(v_{i,j}^{n}-v_{i,j-1}^{n})$$\n", "$$\n", "-\\frac{\\Delta t}{\\rho 2\\Delta y}(p_{i,j+1}^{n}-p_{i,j-1}^{n})\n", "+\\nu\\left(\\frac{\\Delta t}{\\Delta x^2}(v_{i+1,j}^{n}-2v_{i,j}^{n}+v_{i-1,j}^{n})\\right.\n", "+\\left.\\frac{\\Delta t}{\\Delta y^2}(v_{i,j+1}^{n}-2v_{i,j}^{n}+v_{i,j-1}^{n})\\right)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Almost there! Now, we rearrange the pressure-Poisson equation:\n", "\n", "$$\n", "p_{i,j}^{n}=\\frac{(p_{i+1,j}^{n}+p_{i-1,j}^{n})\\Delta y^2+(p_{i,j+1}^{n}+p_{i,j-1}^{n})\\Delta x^2}{2(\\Delta x^2+\\Delta y^2)}-\\frac{\\rho\\Delta x^2\\Delta y^2}{2(\\Delta x^2+\\Delta y^2)} \\times$$\n", "\n", "$$\\left[\\frac{1}{\\Delta t}\\left(\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}+\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right)-\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}\\right. $$\n", "\n", "$$ -2\\frac{u_{i,j+1}-u_{i,j-1}}{2\\Delta y}\\frac{v_{i+1,j}-v_{i-1,j}}{2\\Delta x}-\\left.\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right]$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The initial condition is $u, v, p = 0$ everywhere, and the boundary conditions are:\n", "\n", "$u=1$ at $y=2$ (the \"lid\");\n", "\n", "$u, v=0$ on the other boundaries;\n", "\n", "$\\frac{\\partial p}{\\partial y}=0$ at $y=0$;\n", "\n", "$p=0$ at $y=2$\n", "\n", "$\\frac{\\partial p}{\\partial x}=0$ at $x=0,2$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implementing Cavity Flow\n", "----\n" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm\n", "from matplotlib import pyplot\n", "import numpy\n", "%matplotlib inline\n", "\n", "nx = 41\n", "ny = 41\n", "nt = 500\n", "nit=50\n", "c = 1\n", "dx = 2/(nx-1)\n", "dy = 2/(ny-1)\n", "x = numpy.linspace(0,2,nx)\n", "y = numpy.linspace(0,2,ny)\n", "X,Y = numpy.meshgrid(x,y)\n", "\n", "rho = 1\n", "nu = .1\n", "dt = .001\n", "\n", "u = numpy.zeros((ny, nx))\n", "v = numpy.zeros((ny, nx))\n", "p = numpy.zeros((ny, nx)) \n", "b = numpy.zeros((ny, nx))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The pressure Poisson equation that's written above can be hard to write out without typos. The function `buildUpB` below represents the contents of the square brackets, so that the entirety of the PPE is slightly more manageable. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def buildUpB(b, rho, dt, u, v, dx, dy):\n", " \n", " b[1:-1,1:-1]=rho*(1/dt*((u[1:-1,2:]-u[1:-1,0:-2])/(2*dx)+(v[2:,1:-1]-v[0:-2,1:-1])/(2*dy))-\\\n", " ((u[1:-1,2:]-u[1:-1,0:-2])/(2*dx))**2-\\\n", " 2*((u[2:,1:-1]-u[0:-2,1:-1])/(2*dy)*(v[1:-1,2:]-v[1:-1,0:-2])/(2*dx))-\\\n", " ((v[2:,1:-1]-v[0:-2,1:-1])/(2*dy))**2)\n", "\n", " return b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The function `presPoisson` is also defined to help segregate the different rounds of calculations. Note the presence of the pseudo-time variable `nit`. This sub-iteration in the Poisson calculation helps ensure a divergence-free field. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def presPoisson(p, dx, dy, b):\n", " pn = numpy.empty_like(p)\n", " pn = p.copy()\n", " \n", " for q in range(nit):\n", " pn = p.copy()\n", " p[1:-1,1:-1] = ((pn[1:-1,2:]+pn[1:-1,0:-2])*dy**2+(pn[2:,1:-1]+pn[0:-2,1:-1])*dx**2)/\\\n", " (2*(dx**2+dy**2)) -\\\n", " dx**2*dy**2/(2*(dx**2+dy**2))*b[1:-1,1:-1]\n", "\n", " p[-1,:] =p[-2,:] ##dp/dy = 0 at y = 2\n", " p[0,:] = p[1,:] ##dp/dy = 0 at y = 0\n", " p[:,0]=p[:,1] ##dp/dx = 0 at x = 0\n", " p[:,-1]=0 ##p = 0 at x = 2\n", " \n", " return p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, the rest of the cavity flow equations are wrapped inside the function `cavityFlow`, allowing us to easily plot the results of the cavity flow solver for different lengths of time. " ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def cavityFlow(nt, u, v, dt, dx, dy, p, rho, nu):\n", " un = numpy.empty_like(u)\n", " vn = numpy.empty_like(v)\n", " b = numpy.zeros((ny, nx))\n", " \n", " for n in range(nt):\n", " un = u.copy()\n", " vn = v.copy()\n", " \n", " b = buildUpB(b, rho, dt, u, v, dx, dy)\n", " p = presPoisson(p, dx, dy, b)\n", " \n", " u[1:-1,1:-1] = un[1:-1,1:-1]-\\\n", " un[1:-1,1:-1]*dt/dx*(un[1:-1,1:-1]-un[1:-1,0:-2])-\\\n", " vn[1:-1,1:-1]*dt/dy*(un[1:-1,1:-1]-un[0:-2,1:-1])-\\\n", " dt/(2*rho*dx)*(p[1:-1,2:]-p[1:-1,0:-2])+\\\n", " nu*(dt/dx**2*(un[1:-1,2:]-2*un[1:-1,1:-1]+un[1:-1,0:-2])+\\\n", " dt/dy**2*(un[2:,1:-1]-2*un[1:-1,1:-1]+un[0:-2,1:-1]))\n", "\n", " v[1:-1,1:-1] = vn[1:-1,1:-1]-\\\n", " un[1:-1,1:-1]*dt/dx*(vn[1:-1,1:-1]-vn[1:-1,0:-2])-\\\n", " vn[1:-1,1:-1]*dt/dy*(vn[1:-1,1:-1]-vn[0:-2,1:-1])-\\\n", " dt/(2*rho*dy)*(p[2:,1:-1]-p[0:-2,1:-1])+\\\n", " nu*(dt/dx**2*(vn[1:-1,2:]-2*vn[1:-1,1:-1]+vn[1:-1,0:-2])+\\\n", " (dt/dy**2*(vn[2:,1:-1]-2*vn[1:-1,1:-1]+vn[0:-2,1:-1])))\n", "\n", " u[0,:] = 0\n", " u[:,0] = 0\n", " u[:,-1] = 0\n", " u[-1,:] = 1 #set velocity on cavity lid equal to 1\n", " v[0,:] = 0\n", " v[-1,:]=0\n", " v[:,0] = 0\n", " v[:,-1] = 0\n", " \n", " \n", " return u, v, p" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's start with `nt = 100` and see what the solver gives us:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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5Oo/gFVqZA3/+LK/jW9g5ZxIJJ4+UyscVK7irjehUysVXQUHhdjQ4YC5h5EzB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\nqJyJiIiInAJr7VRrbejwh4uBs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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = numpy.zeros((ny, nx))\n", "v = numpy.zeros((ny, nx))\n", "p = numpy.zeros((ny, nx))\n", "b = numpy.zeros((ny, nx))\n", "nt = 100\n", "u, v, p = cavityFlow(nt, u, v, dt, dx, dy, p, rho, nu)\n", "fig = pyplot.figure(figsize=(11,7), dpi=100)\n", "pyplot.contourf(X,Y,p,alpha=0.5) ###plnttong the pressure field as a contour\n", "pyplot.colorbar()\n", "pyplot.contour(X,Y,p) ###plotting the pressure field outlines\n", "pyplot.quiver(X[::2,::2],Y[::2,::2],u[::2,::2],v[::2,::2]) ##plotting velocity\n", "pyplot.xlabel('X')\n", "pyplot.ylabel('Y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see that two distinct pressure zones are forming and that the spiral pattern expected from lid-driven cavity flow is beginning to form. Experiment with different values of `nt` to see how long the system takes to stabilize. " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cDF4aN4N23aPw8nVj2fwt3P30YJ6Z1B5vChBCMOnJ3ni6O/DIC39RUFjJNx8M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\nfMmX5FM/VHFM+3MxoX36zHGSF1TVvl1EAXNYUxetLR5OZjsDdwPPGGMKg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = numpy.zeros((ny, nx))\n", "v = numpy.zeros((ny, nx))\n", "p = numpy.zeros((ny, nx))\n", "b = numpy.zeros((ny, nx))\n", "nt = 700\n", "u, v, p = cavityFlow(nt, u, v, dt, dx, dy, p, rho, nu)\n", "fig = pyplot.figure(figsize=(11,7), dpi=100)\n", "pyplot.contourf(X,Y,p,alpha=0.5)\n", "pyplot.colorbar()\n", "pyplot.contour(X,Y,p)\n", "pyplot.quiver(X[::2,::2],Y[::2,::2],u[::2,::2],v[::2,::2])\n", "pyplot.xlabel('X')\n", "pyplot.ylabel('Y');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learn More" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interactive module **12 steps to Navier-Stokes** is one of several components of the Computational Fluid Dynamics class taught by Prof. Lorena A. Barba in Boston University between 2009 and 2013. \n", "\n", "For a sample of what the other components of this class are, you can explore the **Resources** section of the Spring 2013 version of [the course's Piazza site](https://piazza.com/bu/spring2013/me702/resources).\n", "\n", "***" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"../styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "> (The cell above executes the style for this notebook.)" ] } ], "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": "3.4.3" } }, "nbformat": 4, "nbformat_minor": 0 }