{ "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 BSD-3 license. (c) Lorena A. Barba, Gilbert F. Forsyth 2017. 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 Navierâ€“Stokes\n", "=====\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Up to now, all of our work has been in one spatial dimension (Steps [1](./01_Step_1.ipynb) to [4](./05_Step_4.ipynb)). We can learn a lot in just 1D, but let's grow up to flatland: two dimensions. \n", "\n", "In the following exercises, you will extend the first four steps to 2D. To extend the 1D finite-difference formulas to partial derivatives in 2D or 3D, just apply the definition: a partial derivative with respect to $x$ is the variation in the $x$ direction *at constant* $y$.\n", "\n", "In 2D space, a rectangular (uniform) grid is defined by the points with coordinates:\n", "\n", "$$x_i = x_0 +i \\Delta x$$\n", "\n", "$$y_i = y_0 +i \\Delta y$$\n", "\n", "Now, define $u_{i,j} = u(x_i,y_j)$ and apply the finite-difference formulas on either variable $x,y$ *acting separately* on the $i$ and $j$ indices. All derivatives are based on the 2D Taylor expansion of a mesh point value around $u_{i,j}$.\n", "\n", "Hence, for a first-order partial derivative in the $x$-direction, a finite-difference formula is:\n", "\n", "$$\\frac{\\partial u}{\\partial x}\\biggr\\rvert_{i,j} = \\frac{u_{i+1,j}-u_{i,j}}{\\Delta x}+\\mathcal{O}(\\Delta x)$$\n", "\n", "and similarly in the $y$ direction. Thus, we can write backward-difference, forward-difference or central-difference formulas for Steps 5 to 12. Let's get started!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Step 5: 2-D Linear Convection\n", "----\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PDE governing 2-D Linear Convection is written as\n", "\n", "$$\\frac{\\partial u}{\\partial t}+c\\frac{\\partial u}{\\partial x} + c\\frac{\\partial u}{\\partial y} = 0$$\n", "\n", "This is the exact same form as with 1-D Linear Convection, except that we now have two spatial dimensions to account for as we step forward in time. \n", "\n", "Again, the timestep will be discretized as a forward difference and both spatial steps will be discretized as backward differences. \n", "\n", "With 1-D implementations, we used $i$ subscripts to denote movement in space (e.g. $u_{i}^n-u_{i-1}^n$). Now that we have two dimensions to account for, we need to add a second subscript, $j$, to account for all the information in the regime. \n", "\n", "Here, we'll again use $i$ as the index for our $x$ values, and we'll add the $j$ subscript to track our $y$ values. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With that in mind, our discretization of the PDE should be relatively straightforward. \n", "\n", "$$\\frac{u_{i,j}^{n+1}-u_{i,j}^n}{\\Delta t} + c\\frac{u_{i, j}^n-u_{i-1,j}^n}{\\Delta x} + c\\frac{u_{i,j}^n-u_{i,j-1}^n}{\\Delta y}=0$$\n", "\n", "As before, solve for the only unknown:\n", "\n", "$$u_{i,j}^{n+1} = u_{i,j}^n-c \\frac{\\Delta t}{\\Delta x}(u_{i,j}^n-u_{i-1,j}^n)-c \\frac{\\Delta t}{\\Delta y}(u_{i,j}^n-u_{i,j-1}^n)$$\n", "\n", "We will solve this equation with the following initial conditions:\n", "\n", "$$u(x,y) = \\begin{cases}\n", "\\begin{matrix}\n", "2\\ \\text{for} & 0.5 \\leq x, y \\leq 1 \\cr\n", "1\\ \\text{for} & \\text{everywhere else}\\end{matrix}\\end{cases}$$\n", "\n", "and boundary conditions:\n", "\n", "$$u = 1\\ \\text{for } \\begin{cases}\n", "\\begin{matrix}\n", "x = 0,\\ 2 \\cr\n", "y = 0,\\ 2 \\end{matrix}\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { 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1dqzaOzRjsdgE65Fm8ZOgs6eaAUBVVWnGcx06dAjvf/81eGTrL3HaSRE8dN9x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WlYXaRHO46hUmxQO2mkLXsy25m+kjcu/YSEn3HNT3fiJRIsHck7n+ygj9O4KmrYsufdlNWUXkVW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\nCvfddx8ADz74INu3b8dqtbJ582ZycnJCv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from mpl_toolkits.mplot3d import Axes3D ##New Library required for projected 3d plots\n", "\n", "import numpy\n", "from matplotlib import pyplot, cm\n", "%matplotlib inline\n", "\n", "###variable declarations\n", "nx = 81\n", "ny = 81\n", "nt = 100\n", "c = 1\n", "dx = 2 / (nx - 1)\n", "dy = 2 / (ny - 1)\n", "sigma = .2\n", "dt = sigma * dx\n", "\n", "x = numpy.linspace(0, 2, nx)\n", "y = numpy.linspace(0, 2, ny)\n", "\n", "u = numpy.ones((ny, nx)) ##create a 1xn vector of 1's\n", "un = numpy.ones((ny, nx)) ##\n", "\n", "###Assign initial conditions\n", "\n", "##set hat function I.C. : u(.5<=x<=1 && .5<=y<=1 ) is 2\n", "u[int(.5 / dy):int(1 / dy + 1),int(.5 / dx):int(1 / dx + 1)] = 2 \n", "\n", "###Plot Initial Condition\n", "##the figsize parameter can be used to produce different sized images\n", "fig = pyplot.figure(figsize=(11, 7), dpi=100)\n", "ax = fig.gca(projection='3d') \n", "X, Y = numpy.meshgrid(x, y) \n", "surf = ax.plot_surface(X, Y, u[:], cmap=cm.viridis)\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3D Plotting Notes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To plot a projected 3D result, make sure that you have added the Axes3D library. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " from mpl_toolkits.mplot3d import Axes3D" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The actual plotting commands are a little more involved than with simple 2d plots." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "python\n", "fig = pyplot.figure(figsize=(11, 7), dpi=100)\n", "ax = fig.gca(projection='3d')\n", "surf2 = ax.plot_surface(X, Y, u[:])\n", "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The first line here is initializing a figure window. The **figsize** and **dpi** commands are optional and simply specify the size and resolution of the figure being produced. You may omit them, but you will still require the \n", " \n", " fig = pyplot.figure()\n", "\n", "The next line assigns the plot window the axes label 'ax' and also specifies that it will be a 3d projection plot. The final line uses the command\n", " \n", " plot_surface()\n", "\n", "which is equivalent to the regular plot command, but it takes a grid of X and Y values for the data point positions. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##### Note\n", "\n", "\n", "The X and Y values that you pass to plot_surface are not the 1-D vectors x and y. In order to use matplotlibs 3D plotting functions, you need to generate a grid of x, y values which correspond to each coordinate in the plotting frame. This coordinate grid is generated using the numpy function meshgrid.\n", "\n", " X, Y = numpy.meshgrid(x, y)\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Iterating in two dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To evaluate the wave in two dimensions requires the use of several nested for-loops to cover all of the i's and j's. Since Python is not a compiled language there can be noticeable slowdowns in the execution of code with multiple for-loops. First try evaluating the 2D convection code and see what results it produces. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jzSToCE0oJHwTiQQ8nl3XutVqxdChQzF06FDVjnv++efjyCOPRN++fdHe3o4n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MAAAg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\nZuwOO/mGQvReM+ZgNhZyMWJesGMRslNpoZ8eSjWLk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = numpy.ones((ny, nx))\n", "u[int(.5 / dy):int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2\n", "\n", "for n in range(nt + 1): ##loop across number of time steps\n", " un = u.copy()\n", " row, col = u.shape\n", " for j in range(1, row):\n", " for i in range(1, col):\n", " u[j, i] = (un[j, i] - (c * dt / dx * (un[j, i] - un[j, i - 1])) -\n", " (c * dt / dy * (un[j, i] - un[j - 1, i])))\n", " u[0, :] = 1\n", " u[-1, :] = 1\n", " u[:, 0] = 1\n", " u[:, -1] = 1\n", "\n", "fig = pyplot.figure(figsize=(11, 7), dpi=100)\n", "ax = fig.gca(projection='3d')\n", "surf2 = ax.plot_surface(X, Y, u[:], cmap=cm.viridis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Array Operations\n", "----------------\n", "\n", "Here the same 2D convection code is implemented, but instead of using nested for-loops, the same calculations are evaluated using array operations. " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jzSToCE0oJHwTiQQ8nl3XutVqxdChQzF06FDVjnv++efjyCOPRN++fdHe3o4n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MAAAg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\nZuwOO/mGQvReM+ZgNhZyMWJesGMRslNpoZ8eSjWLk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u = numpy.ones((ny, nx))\n", "u[int(.5 / dy):int(1 / dy + 1), int(.5 / dx):int(1 / dx + 1)] = 2\n", "\n", "for n in range(nt + 1): ##loop across number of time steps\n", " un = u.copy()\n", " u[1:, 1:] = (un[1:, 1:] - (c * dt / dx * (un[1:, 1:] - un[1:, :-1])) -\n", " (c * dt / dy * (un[1:, 1:] - un[:-1, 1:])))\n", " u[0, :] = 1\n", " u[-1, :] = 1\n", " u[:, 0] = 1\n", " u[:, -1] = 1\n", "\n", "fig = pyplot.figure(figsize=(11, 7), dpi=100)\n", "ax = fig.gca(projection='3d')\n", "surf2 = ax.plot_surface(X, Y, u[:], cmap=cm.viridis)\n", "\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Learn More" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The video lesson that walks you through the details for Step 5 (and onwards to Step 8) is **Video Lesson 6** on You Tube:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { 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"text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import YouTubeVideo\n", "YouTubeVideo('tUg_dE3NXoY')" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 5, "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }