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+Christopher Bell's Final Project for Numerical Mooc
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diff --git a/Final projects/Christopher_Bell/Final Project -- 2D Finite Difference NS & Acoustic Solver.ipynb b/Final projects/Christopher_Bell/Final Project -- 2D Finite Difference NS & Acoustic Solver.ipynb
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+{
+ "metadata": {
+  "name": "final project -- 2d finite difference ns & acoustic solver.ipynb",
+  "signature": "sha256:a2d9982065f27f15da3420a23c08fda4da8c684e786889202f7d5137a1085e41"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "heading",
+     "level": 6,
+     "metadata": {},
+     "source": [
+      "Content was created by Christopher Bell for Professor Lorena Barba's MAE 6286 Numerical Methods at The George Washington University, 2014. References are listed at the end of this document.\n",
+      "\n",
+      "Text and code provided under a Creative Commons Attribution license, CC-BY. (c) Christopher Bell, 2014."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 1,
+     "metadata": {},
+     "source": [
+      "2D Finite Difference Navier-Stokes & Acoustic Solver"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Problem Motivation"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "I choose this problem for two reasons, my desire to write a Navier-Stokes solver and to advanced a project set forth in my undergraduate fluids class. The problem I will be investigating is the effect of buffetting over an open cavity. Most people are familair with this problem from opening their car's sunroof on the highway and hearing that annoying sound. The goal of this project is to model the physics of that system by using a Navier-Stokes solver with acoustics to model cavity flow. The code will begin with a derivation and implementation of the Navier-Stokes solver to get that working before adding the acoustics after."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "2D Navier-Stokes Derivation"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The Navier-Stokes equations and continuity are defined as:\n",
+      "\n",
+      "$$\\frac{\\partial{\\vec{v}}}{\\partial{t}}+\\left(\\vec{v} \\cdot \\nabla \\right)\\vec{v} = \\frac{-1}{\\rho} \\nabla P + \\nu \\nabla^2 \\vec{v}$$\n",
+      "\n",
+      "$$\\nabla \\cdot \\vec{v} = 0$$\n",
+      "\n",
+      "Due to the Laplace operators this equation obviously represents a 3D system; however, for simplicity the z-direction will be ignored and the equations will be solved in 2D."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 5,
+     "metadata": {},
+     "source": [
+      "2D Burgers Equation Derivation & Discretization"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The momentum equation above represents the Burgers Equation in 2D with an additional pressure term. That means we can use what we did in Module 2-04 in deriving the Burgers Equation in 1D but extend it to 2D. The only addition we need to make is a source term. The Cavity Flow will be set up as pressure driven flow and thus a source term, $F$, will be added to the $u$-direction (flow will be left to right the same as the x-direction and y will be perpendicular to the flow direction) equations to model this.\n",
+      "\n",
+      "Burgers Equation in 2D without our additional forcing term is:\n",
+      "\n",
+      "$$\\frac{\\partial u}{\\partial t}+u\\frac{\\partial u}{\\partial x}+v\\frac{\\partial u}{\\partial y}=\\nu\\left(\\frac{\\partial^2 u}{\\partial x^2}+\\frac{\\partial^2 u}{\\partial y^2}\\right)$$\n",
+      "\n",
+      "Incorporating the pressure term and rewritting the equations for each dimension yields:\n",
+      "\n",
+      "$$\\frac{\\partial u}{\\partial t}+u\\frac{\\partial u}{\\partial x}+v\\frac{\\partial u}{\\partial y}=-\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x}+\\nu\\left(\\frac{\\partial^2 u}{\\partial x^2}+\\frac{\\partial^2 u}{\\partial y^2}\\right)$$\n",
+      "\n",
+      "$$\\frac{\\partial v}{\\partial t}+u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial y}=-\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y}+\\nu\\left(\\frac{\\partial^2 v}{\\partial x^2}+\\frac{\\partial^2 v}{\\partial y^2}\\right)$$\n"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Once again as we did in Module 2-04 we will model the Burgers Equation using a forward time backward space scheme. This yields:\n",
+      "\n",
+      "$$\\frac{u_{i,j}^{n+1}-u_{i,j}^{n}}{\\Delta t}+u_{i,j}^{n}\\frac{u_{i,j}^{n}-u_{i-1,j}^{n}}{\\Delta x}+v_{i,j}^{n}\\frac{u_{i,j}^{n}-u_{i,j-1}^{n}}{\\Delta y}=-\\frac{1}{\\rho}\\frac{p_{i+1,j}^{n}-p_{i-1,j}^{n}}{2\\Delta x}+\\nu\\left(\\frac{u_{i+1,j}^{n}-2u_{i,j}^{n}+u_{i-1,j}^{n}}{\\Delta x^2}+\\frac{u_{i,j+1}^{n}-2u_{i,j}^{n}+u_{i,j-1}^{n}}{\\Delta y^2}\\right)+F_{i,j}$$\n",
+      "\n",
+      "$$\\frac{v_{i,j}^{n+1}-v_{i,j}^{n}}{\\Delta t}+u_{i,j}^{n}\\frac{v_{i,j}^{n}-v_{i-1,j}^{n}}{\\Delta x}+v_{i,j}^{n}\\frac{v_{i,j}^{n}-v_{i,j-1}^{n}}{\\Delta y}=-\\frac{1}{\\rho}\\frac{p_{i+1,j}^{n}-p_{i-1,j}^{n}}{2\\Delta x}+\\nu\\left(\\frac{v_{i+1,j}^{n}-2v_{i,j}^{n}+v_{i-1,j}^{n}}{\\Delta x^2}+\\frac{v_{i,j+1}^{n}-2v_{i,j}^{n}+v_{i,j-1}^{n}}{\\Delta y^2}\\right)$$"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Next we need to solve these equations for $u_{i,j}^{n+1}$ & $v_{i,j}^{n+1}$\n",
+      "\n",
+      "$$u_{i,j}^{n+1} = u_{i,j}^n-\\frac{1}{\\rho}\\frac{\\Delta t}{2\\Delta x}\\left(P_{i+1,j}-P_{i-1,j}\\right) + \\nu\\frac{\\Delta t}{\\Delta x^2}\\left(u_{i+1,j}^n-2u_{i,j}^n+u_{i-1,j}^n\\right) + \\nu\\frac{\\Delta t}{\\Delta y^2}\\left(u_{i,j+1}^n-2u_{i,j}^n+u_{i,j-1}^n\\right) - u_{i,j}^n\\frac{\\Delta t}{\\Delta x}\\left(u_{i,j}^n-u_{i-1,j}^n\\right) - v_{i,j}^n\\frac{\\Delta t}{\\Delta y}\\left(u_{i,j}^n-u_{i,j-1}^n\\right) + \\Delta t F_{i,j}$$\n",
+      "\n",
+      "$$v_{i,j}^{n+1} = v_{i,j}^n-\\frac{1}{\\rho}\\frac{\\Delta t}{2\\Delta y}\\left(P_{i+1,j}-P_{i-1,j}\\right) + \\nu\\frac{\\Delta t}{\\Delta x^2}\\left(v_{i+1,j}^n-2v_{i,j}^n+v_{i-1,j}^n\\right) + \\nu\\frac{\\Delta t}{\\Delta y^2}\\left(v_{i,j+1}^n-2v_{i,j}^n+v_{i,j-1}^n\\right) - u_{i,j}^n\\frac{\\Delta t}{\\Delta x}\\left(v_{i,j}^n-v_{i-1,j}^n\\right) - v_{i,j}^n\\frac{\\Delta t}{\\Delta y}\\left(v_{i,j}^n-v_{i,j-1}^n\\right)$$\n",
+      "\n",
+      "This equations can be simplified further if we assume that $\\Delta x$ $=$ $\\Delta y$, but that will not be done to keep the code as general as possible."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 5,
+     "metadata": {},
+     "source": [
+      "2D Poisson Equation Derivation & Discretization"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "As you probably noticed in the Burger's Equation above, we have a pressure term but no way to solve it. That's what the Poisson equation is for. Before we get there we need to solve a problem though. For incompressible flow the continutity equation provides no way to combine a pressure term and a velocity term. This is because unlike compressible flow continuity is only a function of velocity. In compressible flow density is able to change which when combined with an equation such as $PV=nRT$.\n",
+      "\n",
+      "The Laplace equation is defined as:\n",
+      "\n",
+      "$$\\frac{\\partial^2 P}{\\partial x^2} + \\frac{\\partial^2 P}{\\partial y^2} = 0$$\n",
+      "\n",
+      "To form the Poisson Equation a source term is added to the equation, thus providing our driving pressure for our pressure driven flow.\n",
+      "\n",
+      "$$\\frac{\\partial^2 P}{\\partial x^2} + \\frac{\\partial^2 P}{\\partial y^2} = b_{i,j}^n$$\n",
+      "\n",
+      "$b_{i,j}^n$ is a complicated calculation found by taking the divergence of the momentum equation and rewritten in the form we need. Due to the complexity here we will be using Professor Barba's result from her CFD class.\n",
+      "\n",
+      "$$b_{i,j}^n = -\\rho \\left(\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x} + 2 \\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x} + \\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y} \\right)$$\n",
+      "\n",
+      "Now we need to discritize this equation. First we need to think about the physics of the problem. The pressure field will act by spreading out through the computational domain like a diffusion problem which we talked in Module 2-03. Second we need to use our past experience discretizing with second derivatives. This yields:\n",
+      "\n",
+      "$$\\frac{P_{i+1,j}^n - 2P_{i,j} + P_{i-1,j}^n}{\\Delta x^2} + \\frac{P_{i,j+1}^n - 2P_{i,j} + P_{i,j-1}^n}{\\Delta y^2} = b_{i,j}^n$$\n",
+      "\n",
+      "And solving for the pressure at the current location $i,j$:\n",
+      "\n",
+      "$$P_{i,j}^n = \\frac{\\left(P_{i+1,j}^n + P_{i-1,j}^n\\right)\\Delta y^2 + \\left(P_{i,j+1}^n + P_{i,j-1}^n\\right)\\Delta x^2 - b_{i,j}^n \\Delta x^2 \\Delta y^2}{2\\left(\\Delta x^2 + \\Delta y^2 \\right)}$$\n",
+      "\n"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Now we need to descritze our source term $b_{i,j}^n$, using a central scheme\n",
+      "\n",
+      "$$b_{i,j}^n = -\\rho \\left[\\frac{1}{\\Delta t} \\left(\\frac{(u_{i+1,j} - u_{i-1,j}}{2\\Delta x} + \\frac{v_{i,j+1} - v_{i,j-1}}{2\\Delta y}\\right) \\frac{u_{i+1,j}^n + u_{i-1,j}^n}{2\\Delta x} \\frac{u_{i+1,j}^n + u_{i-1,j}^n}{2\\Delta x} + 2 \\frac{u_{i,j+1}^n + u_{i,j-1}^n}{2\\Delta y} \\frac{v_{i+1,j}^n + v_{i-1,j}^n}{2\\Delta x} + \\frac{v_{i,j+1}^n + v_{i,j-1}^n}{2\\Delta y} \\frac{v_{i,j+1}^n + v_{i,j-1}^n}{2\\Delta y}\\right] $$\n",
+      "\n",
+      "Plugging this expression in for $b_{i,j}^n$ and simplfying yields:\n",
+      "\n",
+      "$$P_{i,j}^n = \\frac{\\left(P_{i+1,j}^n + P_{i-1,j}^n\\right)\\Delta y^2 + \\left(P_{i,j+1}^n + P_{i,j-1}^n\\right)\\Delta x^2}{2\\left(\\Delta x^2 + \\Delta y^2\\right)} - \\frac{\\rho \\Delta x^2 \\Delta y^2}{2\\left(\\Delta x^2 + \\Delta y^2\\right)}\\left[\\frac{1}{\\Delta t} \\left(\\frac{u_{i+1,j} - u_{i-1,j}}{2\\Delta x} + \\frac{v_{i,j+1} - v_{i,j-1}}{2\\Delta y}\\right) - \\frac{u_{i+1,j}^n + u_{i-1,j}^n}{2\\Delta x} \\frac{u_{i+1,j}^n + u_{i-1,j}^n}{2\\Delta x} - 2 \\frac{u_{i,j+1}^n + u_{i,j-1}^n}{2\\Delta y} \\frac{v_{i+1,j}^n + v_{i-1,j}^n}{2\\Delta x} - \\frac{v_{i,j+1}^n + v_{i,j-1}^n}{2\\Delta y} \\frac{v_{i,j+1}^n + v_{i,j-1}^n}{2\\Delta y}\\right]$$"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Boundary & Initial Condition Set-up"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The domain will stretch from 0 to 2 meters in both the x and y directions with the cavity occupying the entire domain. The flow will be model somewhat similair to a Couette flow with the top of the domain forcing the fluid. Thus we will set are boundary conditions as follows:\n",
+      "\n",
+      "$u\\left(x,2,t\\right)=1$\n",
+      "\n",
+      "$u\\left(x,y,t\\right)$ & $v\\left(x,y,t\\right) = 0$ everywhere else\n",
+      "\n",
+      "$\\frac{\\partial P\\left(x,0,t\\right)}{\\partial y} = 0$\n",
+      "\n",
+      "$P\\left(x,2,t\\right)=0$\n",
+      "\n",
+      "$\\frac{\\partial P\\left(0 \\& 2,y,t\\right)}{\\partial x} = 0$\n",
+      "\n",
+      "Now we are left with the initial conditions which we will set to zero everywhere for $u, v, P$"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 5,
+     "metadata": {},
+     "source": [
+      "CFL Conditions"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "All of the equations in this notebook are nonlinear PDE's which means we can't use Von Neumann Stability Analysis. So how do we tell if the system is stable? The are some advanced was to look at stability of nonlinear PDE's involving the eigenvalues of the jacobian, but for simplicity we will just pick our spacial and time steps through trial and error to make sure the solution does not blow up.\n",
+      "\n"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Acoustic Solver"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "Expected Physics:"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The acoustic effect that we are modeling is called a Helmholtz resonator. This is a widely studied phenomenon as it comes up a lot in the real world--including our sun roof problem. The vortices that cause this acoustic effect can be found in the image below courtesy of [exa](http://www.exa.com/sunroof--window-buffeting.html)\n",
+      "\n",
+      "<img src='Supporting_Files/buffeting_phenomena.png'height '42'width '42'>\n",
+      "\n",
+      "The general physics of the flow can be seen here courtesy of W. De Roeck et. al.\n",
+      "\n",
+      "<img src='Supporting_Files/Acoustic_schematic.png'height '42'width '42'>\n",
+      "\n",
+      "There are also many animations available to demonstrate the physics of the flow. [University of New South Wales](http://newt.phys.unsw.edu.au/jw/Helmholtz.html) has a nice webpage about Helmholtz Resonators including an animation for a simplified problem. Wikibooks also has a nice gif of the flow over a sunroof.\n",
+      "\n",
+      "<img src='Supporting_Files/Buffeting_car.gif'height '48'width '48'>"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 3,
+     "metadata": {},
+     "source": [
+      "2D Acoustic Equation Derivation & Discritization"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The 2D Acoustic Wave Equation is defined as:\n",
+      "\n",
+      "$$\\frac{\\partial^2 P}{\\partial x^2} + \\frac{\\partial^2 P}{\\partial y^2} - \\frac{1}{c^2}\\frac{\\partial^2 P}{\\partial t^2} = 0$$\n",
+      "\n",
+      "With $c$ being the speed of sound. First we should determine what type of discritization scheme we will be using will have because we have a term we have not dealt with before-an equation sensitive to the second derivative of time."
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "$$\\frac{P_{i+1,j}^n - 2P_{i,j} + P_{i-1,j}^n}{\\Delta x^2} + \\frac{P_{i,j+1}^n - 2P_{i,j} + P_{i,j-1}^n}{\\Delta y^2} - \\frac{1}{c^2}\\frac{P_{i,j}^{n+1} - 2P_{i,j}^n + P_{i,j}^{n-1}}{\\Delta t^2} = 0$$\n",
+      "\n",
+      "$$P_{i,j}^{n+1} = \\frac{c^2\\Delta t^2}{\\Delta x^2}\\left(P_{i+1,j}^n - 2P_{i,j}^n + P_{i-1,j}^n\\right) + \\frac{c^2\\Delta t^2}{\\Delta y^2}\\left(P_{i,j+1}^n - 2P_{i,j}^n + P_{i,j-1}^n\\right) + 2P_{i,j}^n - P_{i,j}^{n-1}$$\n",
+      "\n",
+      "Now we have a new problem, we have a $n-1$ time step that means we need a special way to start off the solution."
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "For simplicity, we will just be ignoring the acoustic solver for the first step and assuming the initial conditions are all zero."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Code"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "First, we need to import our libraries and we will be using a few new ones for this notebook. These new libraries allow use access to more advanced plotting tools. Feel free to read their documentation online."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import numpy as np\n",
+      "from mpl_toolkits.mplot3d import Axes3D\n",
+      "from matplotlib import cm\n",
+      "import matplotlib.pyplot as plt\n",
+      "%matplotlib inline\n",
+      "from matplotlib import animation\n",
+      "from pylab import rcParams\n",
+      "rcParams['figure.figsize'] = (10.0, 8.0)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 20
+    },
+    {
+     "cell_type": "heading",
+     "level": 5,
+     "metadata": {},
+     "source": [
+      "Boundary Conditions, Initial conditions, Grid Creation, and Problem Set-up"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "nx = 41 #number of x grid points\n",
+      "ny = 41 #number of y grid points\n",
+      "dt = .001 #size of time steps\n",
+      "dx = 2.0/(nx-1) #size of x steps\n",
+      "dy = 2.0/(ny-1) #size of y steps\n",
+      "sigma = 1 #CFL\n",
+      "rho = 1 #kg/m^3\n",
+      "nu = .1  #kg/m s\n",
+      "c = 340.29 #m/s\n",
+      "epsilon = .00001 # Residual goal for P\n",
+      "\n",
+      "x = np.linspace(0.0,2.0,nx)\n",
+      "y = np.linspace(0.0,2.0,ny)\n",
+      "Y,X = np.meshgrid(y,x)\n",
+      "\n",
+      "u = np.zeros((ny,nx))\n",
+      "v = np.zeros((ny,nx))\n",
+      "P = np.zeros((ny,nx))\n",
+      "b = np.zeros((ny,nx))"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 21
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We used a new function [Meshgrid](http://docs.scipy.org/doc/numpy/reference/generated/numpy.meshgrid.html) in the last cell you should look it up\n",
+      "\n",
+      "\n",
+      "We also did one other new thing did you notice it? We made 2D variables for $u$, $v$, $P$, and $b$. We need to remember what learned in module 4 for 2D arrays. Mainly, that python defines by the y variable first unlike our intuition.\n",
+      "\n",
+      "You may be wondering why we created an additional $b$ variable. This is to make our life easier as demonstrate by Professor Barba in her CFDPython class. The Poisson equation is quite long and difficult to code without a typo, so we split it up into two variables. The question is how to split it up? Why not use $b_{i,j}^n$ from the derivation of the equation."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def b_ij(u, v, dx, dy, rho):\n",
+      "    \"\"\"Computes the b_ij term in the Poisson equation\n",
+      "    \n",
+      "    Parameters:\n",
+      "    ------\n",
+      "    u:    array of float\n",
+      "          velocity in the x direction\n",
+      "    \n",
+      "    v:    array of float\n",
+      "          velocity in the y direction\n",
+      "    \n",
+      "    dx:   float\n",
+      "          grid step size\n",
+      "        \n",
+      "    dy:   float\n",
+      "          grid step size\n",
+      "          \n",
+      "    rho:  float\n",
+      "          density of air\n",
+      "        \n",
+      "    b:    array of float\n",
+      "          empty array for function\n",
+      "          \n",
+      "    Returns:\n",
+      "    -------\n",
+      "    b:    array of float\n",
+      "          b term of Poisson equation\n",
+      "    \"\"\"\n",
+      "    \n",
+      "    b = np.zeros((ny,nx))\n",
+      "    b[1:-1,1:-1] =  rho*(1/dt*((u[2:,1:-1] - u[0:-2,1:-1])/(2*dx) + (v[1:-1,2:] - v[1:-1,0:-2])/(2*dy))-\\\n",
+      "        ((u[2:,1:-1] - u[0:-2,1:-1])/(2*dx)) * ((u[2:,1:-1] - u[0:-2,1:-1])/(2*dx))-\\\n",
+      "        2*((u[1:-1,2:] - u[1:-1,0:-2])/(2*dy) * (v[2:,1:-1] - v[0:-2,1:-1])/(2*dx))-\\\n",
+      "        ((v[1:-1,2:] - v[1:-1,0:-2])/(2*dy)) * ((v[1:-1,2:] - v[1:-1,0:-2])/(2*dy)))\n",
+      "        \n",
+      "    return b"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 22
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "For the Poisson solver since it does not calculate in time, we will also be calculating the residual at each time step. The L2 norm of the residuals will then be compared to a desired error value."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def Poisson2D(dx, dy, b, P):\n",
+      "    \"\"\"Computes the Poisson equation\n",
+      "    \n",
+      "    Parameters:\n",
+      "    ------\n",
+      "    P:    array of float\n",
+      "          empty array for function\n",
+      "    \n",
+      "    dx:   float\n",
+      "          grid step size\n",
+      "    \n",
+      "    dy:   float\n",
+      "          grid step size\n",
+      "        \n",
+      "    b:    array of float\n",
+      "          b term of Poisson equation\n",
+      "          \n",
+      "    Returns:\n",
+      "    -------\n",
+      "    P:    array of float\n",
+      "          Results of Poisson equation\n",
+      "    \"\"\"\n",
+      "    \n",
+      "    Pn = np.zeros((ny,nx))\n",
+      "    erP = 1\n",
+      "    while erP > epsilon:\n",
+      "        Pn = P.copy()\n",
+      "        P[1:-1,1:-1] = ((Pn[2:,1:-1] + Pn[0:-2,1:-1])*dy**2) + ((Pn[1:-1,2:] + Pn[1:-1,0:-2])*dx**2)/(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",
+      "        errorP = P - Pn\n",
+      "        erP = np.linalg.norm(errorP)\n",
+      "    return P"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 23
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def Burger2D(u, v, P, dt, dx, dy, rho, nu, nt):\n",
+      "    \"\"\"Computes the velocities of the flow\n",
+      "    \n",
+      "    Parameters:\n",
+      "    ------\n",
+      "    u:    array of float\n",
+      "          velocity in the x direction\n",
+      "    \n",
+      "    v:    array of float\n",
+      "          velocity in the y direction\n",
+      "          \n",
+      "    P:    array of float\n",
+      "          Results of Poisson equation\n",
+      "          \n",
+      "    dt:   float\n",
+      "          time step size\n",
+      "    \n",
+      "    dx:   float\n",
+      "          grid step size\n",
+      "    \n",
+      "    dy:   float\n",
+      "          grid step size\n",
+      "          \n",
+      "    rho:  float\n",
+      "          density of air\n",
+      "        \n",
+      "    nu:   float\n",
+      "          Dynamic viscosity of air\n",
+      "          \n",
+      "    nt:   float\n",
+      "          Number of time steps\n",
+      "          \n",
+      "    Returns:\n",
+      "    -------\n",
+      "    u:    array of float\n",
+      "          x direction velocities\n",
+      "          \n",
+      "    v:    array of float\n",
+      "          y direction velocities\n",
+      "    \"\"\"\n",
+      "    un = np.empty_like(u)\n",
+      "    vn = np.empty_like(v)\n",
+      "    bn = np.zeros((ny,nx))\n",
+      "    \n",
+      "    \n",
+      "    for n in range(1,nt):\n",
+      "        Pn=P.copy()\n",
+      "        if n > 1: #acoustic solver\n",
+      "            P[1:-1,1:-1] = (((c**2)*(dt**2))/(dx**2))*\\\n",
+      "                (Pn[1:-1,2:] -2*Pn[1:-1,1:-1] + Pn[1:-1,0:-2])+\\\n",
+      "                (((c**2)*(dt**2))/(dx**2))*\\\n",
+      "                (Pn[2:,1:-1] -2*Pn[1:-1,1:-1] + Pn[0:-2,1:-1])+\\\n",
+      "                2*Pn[1:-1,1:-1] - Pn1[1:-1,1:-1]\n",
+      "            \n",
+      "        un = u.copy()\n",
+      "        vn = v.copy()\n",
+      "        bn = b_ij(u, v, dx, dy, rho)\n",
+      "        P = Poisson2D(dx, dy, bn, P)\n",
+      "        \n",
+      "        u[1:-1,1:-1] = un[1:-1,1:-1] -\\\n",
+      "            (dt/(rho*2*dx))*(P[2:,1:-1] - P[0:-2,1:-1])+\\\n",
+      "            (nu*dt/(dx**2))*(un[2:,1:-1] - 2*un[1:-1,1:-1] + un[0:-2,1:-1])+\\\n",
+      "            (nu*dt/(dy**2))*(un[1:-1,2:] - 2*un[1:-1,1:-1] + un[1:-1,0:-2])-\\\n",
+      "            un[1:-1,1:-1]*(dt/dx)*(un[1:-1,1:-1] - un[0:-2,1:-1])-\\\n",
+      "            vn[1:-1,1:-1]*(dt/dy)*(un[1:-1,1:-1] - un[1:-1,0:-2])\n",
+      "        #using 2: because 2 values are clipped in j\n",
+      "        \n",
+      "        v[1:-1,1:-1] = vn[1:-1,1:-1] -\\\n",
+      "            (dt/(rho*2*dx))*(P[1:-1,2:] - P[1:-1,0:-2])+\\\n",
+      "            (nu*dt/(dx**2))*(vn[2:,1:-1] - 2*vn[1:-1,1:-1] + vn[0:-2,1:-1,])+\\\n",
+      "            (nu*dt/(dy**2))*(vn[1:-1,2:] - 2*vn[1:-1,1:-1] + vn[1:-1,0:-2])-\\\n",
+      "            un[1:-1,1:-1]*(dt/dx)*(vn[1:-1,1:-1] - vn[0:-2,1:-1])-\\\n",
+      "            vn[1:-1,1:-1]*(dt/dy)*(vn[1:-1,1:-1] - un[1:-1,0:-2])\n",
+      "        #using 2: because 2 values are clipped in i\n",
+      "        \n",
+      "        \n",
+      "        u[0,:] = 0 #assign the clipped values\n",
+      "        u[:,0] = 0\n",
+      "        u[:,-1] = 1\n",
+      "        v[0,:] = 0\n",
+      "        v[-1,:]=0\n",
+      "        v[:,0] = 0\n",
+      "        v[:,-1] = 0\n",
+      "        u[-1,:] = 0\n",
+      "        \n",
+      "        Pn1=Pn.copy()\n",
+      "    \n",
+      "    #calculating Vorticity (taking the curl)\n",
+      "    dX = np.gradient(x)\n",
+      "    dY = np.gradient(y)\n",
+      "    dV = np.gradient(v)\n",
+      "    dU = np.gradient(u)\n",
+      "    V_gradient = dV/dX\n",
+      "    U_gradient = dU/dY\n",
+      "        \n",
+      "    Vorticity = V_gradient - U_gradient\n",
+      "        \n",
+      "    return u, v, P, bn, Vorticity"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 24
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Next we are going to use Matplotlib's [Countour Plotting](http://matplotlib.org/examples/pylab_examples/contour_demo.html) ability.\n",
+      "\n"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "u = np.zeros((ny,nx))\n",
+      "v = np.zeros((ny,nx))\n",
+      "P = np.zeros((ny,nx))\n",
+      "nt = 700\n",
+      "u, v, P, bn, Vorticity = Burger2D(u, v, P, dt, dx, dy, rho, nu, nt)\n",
+      "fig = plt.figure(figsize=(11,7), dpi=100)\n",
+      "plt.contourf(X,Y,P,alpha=0.5);    ###plotting the pressure field as a contour\n",
+      "plt.colorbar()\n",
+      "plt.contour(X,Y,P);               ###plotting the pressure field outlines\n",
+      "plt.quiver(X[::2,::2],Y[::2,::2],u[::2,::2],v[::2,::2], units='width') ##plotting velocity\n",
+      "plt.xlabel('X')\n",
+      "plt.ylabel('Y')\n",
+      "fig.suptitle('Pressure Contours and Velocity Vectors', fontsize=14, fontweight='bold')\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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F6nmCeGv8HVS0UeF8AgqEiU36Ev57JJTX8+IwKj7ijFWMCq+mm7WaKINbfiKV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\nKW3nER0/dspYvsdTpvjoXcbyJenwvuM6vO+4sXzLs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+       "text": [
+        "<matplotlib.figure.Figure at 0x89fb3c8>"
+       ]
+      }
+     ],
+     "prompt_number": 25
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "What happens if we increase the time of the simulation?"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "u = np.zeros((ny,nx))\n",
+      "v = np.zeros((ny,nx))\n",
+      "P = np.zeros((ny,nx))\n",
+      "nt = 1000\n",
+      "u, v, P, bn, Vorticity = Burger2D(u, v, P, dt, dx, dy, rho, nu, nt)\n",
+      "fig = plt.figure(figsize=(11,7), dpi=100)\n",
+      "plt.contourf(X,Y,P,alpha=0.5);    ###plotting the pressure field as a contour\n",
+      "plt.colorbar()\n",
+      "plt.contour(X,Y,P);               ###plotting the pressure field outlines\n",
+      "plt.quiver(X[::2,::2],Y[::2,::2],u[::2,::2],v[::2,::2], units='width') ##plotting velocity\n",
+      "plt.xlabel('X')\n",
+      "plt.ylabel('Y')\n",
+      "fig.suptitle('Pressure Contours and Velocity Vectors', fontsize=14, fontweight='bold')\n",
+      "plt.show()\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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cbV5X6HXYyqObsM1eTFRKOpdO6svtY8OorISP98DbT4DOUGdNu3wyWL3zx2yC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ZAAAg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\nAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0xaa16d68>"
+       ]
+      }
+     ],
+     "prompt_number": 26
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "The pressure contours are different! That means we are still in the transient part of our problem. Let's look at this using ANSYS Fluent. This allows us to check our results with a commerical solver and observe the transient effects of the flow. First, we can look at how the pressure contours evolve."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from IPython.display import YouTubeVideo\n",
+      "YouTubeVideo(\"eof4rsxdOXE\")\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "\n",
+        "        <iframe\n",
+        "            width=\"400\"\n",
+        "            height=300\"\n",
+        "            src=\"http://www.youtube.com/embed/eof4rsxdOXE\"\n",
+        "            frameborder=\"0\"\n",
+        "            allowfullscreen\n",
+        "        ></iframe>\n",
+        "        "
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 27,
+       "text": [
+        "<IPython.lib.display.YouTubeVideo at 0xa97c6a0>"
+       ]
+      }
+     ],
+     "prompt_number": 27
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "And now the Velocity vectors..."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "YouTubeVideo(\"5XtVMqCcYPE\")\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "\n",
+        "        <iframe\n",
+        "            width=\"400\"\n",
+        "            height=300\"\n",
+        "            src=\"http://www.youtube.com/embed/5XtVMqCcYPE\"\n",
+        "            frameborder=\"0\"\n",
+        "            allowfullscreen\n",
+        "        ></iframe>\n",
+        "        "
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 28,
+       "text": [
+        "<IPython.lib.display.YouTubeVideo at 0xa97cf60>"
+       ]
+      }
+     ],
+     "prompt_number": 28
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "From these videos we can definetly see that our code is on to something but isn't simulating past the transient part of our problem. Unfortunetly, if we try and simulate any longer our code blows up. This is most likely due to our co-located grid and in the future we should use a staggerred grid. This same problem also makes us use a very viscous fluid compared to air as we need to model a highly dissipative flow.\n",
+      "\n",
+      "Next, let's visualize our Pressure coefficient and acoustic data."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "V = np.sqrt(u**2 + v**2)\n",
+      "V_infinity = np.ones(nx)\n",
+      "C_P = 1 - ((V/V_infinity)**2)\n",
+      "fig = plt.figure(figsize=(11,7), dpi=100)\n",
+      "plt.contourf(X,Y,C_P,alpha=0.5);    ###plotting the pressure field as a contour\n",
+      "plt.colorbar()\n",
+      "plt.contour(X,Y,C_P);               ###plotting the pressure field outlines\n",
+      "plt.xlabel('X')\n",
+      "plt.ylabel('Y')\n",
+      "fig.suptitle('Coefficient of Pressure', fontsize=14, fontweight='bold')\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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nFotH02Lq1BimZWJaJoZlhG3LtojGo2GQeySu6mg8ihWxxoXVMG/56uiB50yH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\ngQ8l9V//agQAAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x8318e80>"
+       ]
+      }
+     ],
+     "prompt_number": 29
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Power Spectral Density\n",
+      "plt.psd(P, NFFT=256, Fs=100, Fc=0);"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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IBB06SPv2SbfeKv34o1SsmN0VAQDgeyxxwghDhkjLl0uLFkn58tldDQAAV86r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\nQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x86ba3c8>"
+       ]
+      }
+     ],
+     "prompt_number": 38
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "#Spectrogram\n",
+      "plt.specgram(x, NFFT=256, Fs=100, Fc=0);"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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+       "text": [
+        "<matplotlib.figure.Figure at 0x8a0b198>"
+       ]
+      }
+     ],
+     "prompt_number": 40
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "This doesn't look right! If we use the equation for a helmholtz resonator we calculate an expected peak frequency of 27 Hz. We don't get that. What's Wrong?\n",
+      "\n",
+      "We need to go back and think about how we defined our problem. Our entire computational domain is the the cavity. This means that our upper boundary is fixed in space. This is where our problem lies. If we look at our fluent velocity vector simulation and the acoustic gif from earlier we notice that there must be a negative pressure gradient in the flow pulling  the flow down into the cavity. This is not possible in our flow because the edge of the cavity is our upper boundary which can not move. This leads to no development of an acoustic wave and thus our incorrect Power Spectral Density and Spectrogram. Going forward we could fix this by expanding our computational grid to the same \"T\" shape seen in the fluent simulations. This would require the use of an immerssed boundary method as well on either side of the cavity to satisfy continuity. Due to time constraints and the complexity of the more robust solver this was unable to be incorporated."
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "Result Confirmation:"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Now we need to check are Navier-Stokes results to make sure they are physical. Thankfully J. Kim and P. Moin have done extensive studys on cavity flow. Below is an image from their 1984 paper showing the velocity vectors in a cavity. As can be seen we are capturing the correct physics although to a lessor effect because our Reynolds number is 20 which is significantly less than Kim & Moin's Reynolds Number.\n",
+      "\n",
+      "<img src=\"Supporting_Files/Kim_Moin_velocity.png\"height '63'width '63'>"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We can also look at the streamfunctions of the flow curtesy of Ercan Erturk. His data matches our data in general but differs once again because of Reynolds Number differences.\n",
+      "<img src='Supporting_Files/Ertuk_Streamfunctions.png' height '42' width'42'>"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "We can also look at the isolated velocity fields to understand the flow better. Take a look at the contours below and make sure you understand what they mean. If you understood the velocity vectors from above then this should reaffirm what you learned from that plot. Its amazing what we can do with python and matplotlib."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "fig = plt.figure(figsize=(11,7), dpi=100)\n",
+      "plt.contourf(X,Y,u,alpha=0.5);\n",
+      "plt.colorbar()\n",
+      "plt.contour(X,Y,u);               \n",
+      "plt.xlabel('X')\n",
+      "plt.ylabel('Y')\n",
+      "fig.suptitle('U Velocity Contours', fontsize=14, fontweight='bold')\n",
+      "plt.show()\n",
+      "\n",
+      "fig = plt.figure(figsize=(11,7), dpi=100)\n",
+      "plt.contourf(X,Y,v,alpha=0.5);\n",
+      "plt.colorbar()\n",
+      "plt.contour(X,Y,v);               \n",
+      "plt.xlabel('X')\n",
+      "plt.ylabel('Y')\n",
+      "fig.suptitle('V Velocity Vectors', fontsize=14, fontweight='bold')\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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B9qDRiY9a2mIXkNEnktUnYKsHttBlsXiNRvaTIYxGlBOpoAw/UdSDPPZbDZ1H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\n7+R1XQAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x829a160>"
+       ]
+      },
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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PBu4nFhNJDGMBNaziRUqYSQHZdD+MZ1/lTPS2ARXOzDYzXm/XszWjYTAayR89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AAAAS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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0xaa32278>"
+       ]
+      }
+     ],
+     "prompt_number": 32
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Can you think of anything else we would want to look at? What about Vorticity?"
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "fig = plt.figure(figsize=(11,7), dpi=100)\n",
+      "plt.contourf(X,Y,Vorticity[1],alpha=0.5);\n",
+      "plt.colorbar()\n",
+      "plt.contour(X,Y,Vorticity[1]);               \n",
+      "plt.xlabel('X')\n",
+      "plt.ylabel('Y')\n",
+      "fig.suptitle('Vorticity', fontsize=14, fontweight='bold')\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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Y9JDtkpKVxfDDujP/hkfZWbTT7nJERCRMxcVEUvrtipC0vfnNRdT5AoycNTEk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\neU4AAAAASUVORK5CYII=\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x829f208>"
+       ]
+      }
+     ],
+     "prompt_number": 33
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "Our results don't look so good when compared to Erturk's.\n",
+      "<img src='Supporting_Files/Ertuk_vorticity.png' height '42' width'42'>\n",
+      "\n",
+      "Once again, these differences are due to the short time our simulation was run and Reynolds number differeces. The short time of the simulation doesn't allow all the physics to sort itself out as our simulation only lasts for one second as can be seen in this [video](https://www.youtube.com/watch?v=wDxRnsvBqT4) the flow is not steady. Thus we are only capturing a snapshot of the flow.\n",
+      "\n",
+      "We can also look at our Fluent results again to observe the transient repsonse of the vorticity that we are missing."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "YouTubeVideo(\"JvTfqA-oDAY\")"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "\n",
+        "        <iframe\n",
+        "            width=\"400\"\n",
+        "            height=300\"\n",
+        "            src=\"http://www.youtube.com/embed/JvTfqA-oDAY\"\n",
+        "            frameborder=\"0\"\n",
+        "            allowfullscreen\n",
+        "        ></iframe>\n",
+        "        "
+       ],
+       "metadata": {},
+       "output_type": "pyout",
+       "prompt_number": 41,
+       "text": [
+        "<IPython.lib.display.YouTubeVideo at 0xa997160>"
+       ]
+      }
+     ],
+     "prompt_number": 41
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "In conclusion, we were able to successfully code a basic Navier Stokes Solver. Move forward it could be improved by the use of a staggered grid and incorporating more rigorous stability criteria designed for nonlinear PDE. On the otherhand, the acoustic solver failed because the domain was defined to narrowly. Going forward this can be over come by expanding the grid  and incorporating an immeresed boundary solution to match the fluent simulations.\n"
+     ]
+    },
+    {
+     "cell_type": "heading",
+     "level": 2,
+     "metadata": {},
+     "source": [
+      "References:"
+     ]
+    },
+    {
+     "cell_type": "markdown",
+     "metadata": {},
+     "source": [
+      "1) Anderson, John D. Computational Fluid Dynamics: The Basics with Applications. New York: McGraw-Hill, 1995.\n",
+      "\n",
+      "2) CFD Python by Lorena Barba\n",
+      "\n",
+      "3) Erturk, Ercan. \"Discussions on Driven Cavity Flow.\" International Journal for Numerical Methods in Fluids 60.3 (2009): 275-94.\n",
+      "\n",
+      "4) Kim, J., and P. Moin. \"Application of a Fractional-step Method to Incompressible Navier-Stokes Equations.\" Journal of Computational Physics 59.2 (1984): 308-23.\n",
+      "\n",
+      "5) Lions, and Tigers, and 4th Order PDE's! Oh, My! by Matt Bornemeier\n",
+      "\n",
+      "6) Panton, Ronald L. Incompressible Flow. New York: Wiley, 1984.\n",
+      "\n",
+      "7) Roeck, W. D., W. Desmet, M. Baelmans, and P. Sas. \"On the Prediction of Near-field Cavity Flow Noise Using Different CAA Techniques.\" (2004)."
+     ]
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "from IPython.core.display import HTML\n",
+      "css_file = 'Supporting_Files/numericalmoocstyle.css'\n",
+      "HTML(open(css_file, \"r\").read())"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "html": [
+        "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
+        "<link href='http://fonts.googleapis.com/css?family=Arvo:400,700,400italic' rel='stylesheet' type='text/css'>\n",
+        "<link href='http://fonts.googleapis.com/css?family=PT+Mono' rel='stylesheet' type='text/css'>\n",
+        "<link href='http://fonts.googleapis.com/css?family=Shadows+Into+Light' rel='stylesheet' type='text/css'>\n",
+        "<link href='http://fonts.googleapis.com/css?family=Nixie+One' rel='stylesheet' type='text/css'>\n",
+        "<style>\n",
+        "\n",
+        "@font-face {\n",
+        "    font-family: \"Computer Modern\";\n",
+        "    src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
+        "}\n",
+        "\n",
+        "#notebook_panel { /* main background */\n",
+        "    background: rgb(245,245,245);\n",
+        "}\n",
+        "\n",
+        "div.cell { /* set cell width */\n",
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diff --git a/Final projects/Christopher_Bell/README.md b/Final projects/Christopher_Bell/README.md
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@@ -0,0 +1,8 @@
+2D_Navier_Stokes_Acoustics
+==========================
+This is my Final Project for a Numerical Methods in Python Class at GWU. This code will start as a 2D FDM NS solver with acoustics for strucutred grid. The flow being solved will be a cavity flow. Going forward I hope to expand this code to include a staggered grid and 3 dimensions.
+
+This may eventually evolve into another FVM solver down the line. Hopefully modeling turbulent flows using dynamic and smagorinsky models for LES simulations based on the initial DNS solver I am creating.
+
+I am also interested in possibly doing a nozzle flow with periodic BC's for compressible flow.
+
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