lessons/15_Step_12.ipynb

{
 "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 Navier–Stokes\n",
    "=====\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Did you make it this far? This is the last step! How long did it take you to write your own Navier–Stokes solver in Python following this interactive module? Let us know!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 12: Channel Flow with Navier–Stokes\n",
    "----\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The only difference between this final step and Step 11 is that we are going to add a source term to the $u$-momentum equation, to mimic the effect of a pressure-driven channel flow. Here are our modified Navier–Stokes equations:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\\frac{\\partial u}{\\partial t}+u\\frac{\\partial u}{\\partial x}+v\\frac{\\partial u}{\\partial y}=-\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x}+\\nu\\left(\\frac{\\partial^2 u}{\\partial x^2}+\\frac{\\partial^2 u}{\\partial y^2}\\right)+F$$\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",
    "$$\\frac{\\partial^2 p}{\\partial x^2}+\\frac{\\partial^2 p}{\\partial y^2}=-\\rho\\left(\\frac{\\partial u}{\\partial x}\\frac{\\partial u}{\\partial x}+2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}+\\frac{\\partial v}{\\partial y}\\frac{\\partial v}{\\partial y}\\right)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Discretized equations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With patience and care, we write the discretized form of the equations. It is highly recommended that you write these in your own hand, mentally following each term as you write it.\n",
    "\n",
    "The $u$-momentum equation:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "& \\frac{u_{i,j}^{n+1}-u_{i,j}^{n}}{\\Delta t}+u_{i,j}^{n}\\frac{u_{i,j}^{n}-u_{i-1,j}^{n}}{\\Delta x}+v_{i,j}^{n}\\frac{u_{i,j}^{n}-u_{i,j-1}^{n}}{\\Delta y} = \\\\\n",
    "& \\qquad -\\frac{1}{\\rho}\\frac{p_{i+1,j}^{n}-p_{i-1,j}^{n}}{2\\Delta x} \\\\\n",
    "& \\qquad +\\nu\\left(\\frac{u_{i+1,j}^{n}-2u_{i,j}^{n}+u_{i-1,j}^{n}}{\\Delta x^2}+\\frac{u_{i,j+1}^{n}-2u_{i,j}^{n}+u_{i,j-1}^{n}}{\\Delta y^2}\\right)+F_{i,j}\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "The $v$-momentum equation:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "& \\frac{v_{i,j}^{n+1}-v_{i,j}^{n}}{\\Delta t}+u_{i,j}^{n}\\frac{v_{i,j}^{n}-v_{i-1,j}^{n}}{\\Delta x}+v_{i,j}^{n}\\frac{v_{i,j}^{n}-v_{i,j-1}^{n}}{\\Delta y} = \\\\\n",
    "& \\qquad -\\frac{1}{\\rho}\\frac{p_{i,j+1}^{n}-p_{i,j-1}^{n}}{2\\Delta y} \\\\\n",
    "& \\qquad +\\nu\\left(\\frac{v_{i+1,j}^{n}-2v_{i,j}^{n}+v_{i-1,j}^{n}}{\\Delta x^2}+\\frac{v_{i,j+1}^{n}-2v_{i,j}^{n}+v_{i,j-1}^{n}}{\\Delta y^2}\\right)\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "And the pressure equation:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "& \\frac{p_{i+1,j}^{n}-2p_{i,j}^{n}+p_{i-1,j}^{n}}{\\Delta x^2} + \\frac{p_{i,j+1}^{n}-2p_{i,j}^{n}+p_{i,j-1}^{n}}{\\Delta y^2} = \\\\\n",
    "& \\qquad \\rho\\left[\\frac{1}{\\Delta t}\\left(\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}+\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right) - \\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x} - 2\\frac{u_{i,j+1}-u_{i,j-1}}{2\\Delta y}\\frac{v_{i+1,j}-v_{i-1,j}}{2\\Delta x} - \\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right]\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As always, we need to re-arrange these equations to the form we need in the code to make the iterations proceed. \n",
    "\n",
    "For the $u$- and $v$ momentum equations, we isolate the velocity at time step `n+1`:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "u_{i,j}^{n+1} = u_{i,j}^{n} & - u_{i,j}^{n} \\frac{\\Delta t}{\\Delta x} \\left(u_{i,j}^{n}-u_{i-1,j}^{n}\\right) - v_{i,j}^{n} \\frac{\\Delta t}{\\Delta y} \\left(u_{i,j}^{n}-u_{i,j-1}^{n}\\right) \\\\\n",
    "& - \\frac{\\Delta t}{\\rho 2\\Delta x} \\left(p_{i+1,j}^{n}-p_{i-1,j}^{n}\\right) \\\\\n",
    "& + \\nu\\left[\\frac{\\Delta t}{\\Delta x^2} \\left(u_{i+1,j}^{n}-2u_{i,j}^{n}+u_{i-1,j}^{n}\\right) + \\frac{\\Delta t}{\\Delta y^2} \\left(u_{i,j+1}^{n}-2u_{i,j}^{n}+u_{i,j-1}^{n}\\right)\\right] \\\\\n",
    "& + \\Delta t F\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "v_{i,j}^{n+1} = v_{i,j}^{n} & - u_{i,j}^{n} \\frac{\\Delta t}{\\Delta x} \\left(v_{i,j}^{n}-v_{i-1,j}^{n}\\right) - v_{i,j}^{n} \\frac{\\Delta t}{\\Delta y} \\left(v_{i,j}^{n}-v_{i,j-1}^{n}\\right) \\\\\n",
    "& - \\frac{\\Delta t}{\\rho 2\\Delta y} \\left(p_{i,j+1}^{n}-p_{i,j-1}^{n}\\right) \\\\\n",
    "& + \\nu\\left[\\frac{\\Delta t}{\\Delta x^2} \\left(v_{i+1,j}^{n}-2v_{i,j}^{n}+v_{i-1,j}^{n}\\right) + \\frac{\\Delta t}{\\Delta y^2} \\left(v_{i,j+1}^{n}-2v_{i,j}^{n}+v_{i,j-1}^{n}\\right)\\right]\n",
    "\\end{split}\n",
    "$$\n",
    "\n",
    "And for the pressure equation, we isolate the term $p_{i,j}^n$ to iterate in pseudo-time:\n",
    "\n",
    "$$\n",
    "\\begin{split}\n",
    "p_{i,j}^{n} = & \\frac{\\left(p_{i+1,j}^{n}+p_{i-1,j}^{n}\\right) \\Delta y^2 + \\left(p_{i,j+1}^{n}+p_{i,j-1}^{n}\\right) \\Delta x^2}{2(\\Delta x^2+\\Delta y^2)} \\\\\n",
    "& -\\frac{\\rho\\Delta x^2\\Delta y^2}{2\\left(\\Delta x^2+\\Delta y^2\\right)} \\\\\n",
    "& \\times \\left[\\frac{1}{\\Delta t} \\left(\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x} + \\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right) - \\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x}\\frac{u_{i+1,j}-u_{i-1,j}}{2\\Delta x} - 2\\frac{u_{i,j+1}-u_{i,j-1}}{2\\Delta y}\\frac{v_{i+1,j}-v_{i-1,j}}{2\\Delta x} - \\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\frac{v_{i,j+1}-v_{i,j-1}}{2\\Delta y}\\right]\n",
    "\\end{split}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial condition is $u, v, p=0$ everywhere, and at the boundary conditions are:\n",
    "\n",
    "$u, v, p$ are periodic on $x=0,2$\n",
    "\n",
    "$u, v =0$ at $y =0,2$\n",
    "\n",
    "$\\frac{\\partial p}{\\partial y}=0$ at $y =0,2$\n",
    "\n",
    "$F=1$ everywhere.\n",
    "\n",
    "Let's begin by importing our usual run of libraries:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "from matplotlib import pyplot, cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In step 11, we isolated a portion of our transposed equation to make it easier to parse and we're going to do the same thing here.  One thing to note is that we have periodic boundary conditions throughout this grid, so we need to explicitly calculate the values at the leading and trailing edge of our `u` vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_up_b(rho, dt, dx, dy, u, v):\n",
    "    b = numpy.zeros_like(u)\n",
    "    b[1:-1, 1:-1] = (rho * (1 / dt * ((u[1:-1, 2:] - u[1:-1, 0:-2]) / (2 * dx) +\n",
    "                                      (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) *\n",
    "                                 (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",
    "    # Periodic BC Pressure @ x = 2\n",
    "    b[1:-1, -1] = (rho * (1 / dt * ((u[1:-1, 0] - u[1:-1,-2]) / (2 * dx) +\n",
    "                                    (v[2:, -1] - v[0:-2, -1]) / (2 * dy)) -\n",
    "                          ((u[1:-1, 0] - u[1:-1, -2]) / (2 * dx))**2 -\n",
    "                          2 * ((u[2:, -1] - u[0:-2, -1]) / (2 * dy) *\n",
    "                               (v[1:-1, 0] - v[1:-1, -2]) / (2 * dx)) -\n",
    "                          ((v[2:, -1] - v[0:-2, -1]) / (2 * dy))**2))\n",
    "\n",
    "    # Periodic BC Pressure @ x = 0\n",
    "    b[1:-1, 0] = (rho * (1 / dt * ((u[1:-1, 1] - u[1:-1, -1]) / (2 * dx) +\n",
    "                                   (v[2:, 0] - v[0:-2, 0]) / (2 * dy)) -\n",
    "                         ((u[1:-1, 1] - u[1:-1, -1]) / (2 * dx))**2 -\n",
    "                         2 * ((u[2:, 0] - u[0:-2, 0]) / (2 * dy) *\n",
    "                              (v[1:-1, 1] - v[1:-1, -1]) / (2 * dx))-\n",
    "                         ((v[2:, 0] - v[0:-2, 0]) / (2 * dy))**2))\n",
    "    \n",
    "    return b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll also define a Pressure Poisson iterative function, again like we did in Step 11.  Once more, note that we have to include the periodic boundary conditions at the leading and trailing edge.  We also have to specify the boundary conditions at the top and bottom of our grid.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pressure_poisson_periodic(p, dx, dy):\n",
    "    pn = numpy.empty_like(p)\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 +\n",
    "                          (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",
    "        # Periodic BC Pressure @ x = 2\n",
    "        p[1:-1, -1] = (((pn[1:-1, 0] + pn[1:-1, -2])* dy**2 +\n",
    "                        (pn[2:, -1] + pn[0:-2, -1]) * dx**2) /\n",
    "                       (2 * (dx**2 + dy**2)) -\n",
    "                       dx**2 * dy**2 / (2 * (dx**2 + dy**2)) * b[1:-1, -1])\n",
    "\n",
    "        # Periodic BC Pressure @ x = 0\n",
    "        p[1:-1, 0] = (((pn[1:-1, 1] + pn[1:-1, -1])* dy**2 +\n",
    "                       (pn[2:, 0] + pn[0:-2, 0]) * dx**2) /\n",
    "                      (2 * (dx**2 + dy**2)) -\n",
    "                      dx**2 * dy**2 / (2 * (dx**2 + dy**2)) * b[1:-1, 0])\n",
    "        \n",
    "        # Wall boundary conditions, pressure\n",
    "        p[-1, :] =p[-2, :]  # dp/dy = 0 at y = 2\n",
    "        p[0, :] = p[1, :]  # dp/dy = 0 at y = 0\n",
    "    \n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we have our familiar list of variables and initial conditions to declare before we start."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "##variable declarations\n",
    "nx = 41\n",
    "ny = 41\n",
    "nt = 10\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",
    "\n",
    "##physical variables\n",
    "rho = 1\n",
    "nu = .1\n",
    "F = 1\n",
    "dt = .01\n",
    "\n",
    "#initial conditions\n",
    "u = numpy.zeros((ny, nx))\n",
    "un = numpy.zeros((ny, nx))\n",
    "\n",
    "v = numpy.zeros((ny, nx))\n",
    "vn = numpy.zeros((ny, nx))\n",
    "\n",
    "p = numpy.ones((ny, nx))\n",
    "pn = numpy.ones((ny, nx))\n",
    "\n",
    "b = numpy.zeros((ny, nx))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the meat of our computation, we're going to reach back to a trick we used in Step 9 for Laplace's Equation.  We're interested in what our grid will look like once we've reached a near-steady state.  We can either specify a number of timesteps `nt` and increment it until we're satisfied with the results, or we can tell our code to run until the difference between two consecutive iterations is very small.  \n",
    "\n",
    "We also have to manage **8** separate boundary conditions for each iteration.  The code below writes each of them out explicitly.  If you're interested in a challenge, you can try to write a function which can handle some or all of these boundary conditions.  If you're interested in tackling that, you should probably read up on Python [dictionaries](http://docs.python.org/2/tutorial/datastructures.html#dictionaries).  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "udiff = 1\n",
    "stepcount = 0\n",
    "\n",
    "while udiff > .001:\n",
    "    un = u.copy()\n",
    "    vn = v.copy()\n",
    "\n",
    "    b = build_up_b(rho, dt, dx, dy, u, v)\n",
    "    p = pressure_poisson_periodic(p, dx, dy)\n",
    "\n",
    "    u[1:-1, 1:-1] = (un[1:-1, 1:-1] -\n",
    "                     un[1:-1, 1:-1] * dt / dx * \n",
    "                    (un[1:-1, 1:-1] - un[1:-1, 0:-2]) -\n",
    "                     vn[1:-1, 1:-1] * dt / dy * \n",
    "                    (un[1:-1, 1:-1] - un[0:-2, 1:-1]) -\n",
    "                     dt / (2 * rho * dx) * \n",
    "                    (p[1:-1, 2:] - p[1:-1, 0:-2]) +\n",
    "                     nu * (dt / dx**2 * \n",
    "                    (un[1:-1, 2:] - 2 * un[1:-1, 1:-1] + un[1:-1, 0:-2]) +\n",
    "                     dt / dy**2 * \n",
    "                    (un[2:, 1:-1] - 2 * un[1:-1, 1:-1] + un[0:-2, 1:-1])) + \n",
    "                     F * dt)\n",
    "\n",
    "    v[1:-1, 1:-1] = (vn[1:-1, 1:-1] -\n",
    "                     un[1:-1, 1:-1] * dt / dx * \n",
    "                    (vn[1:-1, 1:-1] - vn[1:-1, 0:-2]) -\n",
    "                     vn[1:-1, 1:-1] * dt / dy * \n",
    "                    (vn[1:-1, 1:-1] - vn[0:-2, 1:-1]) -\n",
    "                     dt / (2 * rho * dy) * \n",
    "                    (p[2:, 1:-1] - p[0:-2, 1:-1]) +\n",
    "                     nu * (dt / dx**2 *\n",
    "                    (vn[1:-1, 2:] - 2 * vn[1:-1, 1:-1] + vn[1:-1, 0:-2]) +\n",
    "                     dt / dy**2 * \n",
    "                    (vn[2:, 1:-1] - 2 * vn[1:-1, 1:-1] + vn[0:-2, 1:-1])))\n",
    "\n",
    "    # Periodic BC u @ x = 2     \n",
    "    u[1:-1, -1] = (un[1:-1, -1] - un[1:-1, -1] * dt / dx * \n",
    "                  (un[1:-1, -1] - un[1:-1, -2]) -\n",
    "                   vn[1:-1, -1] * dt / dy * \n",
    "                  (un[1:-1, -1] - un[0:-2, -1]) -\n",
    "                   dt / (2 * rho * dx) *\n",
    "                  (p[1:-1, 0] - p[1:-1, -2]) + \n",
    "                   nu * (dt / dx**2 * \n",
    "                  (un[1:-1, 0] - 2 * un[1:-1,-1] + un[1:-1, -2]) +\n",
    "                   dt / dy**2 * \n",
    "                  (un[2:, -1] - 2 * un[1:-1, -1] + un[0:-2, -1])) + F * dt)\n",
    "\n",
    "    # Periodic BC u @ x = 0\n",
    "    u[1:-1, 0] = (un[1:-1, 0] - un[1:-1, 0] * dt / dx *\n",
    "                 (un[1:-1, 0] - un[1:-1, -1]) -\n",
    "                  vn[1:-1, 0] * dt / dy * \n",
    "                 (un[1:-1, 0] - un[0:-2, 0]) - \n",
    "                  dt / (2 * rho * dx) * \n",
    "                 (p[1:-1, 1] - p[1:-1, -1]) + \n",
    "                  nu * (dt / dx**2 * \n",
    "                 (un[1:-1, 1] - 2 * un[1:-1, 0] + un[1:-1, -1]) +\n",
    "                  dt / dy**2 *\n",
    "                 (un[2:, 0] - 2 * un[1:-1, 0] + un[0:-2, 0])) + F * dt)\n",
    "\n",
    "    # Periodic BC v @ x = 2\n",
    "    v[1:-1, -1] = (vn[1:-1, -1] - un[1:-1, -1] * dt / dx *\n",
    "                  (vn[1:-1, -1] - vn[1:-1, -2]) - \n",
    "                   vn[1:-1, -1] * dt / dy *\n",
    "                  (vn[1:-1, -1] - vn[0:-2, -1]) -\n",
    "                   dt / (2 * rho * dy) * \n",
    "                  (p[2:, -1] - p[0:-2, -1]) +\n",
    "                   nu * (dt / dx**2 *\n",
    "                  (vn[1:-1, 0] - 2 * vn[1:-1, -1] + vn[1:-1, -2]) +\n",
    "                   dt / dy**2 *\n",
    "                  (vn[2:, -1] - 2 * vn[1:-1, -1] + vn[0:-2, -1])))\n",
    "\n",
    "    # Periodic BC v @ x = 0\n",
    "    v[1:-1, 0] = (vn[1:-1, 0] - un[1:-1, 0] * dt / dx *\n",
    "                 (vn[1:-1, 0] - vn[1:-1, -1]) -\n",
    "                  vn[1:-1, 0] * dt / dy *\n",
    "                 (vn[1:-1, 0] - vn[0:-2, 0]) -\n",
    "                  dt / (2 * rho * dy) * \n",
    "                 (p[2:, 0] - p[0:-2, 0]) +\n",
    "                  nu * (dt / dx**2 * \n",
    "                 (vn[1:-1, 1] - 2 * vn[1:-1, 0] + vn[1:-1, -1]) +\n",
    "                  dt / dy**2 * \n",
    "                 (vn[2:, 0] - 2 * vn[1:-1, 0] + vn[0:-2, 0])))\n",
    "\n",
    "\n",
    "    # Wall BC: u,v = 0 @ y = 0,2\n",
    "    u[0, :] = 0\n",
    "    u[-1, :] = 0\n",
    "    v[0, :] = 0\n",
    "    v[-1, :]=0\n",
    "    \n",
    "    udiff = (numpy.sum(u) - numpy.sum(un)) / numpy.sum(u)\n",
    "    stepcount += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that we've also included a variable `stepcount` to see how many iterations our loop went through before our stop condition was met.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "499\n"
     ]
    }
   ],
   "source": [
    "print(stepcount)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you want to see how the number of iterations increases as our `udiff` condition gets smaller and smaller, try defining a function to perform the `while` loop written above that takes an input `udiff` and outputs the number of iterations that the function runs.  \n",
    "\n",
    "For now, let's look at our results.  We've used the quiver function to look at the cavity flow results and it works well for channel flow, too.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CINCxY8fw2GOP6b99xMbGwtXVtcEazHXmzBkkJSXpp/hBgwbZxLc9Uy5cuICYmBgkJSVB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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdc2a11f630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure(figsize = (11,7), dpi=100)\n",
    "pyplot.quiver(X[::3, ::3], Y[::3, ::3], u[::3, ::3], v[::3, ::3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The structures in the `quiver` command that look like `[::3, ::3]` are useful when dealing with large amounts of data that you want to visualize.  The one used above tells `matplotlib` to only plot every 3rd data point.  If we leave it out, you can see that the results can appear a little crowded.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3R+Tn59OMGTO425I2bNjA3ZYUFBTEdGekPEVFRTRz5kzutqTNmzczvRpQnlu3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PQ9dOhQnZ3Ev/76S4eWtGTJEuTm5jJspIuLC8aOHatDGPH19eXoLwDg6enJ0Fq9evViYzs4OHB9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\nDoXhw4dD//79RZ/yWFpagqenJ3nOhg0bBh4eHqJ9N2zYENq3b098d+zYUbR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9a32Lf0Bg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdc2a11f668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = pyplot.figure(figsize = (11,7), dpi=100)\n",
    "pyplot.quiver(X, Y, u, v);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn more\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### What is the meaning of the $F$ term?\n",
    "\n",
    "Step 12 is an exercise demonstrating the problem of flow in a channel or pipe. If you recall from your fluid mechanics class, a specified pressure gradient is what drives Poisseulle flow. \n",
    "\n",
    "Recall the $x$-momentum equation:\n",
    "\n",
    "$$\\frac{\\partial u}{\\partial t}+u \\cdot \\nabla u = -\\frac{\\partial p}{\\partial x}+\\nu \\nabla^2 u$$\n",
    "\n",
    "What we actually do in Step 12 is split the pressure into steady and unsteady components $p=P+p'$. The applied steady pressure gradient is the constant $-\\frac{\\partial P}{\\partial x}=F$ (interpreted as a source term), and the unsteady component is $\\frac{\\partial p'}{\\partial x}$. So the pressure that we solve for in Step 12 is actually $p'$, which for a steady flow is in fact equal to zero everywhere.\n",
    "\n",
    "<b>Why did we do this?</b>\n",
    "\n",
    "Note that we use periodic boundary conditions for this flow. For a flow with a constant pressure gradient, the value of pressure on the left edge of the domain must be different from the pressure at the right edge. So we cannot apply periodic boundary conditions on the pressure directly. It is easier to fix the gradient and then solve for the perturbations in pressure.\n",
    "\n",
    "<b>Shouldn't we always expect a uniform/constant $p'$ then?</b>\n",
    "\n",
    "That's true only in the case of steady laminar flows. At high Reynolds numbers, flows in channels can become turbulent, and we will see unsteady fluctuations in the pressure, which will result in non-zero values for $p'$. \n",
    "\n",
    "In step 12, note that the pressure field itself is not constant, but it's the pressure perturbation field that is. The pressure field varies linearly along the channel with slope equal to the pressure gradient. Also, for incompressible flows, the absolute value of the pressure is inconsequential.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### And explore more CFD materials online"
   ]
  },
  {
   "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 othe 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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<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",
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       "        font-family: 'Alegreya Sans', sans-serif;\n",
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       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    h3{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "        margin-top:12px;\n",
       "        margin-bottom: 3px;\n",
       "       }\n",
       "\th4{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "       }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\t   \n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
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       "        font-size: 120%;\n",
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       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\";\n",
       "\t\t\tfont-size: 90%;\n",
       "    }\n",
       "/*    .prompt{\n",
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       "    }*/\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 50pt;\n",
       "\t\tline-height: 100%;\n",
       "        color:#CD2305;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\t\n",
       "    .text_cell_render h5 {\n",
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       "        color: #CD2305;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }  \n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
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       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
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      ]
     },
     "execution_count": 9,
     "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.)"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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   "name": "python",
   "nbconvert_exporter": "python",
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