{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 12: Channel Flow with Navier-Stokes\n",
    "\n",
    "The only difference between this step and Step 11 is that we add a source term to the u-momentum equation, to mimic the effect of a pressure-driven channel flow. her's how the Navier-Stokes equations get modified to account for it:\n",
    "\n",
    "\n",
    "$$  \\frac{\\partial u}{ \\partial t} + u \\frac{\\partial u}{ \\partial x} +  v\\frac{\\partial u}{ \\partial y} = -  \\frac{1}{ \\rho } \\frac{\\partial p}{ \\partial x} + \\nu \\left ( \\frac{\\partial^2 u}{ \\partial x^2} + \\frac{\\partial^2 u}{ \\partial y^2} \\right ) + F $$\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",
    "\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",
    "\n",
    "\n",
    "## Discretization\n",
    "\n",
    "We already discretized these equations in the previous step but now we must compensate for the new addition for the new F term. For the \n",
    "\n",
    "$$ \\frac{u^{n+1}_{i,j} - u^n_{i,j}}{\\Delta t} + u^n_{i,j} \\frac{u^{n}_{i,j} - u^n_{i-1,j}}{\\Delta x} + v^n_{i,j} \\frac{u^{n}_{i,j} - u^n_{i,j-1}}{\\Delta y} = - \\frac{1}{\\rho} \\frac{p^{n}_{i+1,j}-p^{n}_{i-1,j}}{ 2 \\Delta x} + \\nu \\left ( \\frac{u^{n}_{i+1,j}-2 u^{n}_{i,j} + u^{n}_{i-1,j}}{ \\Delta x^2} + \\frac{u^{n}_{i,j+1}-2 u^{n}_{i,j} + u^{n}_{i,j-1}}{ \\Delta y^2} \\right ) +F_{i,j}\n",
    "$$\n",
    "\n",
    "Similarly for the v equation:\n",
    "\n",
    "$$ \\frac{v^{n+1}_{i,j} - v^n_{i,j}}{\\Delta t} + u^n_{i,j} \\frac{v^{n}_{i,j} - v^n_{i-1,j}}{\\Delta x} + v^n_{i,j} \\frac{v^{n}_{i,j} - v^n_{i,j-1}}{\\Delta y} = - \\frac{1}{\\rho} \\frac{p^{n}_{i,j+1}-p^{n}_{i,j-1}}{ 2 \\Delta y} + \\nu \\left ( \\frac{v^{n}_{i+1,j}-2 v^{n}_{i,j} + v^{n}_{i-1,j}}{ \\Delta x^2} + \\frac{v^{n}_{i,j+1}-2 v^{n}_{i,j} + v^{n}_{i,j-1}}{ \\Delta y^2} \\right )\n",
    "$$\n",
    "\n",
    "Finally the discretized pressure-poisson equation can be written like so:\n",
    "\n",
    "$$ \\frac{p^n_{i+1,j} - 2 p^n_{i,j} + p^n_{i-1,j}}{\\Delta x^2} + \\frac{p^n_{i,j+1} - 2 p^n_{i,j} + p^n_{i,j-1}}{\\Delta y^2} = \\rho \\left [ \\frac{1}{\\Delta t} \\left ( \\frac{u^n_{i+1,j} -  u^n_{i-1,j}}{2 \\Delta x} + \\frac{v^n_{i+1,j} -  v^n_{i-1,j}}{2 \\Delta y} \\right ) - \\frac{u_{i+1,j} - u_{i-1,j}}{2 \\Delta x} \\frac{u_{i+1,j} u_{i-1,j}}{2 \\Delta x} - 2\\frac{u_{i,j+1} - u_{i,j-1}}{2 \\Delta y} \\frac{v_{i+1,j} - v_{i-1,j}}{2 \\Delta x} - \\frac{v_{i,j+1} - v_{i,j-1}}{2 \\Delta y} \\frac{v_{i,j+1} - v_{i,j-1}}{2 \\Delta y} \\right ]\n",
    "$$\n",
    "\n",
    "As always, we shall write these equations in a rearranged form 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",
    "\n",
    "The momentum in the u direction:\n",
    "\n",
    "$$ u^{n+1}_{i,j} = u^{n}_{i,j} - u^{n}_{i,j} \\frac{\\Delta t}{\\Delta x} \\left ( u^n_{i,j} - u^n_{i-1,j} \\right ) - v^n_{i,j} \\frac{\\Delta t}{\\Delta y} \\left ( u^n_{i,j} - u^n_{i,j-1} \\right ) - \\frac{\\Delta t}{ \\rho 2 \\Delta x} \\left ( p^n_{i-1,j} - p^n_{i-1,j} \\right ) + \\nu \\left ( \\frac{\\Delta t}{\\Delta x ^2} \\left ( u^n_{i+1,j} - 2 u^n_{i,j} + u^{n}{i-1, j} \\right ) + \\frac{\\Delta t}{\\Delta y^2} \\left ( u^n_{i,j+1} - 2u^n_{i,j} + u^n_{i,j-1} \\right ) \\right ) + F \\Delta t\n",
    "$$\n",
    "\n",
    "The momentum in the v direction:\n",
    "\n",
    "$$ v^{n+1}_{i,j} = v^{n}_{i,j} - u^{n}_{i,j} \\frac{\\Delta t}{\\Delta x} \\left ( v^n_{i,j} - v^n_{i-1,j} \\right ) - v^n_{i,j} \\frac{\\Delta t}{\\Delta y} \\left ( v^n_{i,j} -  v^n_{i,j-1} \\right ) - \\frac{\\Delta t}{ \\rho 2 \\Delta y} \\left ( p^n_{i,j+1} - p^n_{i,j-1} \\right ) + \\nu \\left ( \\frac{\\Delta t}{\\Delta x ^2} \\left ( v^n_{i+1,j} - 2 v^n_{i,j} + v^{n}{i-1, j} \\right ) + \\frac{\\Delta t}{\\Delta y^2} \\left ( v^n_{i,j+1} - 2v^n_{i,j} + v^n_{i,j-1} \\right ) \\right )\n",
    "$$\n",
    "\n",
    "Last but not least, the Pressure-poisson equation:\n",
    "\n",
    "$$p^n_{i,j} = \\frac{\\left ( p^n_{i+1,j} + p^n_{i-1,j} \\right )\\Delta y^2 + \\left ( p^n_{i,j+1} + p^n_{i,j-1} \\right ) \\Delta x^2  }{2 \\left ( \\Delta x^2 + \\Delta y^2 \\right )} - \\frac{\\rho \\Delta x^2 \\Delta y^2}{2\\left (\\Delta x^2 + \\Delta y^2 \\right )} \\times \\left [ \\frac{1}{\\Delta t} \\left ( \\frac{u_{i+1, j} - u_{i-1,j}}{2 \\Delta x} + \\frac{v_{i, j+1} - v_{i,j-1}}{2 \\Delta y} \\right ) - \\frac{u_{i+1,j} - u_{i-1,j}}{2 \\Delta x} \\frac{u_{i+1,j} - u_{i-1,j}}{2 \\Delta x} - 2 \\frac{u_{i,j+1} - u_{i,j-1}}{2 \\Delta y} \\frac{v_{i+1,j} - v_{i-1,j}}{2 \\Delta x} - \\frac{v_{i,j+1} - v_{i,j-1}}{2 \\Delta y} \\frac{v_{i,j+1} - v_{i,j-1}}{2 \\Delta y} \\right ]\n",
    "$$\n",
    "\n",
    "## Initial and Boundary Conditions\n",
    "\n",
    "The initial conditions are that $ u,v,p = 0$ everywhere and the boundary conditions are as follows:\n",
    "\n",
    "$ u,v,p \\ \\text{are periodic on} \\ x = 0,2 $\n",
    "\n",
    "$ u,v = 0 \\ \\text{at} \\ y = 0,2 $\n",
    "\n",
    "$ \\frac{\\partial p}{\\partial y} = 0 \\ \\text{at} \\ y = 0,2$\n",
    "\n",
    "$ F = 1$ everywhere.\n",
    "\n",
    "We now have all we need to begin the simulation! Let's start by importing all the libraries that we shall use and then declare some key functions and variables.\n",
    "\n",
    "## Libraries and Variable declarations\n",
    "\n",
    "### Lib import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adding inline command to make plots appear under comments\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In step 11 we isolated a part of our tansposed equation ot make it easier to read and we're going to do the same here. One thing to note is that since we have periodic boundary conditions throughout hte grid we need to explicityly calculate the values at the leading and trailing edge of our `u` vector.\n",
    "\n",
    "## Function Declarations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def build_up_b(rho, dt, dx, dy, u , v):\n",
    "    b = np.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",
    "    return b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also define a periodic pressure poisson iterative function as we did in step 11. Once again we include the periodic boundary conditions at the leading and trailing edge. We also ahve to specify boundary conditions at the top and bottom of our grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pressure_poisson_periodic(p, dx, dy):\n",
    "    pn = np.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": [
    "### Variable Declarations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "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",
    "\n",
    "#Initializing arrays\n",
    "x = np.linspace(0, 2, nx)\n",
    "y = np.linspace(0, 2, ny)\n",
    "X,Y = np.meshgrid(x,y)\n",
    "\n",
    "rho = 1\n",
    "nu = .1\n",
    "F = 1\n",
    "dt = 0.01\n",
    "\n",
    "#Initializing tu,v and pressure arrays\n",
    "u  = np.zeros((nx, ny))\n",
    "un  = np.zeros((nx, ny))\n",
    "\n",
    "v  = np.zeros((nx, ny))\n",
    "vn  = np.zeros((nx, ny))\n",
    "\n",
    "p  = np.ones((nx, ny))\n",
    "pn  = np.ones((nx, ny))\n",
    "\n",
    "b  = np.zeros((nx, ny))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving channel flow  in 2D\n",
    "\n",
    "Next comes the actual core code of our ocmputation and we will reach back to step 9 when we worked on laplace's equation to use a trick we developed then. Since we're only interested in what the grid will look like once we have reached a near-steady-state solution we could either specify a number of timesteps `nt` and increment that value until we're satisfied, or we can tell our code to run until the difference between two consecutive iterations gets samall.\n",
    "\n",
    "There are also 8 separate boundary conditions that must be met at each iteration. The code below writes them all explicitely."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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 = (np.sum(u) - np.sum(un)) / np.sum(u)\n",
    "    stepcount += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code above also includes a new variable called stepcout that keeps track of how many iterations the loop went through before the stop condition was met."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "498\n"
     ]
    }
   ],
   "source": [
    "print(stepcount)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1100x700 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (11,7), dpi=100)\n",
    "plt.quiver(X[::3, ::3], Y[::3, ::3], u[::3, ::3], v[::3, ::3]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Results\n",
    "\n",
    "This final image brings this module to a close and showcases how far we have come. Animating this would not be very useful since there is very little transient activity and we only care about the steady state solution. Hence we will skip the work on making an animation for this last step."
   ]
  }
 ],
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