11_Navier-Stokes_Cavity_Flow_in_2D_EJW.ipynb

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    "# Navier-Stokes equations in 2D (for an incompressible fluid)\n",
    "\n",
    "By this point, we have all of the building blocks needed to solve the Navier-Stokes equations for an incompressible fluid in 2D.\n",
    "\n",
    "The two governing equations in this case are the continuity equation (which encapsulates the conservation of mass of the fluid) and the Navier-Stokes equation (which encodes the conservation of momentum of the fluid). The continuity equation can be expressed as\n",
    "\n",
    "\\begin{align}\n",
    "  \\frac{\\partial \\rho}{\\partial t} + \\nabla\\left(\\rho \\vec{u}\\right) = 0,\n",
    "\\end{align}\n",
    "\n",
    "where $\\rho=\\rho(\\vec{x},t)$ is the mass density of the fluid and $\\vec{u}=\\vec{u}(\\vec{x},t)$ is the velocity of the fluid. The Navier-Stokes or momentum equation takes the form \n",
    "\n",
    "\\begin{align}\n",
    "  \\rho\\left(\\frac{\\partial \\vec{u}}{\\partial t} + \\left(\\vec{u}\\cdot\\nabla\\right)\\vec{u}\\right)\n",
    "  = -\\nabla\\bar{p} + \\mu\\nabla^2\\vec{u} + \\frac{1}{3}\\mu\\nabla(\\nabla\\cdot\\vec{u}) \n",
    "  + \\rho\\vec{g} + \\vec{f}_\\mathrm{ext}, \n",
    "\\end{align}\n",
    "\n",
    "where $\\mu$ is the dynamic viscosity of the fluid and $\\bar{p}$ is the thermodynamical pressure, related to the mechanical pressure and bulk viscosity $\\zeta$ by\n",
    "\n",
    "\\begin{align}\n",
    "  \\bar{p} = p - \\zeta\\nabla\\cdot\\vec{u}.\n",
    "\\end{align}\n",
    "\n",
    "The acceleration due to gravity is denoted by $\\vec{g}$. The sum of external forces on the fluid (per unit volume) is given by $\\vec{f}_\\mathrm{ext}$. In what follows, we will be considering fluid flow in the absence of external forces, including gravity (i.e., 2D flow in the horizontal plane, so that gravitational forces play no role in the fluid motion). Hence we set $\\vec{g}=0$ and $\\vec{f}_\\mathrm{ext}=0$ from here on.\n",
    "\n",
    "Incompressible fluid implies $\\rho(\\vec{x},t)=\\rho=\\text{const}$, which combined with the continuity equation implies $\\nabla\\cdot\\vec{u}=0$. With this, Navier-Stokes simplifes to \n",
    "\n",
    "\\begin{align}\n",
    "  \\frac{\\partial \\vec{u}}{\\partial t} + \\left(\\vec{u}\\cdot\\nabla\\right)\\vec{u}\n",
    "  = -\\frac{1}{\\rho}\\nabla{p} + \\nu\\nabla^2\\vec{u},\n",
    "\\end{align}\n",
    "\n",
    "where $\\nu\\equiv\\mu/\\rho$, which we will also assume is constant. \n",
    "\n",
    "Now we consider 2D fluid motion, letting $\\vec{u}(\\vec{x},t)=\\vec{u}(x,y,t)=[u(x,y,t),v(x,y,t)]$. In terms of these components, the Navier-Stokes equation becomes\n",
    "\n",
    "\\begin{align}\n",
    "  & \\frac{\\partial u}{\\partial t} + u\\frac{\\partial u}{\\partial x} + v\\frac{\\partial u}{\\partial y}\n",
    "  = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial x} \n",
    "  + \\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}\n",
    "  = -\\frac{1}{\\rho}\\frac{\\partial p}{\\partial y} \n",
    "  + \\nu\\left(\\frac{\\partial^2 v}{\\partial x^2} + \\frac{\\partial^2 v}{\\partial y^2}\\right),\n",
    "\\end{align}\n",
    "\n",
    "where $u=u(x,y,t)$, $v=v(x,y,t)$, and $p=p(x,y,t)$. You should recognize many of the terms that appear here. These equations are nearly identical to the 2D Burger's equations that we have already solved (Step 8). The only new terms are the pressure gradients on the right-hand sides. These terms introduce a slight complication, stemming from the fact that we don't have an evolution equation for the pressure. So how can we evolve it?\n",
    "\n",
    "Pressure is related to the density of the fluid through an equation of state. Evolution of the density and pressure are governed by the continuity equation. But for an incomressible fluid, the continuity equation yields the non-dynamical constraint, $\\nabla\\cdot\\vec{u}=0$. So there must also be a constraint on the pressure. To obtain it, we take a divergence of the Navier-Stokes equation. If we do this analytically, after some simplifications this leads to the following Poisson equation for the pressure\n",
    "\n",
    "\\begin{align}\n",
    "  \\left(\\frac{\\partial^2 p}{\\partial x^2} + \\frac{\\partial^2 p}{\\partial y^2}\\right)\n",
    "  = -\\rho\\left(\\left(\\frac{\\partial u}{\\partial x}\\right)^2\n",
    "  + 2\\frac{\\partial u}{\\partial y}\\frac{\\partial v}{\\partial x}\n",
    "  + \\left(\\frac{\\partial v}{\\partial y}\\right)^2\\right).\n",
    "\\end{align}\n",
    "\n",
    "However, we cannot expect $\\nabla\\cdot\\vec{u}=0$ to remain satisfied in the discrete world. Numerical errors will always creep in, violating the incompressibility constraint. There are two approaches for handling this. One approach is to enforce the constraint on the initial data once and for all, and then evolve those data freely (checking to what extent the constraint is still satisfied at the end). This is called free evolution. The second approach, called constrained evolution, is to enforce the constraint at each step in the evolution. We will take the second approach.\n",
    "\n",
    "Let's return to the step where we take the divergence of Navier-Stokes and proceed a bit more cautiously. Taking a divergence yields\n",
    "\n",
    "\\begin{align}\n",
    "  \\rho\\left(\\frac{\\partial}{\\partial t}(\\nabla\\cdot\\vec{u}) \n",
    "  + \\nabla\\cdot\\left(\\vec{u}\\cdot\\nabla\\right)\\vec{u}\\right)\n",
    "  = -\\nabla^2(p - \\zeta(\\nabla\\cdot\\vec{u})) + \\mu\\nabla\\cdot(\\nabla^2\\vec{u}) \n",
    "  + \\frac{1}{3}\\mu\\nabla\\cdot(\\nabla(\\nabla\\cdot\\vec{u})).\n",
    "\\end{align}\n",
    "\n",
    "Here we do not assume that $\\nabla\\cdot\\vec{u}$ is exactly zero. However when we discretize this equation, the higher-order derivatives will be more accurate than the rest of our code allows. So these terms can be neglected. Dropping all third derivatives and re-arranging yields\n",
    "\n",
    "\\begin{align}\n",
    "  \\nabla^2p\n",
    "  = -\\rho\\left(\\frac{\\partial}{\\partial t}(\\nabla\\cdot\\vec{u}) \n",
    "  + \\nabla\\cdot\\left(\\vec{u}\\cdot\\nabla\\right)\\vec{u}\\right).\n",
    "\\end{align}\n",
    "\n",
    "We now discretize in time and re-write this as \n",
    "\n",
    "\\begin{align}\n",
    "  (\\nabla\\cdot\\vec{u})^{n+1}\n",
    "  = (\\nabla\\cdot\\vec{u})^{n} \n",
    "  - \\Delta{t}\\left(\\frac{1}{\\rho}\\nabla^2p^{n} \n",
    "  + \\nabla\\cdot\\left(\\vec{u}^{n}\\cdot\\nabla\\right)\\vec{u}^{n}\\right).\n",
    "\\end{align}\n",
    "\n",
    "To enforce the incompressibility constraint, we want $(\\nabla\\cdot\\vec{u})^{n+1}=0$. In other words, at each step small constraint violations may be present. But to keep those violations from accumulating, or propagating, we set them to zero at the beginning of each step. At long last, this gives the constraint equation\n",
    "\n",
    "\\begin{align}\n",
    "  \\nabla^2p^{n} \n",
    "  = \\rho\\left(\\frac{1}{\\Delta{t}}(\\nabla\\cdot\\vec{u})^{n}\n",
    "  - \\nabla\\cdot\\left(\\vec{u}^{n}\\cdot\\nabla\\right)\\vec{u}^{n}\\right).\n",
    "\\end{align}\n",
    "\n",
    "Writing this in terms of components yields\n",
    "\n",
    "\\begin{align}\n",
    "  \\left(\\frac{\\partial^2 p^{n}}{\\partial x^2} + \\frac{\\partial^2 p^{n}}{\\partial y^2}\\right)\n",
    "  = \\rho\\left[\n",
    "  \\frac{1}{\\Delta{t}}\\left(\\frac{\\partial u^{n}}{\\partial x} + \\frac{\\partial v^{n}}{\\partial y}\\right)\n",
    "  - \\left(\\frac{\\partial u^{n}}{\\partial x}\\right)^2\n",
    "  - 2\\frac{\\partial u^{n}}{\\partial y}\\frac{\\partial v^{n}}{\\partial x}\n",
    "  - \\left(\\frac{\\partial v^{n}}{\\partial y}\\right)^2\n",
    "  - u^{n}\\frac{\\partial^2 u^{n}}{\\partial x^2} \n",
    "  - u^{n}\\frac{\\partial^2 v^{n}}{\\partial x \\partial y}\n",
    "  - v^{n}\\frac{\\partial^2 v^{n}}{\\partial x \\partial y} \n",
    "  - v^{n}\\frac{\\partial^2 v^{n}}{\\partial y^2}\n",
    "  \\right].\n",
    "\\end{align}\n",
    "\n",
    "Ensuring that this equation is satisfied will enforce $\\nabla\\cdot\\vec{u}^{n+1}=0$ at every new time step. \n",
    "\n",
    "In sum, we need to evolve the two momentum equations (the Navier-Stokes equations) while simultaneously satisfying the Poisson constraint equation for the pressure. Before solving, we also need initial conditions and boudary conditions, which we turn to now."
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    "## Cavity flow in 2D\n",
    "\n",
    "Here we will consider flow in a 2D cavity that is exposed on one side. We take the cavity to be rectangular, with edges at $x=0$, $x=L_{x}$, $y=0$ and $y=L_{y}$. We will take the boundary at $y=L_{y}$ to be open. Think of a very thin aquarium tank whose topside is exposed to the air. We are going to neglect any flow out of the vertical plane (for that, we would need 3D equations). We are also going to ignore gravity.\n",
    "\n",
    "The situation we want to solve for is when the fluid at the upper exposed boundary is given a constant horizontal flow. (For example, a constant wind blowing across the surface of the fluid.) \n",
    "\n",
    "The initial and boundary conditions that we will use to model this situation are the following. Initially, all fields are set to zero\n",
    "\n",
    "\\begin{align}\n",
    "  & u(x,y,0) = 0 \\\\\n",
    "  & v(x,y,0) = 0 \\\\\n",
    "  & p(x,y,0) = 0\n",
    "\\end{align}\n",
    "\n",
    "The boundary conditions for pressure are\n",
    "\n",
    "\\begin{align}\n",
    "  & \\frac{\\partial p}{\\partial x}(0,y,t) = 0 \\\\\n",
    "  & \\frac{\\partial p}{\\partial x}(L_{x},y,t) = 0 \\\\\n",
    "  & \\frac{\\partial p}{\\partial x}(x,0,t) = 0 \\\\\n",
    "  & p(x,L_{y},t) = 0.\n",
    "\\end{align}\n",
    "\n",
    "The boundary conditions for the velocity field are\n",
    "\n",
    "\\begin{align}\n",
    "  & u(0,y,t) = v(0,y,t) = 0 \\\\\n",
    "  & u(L_{x},y,t) = v(L_{x},y,t) = 0 \\\\\n",
    "  & u(x,0,t) = v(x,0,t) = 0 \\\\\n",
    "  & u(x,L_{y},t) = 1 \\quad,\\quad v(x,L_{y},t) = 0.\n",
    "\\end{align}\n",
    "\n",
    "We solve the above Navier-Stokes equations along with the pressure constraint, subject to these initial conditions and boundary conditions. Next we turn to the task of discretizing the system of equations using finite differences."
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    "## Discretization and evolution scheme\n",
    "\n",
    "As before, we take the boundary to be a 2D rectangular grid with dimensions $L_x$ and $L_y$. \n",
    "\n",
    "We treat the evolution equations (momentum equations) as we did for Burger's equation in 2D. We treat time derivatives with forward differences, advection terms with backward differences, and all other spatial derivatives with centered differences. This yields the difference equations\n",
    "\n",
    "\\begin{align}\n",
    "  & u^{n+1}_{i,j} = u^{n}_{i,j} \n",
    "  - \\frac{\\Delta{t}}{\\Delta{x}}u^{n}_{i,j}\\left(u^{n}_{i,j} - u^{n}_{i-1,j}\\right)\n",
    "  - \\frac{\\Delta{t}}{\\Delta{y}}v^{n}_{i,j}\\left(u^{n}_{i,j} - u^{n}_{i,j-1}\\right)\n",
    "  - \\frac{\\Delta{t}}{2\\rho\\Delta{x}}\\left(p^{n}_{i+1,j} - p^{n}_{i-1,j}\\right)\n",
    "  \\\\ & \\quad\\quad\\quad\n",
    "  + \\frac{\\nu\\Delta{t}}{(\\Delta{x})^2}\\left(u^{n}_{i+1,j} - 2u^{n}_{i,j} + u^{n}_{i-1,j}\\right)\n",
    "  + \\frac{\\nu\\Delta{t}}{(\\Delta{y})^2}\\left(u^{n}_{i,j+1} - 2u^{n}_{i,j} + u^{n}_{i,j-1}\\right)\n",
    "\\end{align}\n",
    "\n",
    "\\begin{align}\n",
    "  & v^{n+1}_{i,j} = v^{n}_{i,j} \n",
    "  - \\frac{\\Delta{t}}{\\Delta{x}}u^{n}_{i,j}\\left(v^{n}_{i,j} - v^{n}_{i-1,j}\\right)\n",
    "  - \\frac{\\Delta{t}}{\\Delta{y}}v^{n}_{i,j}\\left(v^{n}_{i,j} - v^{n}_{i,j-1}\\right)\n",
    "  - \\frac{\\Delta{t}}{2\\rho\\Delta{y}}\\left(p^{n}_{i+1,j} - p^{n}_{i,j-1}\\right)\n",
    "  \\\\ & \\quad\\quad\\quad\n",
    "  + \\frac{\\nu\\Delta{t}}{(\\Delta{x})^2}\\left(v^{n}_{i+1,j} - 2v^{n}_{i,j} + v^{n}_{i-1,j}\\right)\n",
    "  + \\frac{\\nu\\Delta{t}}{(\\Delta{y})^2}\\left(v^{n}_{i,j+1} - 2v^{n}_{i,j} + v^{n}_{i,j-1}\\right).\n",
    "\\end{align}\n",
    "\n",
    "We treat the constraint equation as we did for Poisson's equation. We discretize the spatial derivatives using centered finite differences to setup the relaxation equation\n",
    "\n",
    "\\begin{align}\n",
    "  p^{[r+1]}_{i,j} =\n",
    "  \\frac{(\\Delta{y})^2\\left(p^{[r]}_{i+1,j} + p^{[r]}_{i-1,j}\\right)\n",
    "  + (\\Delta{x})^2\\left(p^{[r]}_{i,j+1} + p^{[r]}_{i,j-1}\\right)\n",
    "  - (\\Delta{x})^2(\\Delta{y})^2 s_{i,j}}{2\\left((\\Delta{x})^2 + (\\Delta{y})^2\\right)},\n",
    "\\end{align}\n",
    "\n",
    "where the source function is given by \n",
    "\n",
    "\\begin{align}\n",
    "  s_{i,j} = \n",
    "  &\\rho\\left[\n",
    "  \\frac{1}{2\\Delta{t}\\Delta{x}}(u^{n}_{i+1,j} - u^{n}_{i-1,j})\n",
    "  +\\frac{1}{2\\Delta{t}\\Delta{y}}(v^{n}_{i,j+1} - v^{n}_{i,j-1})\\right.\n",
    "  \\\\\n",
    "  &\\quad\n",
    "  -\\frac{1}{4(\\Delta{x})^2}(u^{n}_{i+1,j} - u^{n}_{i-1,j})^2\n",
    "  - \\frac{1}{2\\Delta{x}\\Delta{y}}(u^{n}_{i,j+1} - u^{n}_{i,j-1})(v^{n}_{i+1,j} - v^{n}_{i-1,j})\n",
    "  - \\frac{1}{4(\\Delta{y})^2}(v^{n}_{i,j+1} - v^{n}_{i,j-1})^2\n",
    "  \\\\\n",
    "  &\\quad\n",
    "  - \\frac{1}{(\\Delta{x})^2}u^{n}_{i,j}\\left(u^{n}_{i+1,j} - 2u^{n}_{i,j} + u^{n}_{i-1,j}\\right)\n",
    "  - \\frac{1}{4\\Delta{x}\\Delta{y}}u^{n}_{i,j}\n",
    "    \\left(u^{n}_{i+1,j+1} - u^{n}_{i+1,j-1} - u^{n}_{i-1,j+1} + u^{n}_{i-1,j-1}\\right)\n",
    "  \\\\\n",
    "  &\\quad\\left.\n",
    "  - \\frac{1}{4\\Delta{x}\\Delta{y}}v^{n}_{i,j}\n",
    "    \\left(v^{n}_{i+1,j+1} - v^{n}_{i+1,j-1} - v^{n}_{i-1,j+1} + v^{n}_{i-1,j-1}\\right)\n",
    "  - \\frac{1}{(\\Delta{y})^2}v^{n}_{i,j}\\left(v^{n}_{i,j+1} - 2v^{n}_{i,j} + v^{n}_{i,j-1}\\right)\n",
    "  \\right].\n",
    "\\end{align}\n",
    "\n",
    "The idea to solve is the following. Use the initial data for $u$ and $v$ to construct the source function $s$. Then solve the pressure constraint equation to obtain $p$. Then feed this into the evolution equation (Navier-Stokes equations) and solve for $u$ and $v$ at the next time step. Repeat for as many time steps as desired. Now let's code it up!\n",
    "\n",
    "(The below is lengthy. To help with organization, several subroutines have been introduced. To decipher the code, it will help to first look at the \"main\" routine, which here is called \"navstokes2D\". This appears toward the bottom of the page.)"
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   "source": [
    "import numpy as np\n",
    "import time\n",
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "from mpl_toolkits.mplot3d import axes3d"
   ]
  },
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   "cell_type": "code",
   "execution_count": 2,
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    "# calculate rhs for pressure constraint\n",
    "def poisson_rhs(un, vn, dx, dy, dt, rho):\n",
    "\n",
    "    # print message (debugging)\n",
    "    #print('re-calculating rhs for pressure equation...')\n",
    "\n",
    "    # initialize arrays\n",
    "    dudx = np.zeros_like(un)\n",
    "    dvdx = np.zeros_like(vn)\n",
    "    dudy = np.zeros_like(un)\n",
    "    dvdy = np.zeros_like(vn)\n",
    "    ududxx = np.zeros_like(un)\n",
    "    vdudxy = np.zeros_like(vn)\n",
    "    udvdyx = np.zeros_like(un)\n",
    "    vdvdyy = np.zeros_like(vn)\n",
    "\n",
    "    # interior points\n",
    "    dudx[1:-1, 1:-1] = (un[2:, 1:-1] - un[0:-2, 1:-1])/(2*dx) #centered x difference\n",
    "    dvdx[1:-1, 1:-1] = (vn[2:, 1:-1] - vn[0:-2, 1:-1])/(2*dx) #centered x difference\n",
    "    dudy[1:-1, 1:-1] = (un[1:-1, 2:] - un[1:-1, 0:-2])/(2*dy) #centered y difference\n",
    "    dvdy[1:-1, 1:-1] = (vn[1:-1, 2:] - vn[1:-1, 0:-2])/(2*dy) #centered y difference\n",
    "\n",
    "    ududxx[1:-1,1:-1] = un[1:-1,1:-1]*(un[2:,1:-1] - 2*un[1:-1,1:-1] + un[0:-2,1:-1])/(dx*dx) #centered x difference\n",
    "    vdvdyy[1:-1,1:-1] = vn[1:-1,1:-1]*(vn[2:,1:-1] - 2*vn[1:-1,1:-1] + vn[0:-2,1:-1])/(dy*dy) #centered x difference\n",
    "    vdudxy[1:-1,1:-1] = vn[1:-1,1:-1]*(un[2:,2:] - un[2:,0:-2] - un[0:-2,2:] + un[0:-2,0:-2])/(4*dx*dy) #centered differences\n",
    "    udvdyx[1:-1,1:-1] = un[1:-1,1:-1]*(vn[2:,2:] - vn[2:,0:-2] - vn[0:-2,2:] + vn[0:-2,0:-2])/(4*dx*dy) #centered differences\n",
    "\n",
    "#    # boundary edge x=0\n",
    "#    dudx[0, 1:-1] = (un[1, 1:-1] - un[0, 1:-1])/dx #forward x difference\n",
    "#    dvdx[0, 1:-1] = (vn[1, 1:-1] - vn[0, 1:-1])/dx #forward x difference\n",
    "#    dudy[0, 1:-1] = 0.5*(un[0, 2:] - un[0, 0:-2])/dy #centered y difference\n",
    "#    dvdy[0, 1:-1] = 0.5*(vn[0, 2:] - vn[0, 0:-2])/dy #centered y difference\n",
    "\n",
    "#    # boundary edge x=Lx\n",
    "#    dudx[-1, 1:-1] = (un[-2, 1:-1] - un[-1, 1:-1])/dx #forward x difference\n",
    "#    dvdx[-1, 1:-1] = (vn[-2, 1:-1] - vn[-1, 1:-1])/dx #forward x difference\n",
    "#    dudy[-1, 1:-1] = 0.5*(un[-1, 2:] - un[-1, 0:-2])/dy #centered y difference\n",
    "#    dvdy[-1, 1:-1] = 0.5*(vn[-1, 2:] - vn[-1, 0:-2])/dy #centered y difference\n",
    "\n",
    "#    # boundary edge y=0\n",
    "#    dudx[1:-1, 0] = 0.5*(un[2:, 0] - un[0:-2, 0])/dx #centered x difference\n",
    "#    dvdx[1:-1, 0] = 0.5*(vn[2:, 0] - vn[0:-2, 0])/dx #centered x difference\n",
    "#    dudy[1:-1, 0] = (un[1:-1, 1] - un[1:-1, 0])/dy #forward y difference\n",
    "#    dvdy[1:-1, 0] = (vn[1:-1, 1] - vn[1:-1, 0])/dy #forward y difference\n",
    "\n",
    "#    # boundary edge y=Ly\n",
    "#    dudx[1:-1, -1] = 0.5*(un[2:, -1] - un[0:-2, -1])/dx #centered x difference\n",
    "#    dvdx[1:-1, -1] = 0.5*(vn[2:, -1] - vn[0:-2, -1])/dx #centered x difference\n",
    "#    dudy[1:-1, -1] = (un[1:-1, -2] - un[1:-1, -1])/dy #forward y difference\n",
    "#    dvdy[1:-1, -1] = (vn[1:-1, -2] - vn[1:-1, -1])/dy #forward y difference\n",
    "\n",
    "#    # boundary corner x=0, y=0\n",
    "#    dudx[0, 0] = (un[1, 0] - un[0, 0])/dx #forward x difference\n",
    "#    dvdx[0, 0] = (vn[1, 0] - vn[0, 0])/dx #forward x difference\n",
    "#    dudy[0, 0] = (un[0, 1] - un[0, 0])/dy #forward y difference\n",
    "#    dvdy[0, 0] = (vn[0, 1] - vn[0, 0])/dy #forward y difference\n",
    "#    # boundary corner x=0, y=Ly\n",
    "#    dudx[0, -1] = (un[1, -1] - un[0, -1])/dx #forward x difference\n",
    "#    dvdx[0, -1] = (vn[1, -1] - vn[0, -1])/dx #forward x difference\n",
    "#    dudy[0, -1] = (un[0, -2] - un[0, -1])/dy #forward y difference\n",
    "#    dvdy[0, -1] = (vn[0, -2] - vn[0, -1])/dy #forward y difference\n",
    "#    # boundary corner x=Lx, y=0\n",
    "#    dudx[-1, 0] = (un[-2, 0] - un[-1, 0])/dx #forward x difference\n",
    "#    dvdx[-1, 0] = (vn[-2, 0] - vn[-1, 0])/dx #forward x difference\n",
    "#    dudy[-1, 0] = (un[-1, 1] - un[-1, 0])/dy #forward y difference\n",
    "#    dvdy[-1, 0] = (vn[-1, 1] - vn[-1, 0])/dy #forward y difference\n",
    "#    # boundary corner x=Lx, y=Ly\n",
    "#    dudx[-1, -1] = (un[-2, -1] - un[-1, -1])/dx #forward x difference\n",
    "#    dvdx[-1, -1] = (vn[-2, -1] - vn[-1, -1])/dx #forward x difference\n",
    "#    dudy[-1, -1] = (un[-1, -2] - un[-1, -1])/dy #forward y difference\n",
    "#    dvdy[-1, -1] = (vn[-1, -2] - vn[-1, -1])/dy #forward y difference\n",
    "\n",
    "    # return source function\n",
    "    return rho*((dudx + dvdy)/dt - (dudx*dudx + 2*dudy*dvdx + dvdy*dvdy) - ududxx - vdudxy - udvdyx - vdvdyy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# poisson boundary conditions at x=0\n",
    "def poisson_bcs_x0(p):\n",
    "    \n",
    "    #bn = 0*p[0,:] # dirichlet, p=0\n",
    "    bn = p[1,:] # neumann, dp/dx=0\n",
    "    \n",
    "    return bn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# poisson boundary conditions at x=Lx\n",
    "def poisson_bcs_xL(p):\n",
    "    \n",
    "    #bn = 0*p[-1,:] # dirichlet, p=0\n",
    "    bn = p[-2,:] # neumann, dp/dx=0\n",
    "    \n",
    "    return bn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# poisson boundary conditions at y=0\n",
    "def poisson_bcs_y0(p):\n",
    "    \n",
    "    #bn = 0*pn[:,0] # dirichlet, p=0\n",
    "    bn = p[:,1] # neumann, dp/dy=0\n",
    "    \n",
    "    return bn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# poisson boundary conditions at y=Ly\n",
    "def poisson_bcs_yL(p):\n",
    "    \n",
    "    bn = 0*p[:,-1] # dirichlet, p=0\n",
    "    #bn = p[:,-2] # neumann, dp/dy=0\n",
    "    \n",
    "    return bn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solve poisson eqn\n",
    "def poisson_solve(p, rhs, dx, dy, omega, tol, maxiter):\n",
    "    \"\"\"\n",
    "    Solve the Poisson equation in 2D using SOR method.\n",
    "    \n",
    "    INPUT:\n",
    "    p = pressure grid function at previous iteration\n",
    "    rhs = source grid function\n",
    "    dx = grid spacing in the x direction\n",
    "    dy = grid spacing in the y direction\n",
    "    omega = over-relaxation parameter\n",
    "    tol = desired tolerance of solution\n",
    "    maxiter = maximum allowed number of iterations\n",
    "    \n",
    "    OUTPUT:\n",
    "    updated pressure\n",
    "    \"\"\"\n",
    "\n",
    "    # print message (debugging)\n",
    "    #print('solving pressure contraint equation...')\n",
    "\n",
    "    # get number of grid points along each axis \n",
    "    nx = len(p[:,0])\n",
    "    ny = len(p[0,:])\n",
    "   \n",
    "    # grid spacing factors\n",
    "    cx = dx*dx/(dx*dx + dy*dy)\n",
    "    cy = dy*dy/(dx*dx + dy*dy)\n",
    "\n",
    "    # sor iteration\n",
    "    for r in range(maxiter):\n",
    "        \n",
    "        # print iteration number (debugging)\n",
    "        #print('  iteration',r)\n",
    "        \n",
    "        # copy solution from previous iteration\n",
    "        pn = np.copy(p)\n",
    "        \n",
    "        # update solution at interior points\n",
    "        p[1:-1,1:-1] = (1 - omega)*pn[1:-1,1:-1] \\\n",
    "        + omega*0.5*cx*(pn[1:-1,2:] + pn[1:-1,0:-2]) \\\n",
    "        + omega*0.5*cy*(pn[2:,1:-1] + pn[0:-2,1:-1]) \\\n",
    "        - omega*0.5*cx*cy*(dx*dx + dy*dy)*rhs[1:-1,1:-1]\n",
    "\n",
    "        # update solution at boundary points\n",
    "        # calculate boundary arrays\n",
    "        bx0 = poisson_bcs_x0(p)\n",
    "        bxL = poisson_bcs_xL(p)\n",
    "        by0 = poisson_bcs_y0(p)\n",
    "        byL = poisson_bcs_yL(p)\n",
    "        # update edges\n",
    "        p[0,:] = bx0\n",
    "        p[-1,:] = bxL\n",
    "        p[:,0] = by0\n",
    "        p[:,-1] = byL\n",
    "        #p[   0, 1:-1] = bx0[1:-1]\n",
    "        #p[  -1, 1:-1] = bxL[1:-1]\n",
    "        #p[1:-1,    0] = by0[1:-1]\n",
    "        #p[1:-1,   -1] = byL[1:-1]\n",
    "        # update corners\n",
    "        #p[   0,    0] = 0.5*(bx0[ 0] + by0[ 0])\n",
    "        #p[   0,   -1] = 0.5*(bx0[-1] + byL[ 0])\n",
    "        #p[  -1,    0] = 0.5*(bxL[ 0] + by0[-1])\n",
    "        #p[  -1,   -1] = 0.5*(bxL[-1] + byL[-1])\n",
    "        \n",
    "        # calculate relative error, check tolerance\n",
    "        #err = la.norm(p - pn, 2)/la.norm(p, 2)\n",
    "        #if err <= tol:\n",
    "        #    break\n",
    "    \n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evolution boundary conditions at x=0\n",
    "def evolve_bcs_x0(u, v):\n",
    "    \n",
    "    # bc for u\n",
    "    ubn = 0*u[0,:] # dirichlet, u=0\n",
    "    #ubn = u[1,:] # neumann, du/dx=0\n",
    "    \n",
    "    # bc for v\n",
    "    vbn = 0*v[0,:] # dirichlet, v=0\n",
    "    #vbn = v[1,:] # neumann, dv/dx=0\n",
    "    \n",
    "    return ubn, vbn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evolution boundary conditions at x=Lx\n",
    "def evolve_bcs_xL(u, v):\n",
    "    \n",
    "    # bc for u\n",
    "    ubn = 0*u[-1,:] # dirichlet, u=0\n",
    "    #ubn = u[-2,:] # neumann, du/dx=0\n",
    "    \n",
    "    # bc for v\n",
    "    vbn = 0*v[-1,:] # dirichlet, v=0\n",
    "    #vbn = v[-2,:] # neumann, dv/dx=0\n",
    "    \n",
    "    return ubn, vbn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evolution boundary conditions at y=0\n",
    "def evolve_bcs_y0(u, v):\n",
    "\n",
    "    # bc for u\n",
    "    ubn = 0*u[:,0] # dirichlet, u=0\n",
    "    #ubn = u[:,1] # neumann, du/dy=0\n",
    "    \n",
    "    # bc for v\n",
    "    vbn = 0*v[:,0] # dirichlet, v=0\n",
    "    #vbn = v[:,1] # neumann, dv/dy=0\n",
    "    \n",
    "    return ubn, vbn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evolution boundary conditions at y=Ly\n",
    "def evolve_bcs_yL(u, v):\n",
    "    \n",
    "    # bc for u\n",
    "    ubn = np.ones_like(u[:,-1]) # dirichlet, u=1\n",
    "    #ubn = 0*u[:,0] # dirichlet, u=0\n",
    "    #ubn = u[:,-2] # neumann, du/dy=0\n",
    "    \n",
    "    # bc for v\n",
    "    vbn = 0*v[:,-1] # dirichlet, v=0\n",
    "    #vbn = v[:,-2] # neumann, dv/dy=0\n",
    "    \n",
    "    return ubn, vbn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# evolve momentum equations\n",
    "def evolve(un, vn, p, dx, dy, dt, nu, rho):\n",
    "    \"\"\"\n",
    "    evolve the momentum equations in 2D\n",
    "    \n",
    "    INPUT:\n",
    "    un = u grid function at previous time step\n",
    "    vn = v grid function at previous time step\n",
    "    p = pressure grid function\n",
    "    dx = grid spacing in the x direction\n",
    "    dy = grid spacing in the y direction\n",
    "    dt = time step size\n",
    "    nu = viscosity coefficient \n",
    "    rho = fluid density\n",
    "    \n",
    "    OUTPUT:\n",
    "    updated u, v\n",
    "    \"\"\"\n",
    "\n",
    "    # print message (debugging)\n",
    "    #print('evolving momentum equations at time step...')\n",
    "\n",
    "    # get number of grid points along each axis \n",
    "    nx = len(un[:,0])\n",
    "    ny = len(un[0,:])\n",
    "   \n",
    "    # initialize output\n",
    "    u = np.zeros_like(un)\n",
    "    v = np.zeros_like(vn)\n",
    "    \n",
    "    # update solution at interior points\n",
    "    u[1:-1, 1:-1] = un[1:-1, 1:-1] \\\n",
    "    - dt/dx*un[1:-1, 1:-1]*(un[1:-1, 1:-1] - un[0:-2, 1:-1]) \\\n",
    "    - dt/dy*vn[1:-1, 1:-1]*(un[1:-1, 1:-1] - un[1:-1, 0:-2]) \\\n",
    "    - 0.5*dt/(rho*dx)*(p[2:, 1:-1] - p[0:-2, 1:-1]) \\\n",
    "    + nu*dt/(dx*dx)*(un[2:  , 1:-1] - 2*un[1:-1, 1:-1] + un[0:-2, 1:-1]) \\\n",
    "    + nu*dt/(dy*dy)*(un[1:-1, 2:  ] - 2*un[1:-1, 1:-1] + un[1:-1, 0:-2])\n",
    "\n",
    "    v[1:-1, 1:-1] = vn[1:-1, 1:-1] \\\n",
    "    - dt/dx*un[1:-1, 1:-1]*(vn[1:-1, 1:-1] - vn[0:-2, 1:-1]) \\\n",
    "    - dt/dy*vn[1:-1, 1:-1]*(vn[1:-1, 1:-1] - vn[1:-1, 0:-2]) \\\n",
    "    - 0.5*dt/(rho*dy)*(p[1:-1, 2:] - p[1:-1, 0:-2]) \\\n",
    "    + nu*dt/(dx*dx)*(vn[2:  , 1:-1] - 2*vn[1:-1, 1:-1] + vn[0:-2, 1:-1]) \\\n",
    "    + nu*dt/(dy*dy)*(vn[1:-1, 2:  ] - 2*vn[1:-1, 1:-1] + vn[1:-1, 0:-2])\n",
    "    \n",
    "    # update solution at boundary points\n",
    "    # calculate boundary arrays\n",
    "    ux0, vx0 = evolve_bcs_x0(u, v)\n",
    "    uxL, vxL = evolve_bcs_xL(u, v)\n",
    "    uy0, vy0 = evolve_bcs_y0(u, v)\n",
    "    uyL, vyL = evolve_bcs_yL(u, v)\n",
    "    # update u at the edges\n",
    "    u[0,:] = ux0\n",
    "    u[-1,:] = uxL\n",
    "    u[:,0] = uy0\n",
    "    u[:,-1] = uyL\n",
    "    #u[   0, 1:-1] = ux0[1:-1]\n",
    "    #u[  -1, 1:-1] = uxL[1:-1]\n",
    "    #u[1:-1,    0] = uy0[1:-1]\n",
    "    #u[1:-1,   -1] = uyL[1:-1]\n",
    "    # update u at the corners\n",
    "    #u[   0,    0] = 0.5*(ux0[ 0] + uy0[ 0])\n",
    "    #u[   0,   -1] = 0.5*(ux0[-1] + uyL[ 0])\n",
    "    #u[  -1,    0] = 0.5*(uxL[ 0] + uy0[-1])\n",
    "    #u[  -1,   -1] = 0.5*(uxL[-1] + uyL[-1])\n",
    "    # update v at the edges\n",
    "    v[0,:] = vx0\n",
    "    v[-1,:] = vxL\n",
    "    v[:,0] = vy0\n",
    "    v[:,-1] = vyL\n",
    "    #v[   0, 1:-1] = vx0[1:-1]\n",
    "    #v[  -1, 1:-1] = vxL[1:-1]\n",
    "    #v[1:-1,    0] = vy0[1:-1]\n",
    "    #v[1:-1,   -1] = vyL[1:-1]\n",
    "    # update v at the corners\n",
    "    #v[   0,    0] = 0.5*(vx0[ 0] + vy0[ 0])\n",
    "    #v[   0,   -1] = 0.5*(vx0[-1] + vyL[ 0])\n",
    "    #v[  -1,    0] = 0.5*(vxL[ 0] + vy0[-1])\n",
    "    #v[  -1,   -1] = 0.5*(vxL[-1] + vyL[-1])\n",
    "    \n",
    "    return u, v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot solution\n",
    "def surfplot(timeStep, X, Y, U, zmax, axis, fig):\n",
    "    axis.cla()                   #clear previous plot\n",
    "    axis.set_zlim(0, zmax) #set z limits of plot\n",
    "    axis.set_xlabel('x')         #set x-axis label\n",
    "    axis.set_ylabel('y')         #set y-axis label\n",
    "    axis.set_zlabel('u(x,y,t)')  #set z-axis label\n",
    "    axis.set_title('time %.2f' % (timeStep)) #set title \n",
    "    axis.plot_surface(X, Y, U, rstride=2, cstride=2, cmap='viridis') #plot u vs x,y\n",
    "    fig.canvas.draw()            #redraw figure\n",
    "    time.sleep(0.05)             #pause"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot solution\n",
    "def vectplot(timeStep, X, Y, U, V, P, axis, fig):\n",
    "    axis.cla()                   #clear previous plot\n",
    "    axis.set_xlabel('x')         #set x-axis label\n",
    "    axis.set_ylabel('y')         #set y-axis label\n",
    "    axis.set_title('time %.2f' % (timeStep)) #set title \n",
    "    axis.contourf(X, Y, P, alpha=0.5, cmap=cm.viridis) # pressure color gradient\n",
    "    #axis.colorbar()\n",
    "    #axis.contour(X, Y, P, cmap=cm.viridis) # pressure contours\n",
    "    axis.quiver(X[::2, ::2], Y[::2, ::2], U[::2, ::2], V[::2, ::2]) # velocity vector field\n",
    "    fig.canvas.draw()            #redraw figure\n",
    "    #time.sleep(0.05)             #pause"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solve Navier-Stokes equations in 2D  \n",
    "def navstokes2D(Lx, Ly, nx, ny, nt):\n",
    "    \"\"\"\n",
    "    solve Navier-Stokes equations in 2D\n",
    "    \n",
    "    Lx = size of spatial grid in the x direction\n",
    "    Ly = size of spatial grid in the y direction\n",
    "    nx = total number of spatial grid points in the x direction\n",
    "    ny = total number of spatial grid points in the y direction\n",
    "    \"\"\"\n",
    "    # physical parameters\n",
    "    nu = 0.1 #diffusivity\n",
    "    rho = 1.0 #density of fluid\n",
    "\n",
    "    # setup spatial grid (vertex-centered)\n",
    "    dx = Lx/(nx-1.)   # grid spacing in x direction\n",
    "    dy = Ly/(ny-1.)   # grid spacing in y direction\n",
    "    x = np.linspace(0, Lx, nx) # x grid\n",
    "    y = np.linspace(0, Ly, ny) # y grid\n",
    "    X, Y = np.meshgrid(x, y, indexing='ij')\n",
    "\n",
    "    # setup time grid\n",
    "    sigma = 0.1\n",
    "    dt = sigma*dx*dy/nu # size of timesteps\n",
    "    print('time step size is',dt)\n",
    "\n",
    "    # sor parameters\n",
    "    tol = 1.0e-3\n",
    "    maxiter = 20\n",
    "    omega = 1.0 #WARNING: over-relaxation (omega>1) seems to be unstable. I'm not sure why.\n",
    "    \n",
    "    # initialize grid functions\n",
    "    u = np.zeros((nx,ny))  # x-velocity at the current step\n",
    "    un = np.zeros((nx,ny)) # x-velocity at the previous step\n",
    "    v = np.zeros((nx,ny))  # y-velocity at the current step\n",
    "    vn = np.zeros((nx,ny)) # y-velocity at the previous step\n",
    "    p = np.zeros((nx,ny))  # pressure at the current step\n",
    "    pn = np.zeros((nx,ny)) # pressure at the previous step\n",
    "    \n",
    "    # create surface plot\n",
    "    #fig = plt.figure(figsize=(7, 5), dpi=100)\n",
    "    #ax1 = fig.gca(projection='3d') \n",
    "\n",
    "    # create vector plot    \n",
    "    fig = plt.figure(figsize=(7,5), dpi=100)\n",
    "    ax1 = fig.add_subplot(1,1,1)\n",
    "\n",
    "    # solve\n",
    "    for n in range(nt):\n",
    "\n",
    "        # copy solution from previous time step\n",
    "        un = u.copy()\n",
    "        vn = v.copy()\n",
    "        pn = p.copy()\n",
    "\n",
    "        # calculate rhs for pressure constraint\n",
    "        sn = poisson_rhs(un, vn, dx, dy, dt, rho)\n",
    "        \n",
    "        # solve pressure constraint\n",
    "        p = poisson_solve(pn, sn, dx, dy, omega, tol, maxiter)\n",
    "\n",
    "        # evolve momentum equations\n",
    "        u, v = evolve(un, vn, p, dx, dy, dt, nu, rho)\n",
    "        \n",
    "        #plot solution\n",
    "        vectplot(n, X, Y, u, v, p, ax1, fig)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "time step size is 0.0025000000000000005\n"
     ]
    },
    {
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       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.5/dist-packages/numpy/ma/core.py:6442: MaskedArrayFutureWarning: In the future the default for ma.maximum.reduce will be axis=0, not the current None, to match np.maximum.reduce. Explicitly pass 0 or None to silence this warning.\n",
      "  return self.reduce(a)\n",
      "/usr/local/lib/python3.5/dist-packages/numpy/ma/core.py:6442: MaskedArrayFutureWarning: In the future the default for ma.minimum.reduce will be axis=0, not the current None, to match np.minimum.reduce. Explicitly pass 0 or None to silence this warning.\n",
      "  return self.reduce(a)\n"
     ]
    }
   ],
   "source": [
    "navstokes2D(2, 2, 41, 41, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": 2
}