Raleigh-Taylor-Instability.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNUMsonk5MUzVYyMYuTHAYx",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/costpetrides/Fluid-Dynamics-Navier-Stokes/blob/main/Raleigh-Taylor-Instability.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pip install imageio"
      ],
      "metadata": {
        "id": "dOR9QUa8Jipq",
        "outputId": "4c7b6154-2798-44b7-bdd0-977f60593993",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: imageio in /usr/local/lib/python3.10/dist-packages (2.36.1)\n",
            "Requirement already satisfied: numpy in /usr/local/lib/python3.10/dist-packages (from imageio) (1.26.4)\n",
            "Requirement already satisfied: pillow>=8.3.2 in /usr/local/lib/python3.10/dist-packages (from imageio) (11.0.0)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "import imageio\n",
        "import os\n",
        "\n",
        "def main():\n",
        "    \"\"\" Finite Volume simulation \"\"\"\n",
        "\n",
        "    # Simulation parameters\n",
        "    N                      = 64  # resolution N x 3N\n",
        "    boxsizeX               = 0.5\n",
        "    boxsizeY               = 1.5\n",
        "    gamma                  = 1.4  # ideal gas gamma\n",
        "    courant_fac            = 0.4\n",
        "    t                      = 0\n",
        "    tEnd                   = 15\n",
        "    tOut                   = 0.1  # draw frequency\n",
        "    useSlopeLimiting       = False\n",
        "    plotRealTime = True  # switch on for plotting as the simulation goes along\n",
        "\n",
        "    # Mesh\n",
        "    dx = boxsizeX / N\n",
        "    vol = dx**2\n",
        "    xlin = np.linspace(0.5*dx, boxsizeX-0.5*dx, N)\n",
        "    ylin = np.linspace(0.5*dx, boxsizeY-0.5*dx, 3*N)\n",
        "    Y, X = np.meshgrid(ylin, xlin)\n",
        "\n",
        "    # Generate Initial Conditions - heavy fluid on top of light, with perturbation\n",
        "    g = -0.1  # gravity\n",
        "    w0 = 0.0025\n",
        "    P0 = 2.5\n",
        "    rho = 1. + (Y > 0.75)\n",
        "    vx = np.zeros(X.shape)\n",
        "    vy = w0 * (1-np.cos(4*np.pi*X)) * (1-np.cos(4*np.pi*Y/3))\n",
        "    P = P0 + g * (Y-0.75) * rho\n",
        "\n",
        "    rho, vx, vy, P = addGhostCells(rho, vx, vy, P)\n",
        "\n",
        "    # Get conserved variables\n",
        "    Mass, Momx, Momy, Energy = getConserved(rho, vx, vy, P, gamma, vol)\n",
        "\n",
        "    # Create a folder to store frames\n",
        "    if not os.path.exists('frames'):\n",
        "        os.makedirs('frames')\n",
        "\n",
        "    outputCount = 1\n",
        "\n",
        "    # Simulation Main Loop\n",
        "    while t < tEnd:\n",
        "\n",
        "        # get Primitive variables\n",
        "        rho, vx, vy, P = getPrimitive(Mass, Momx, Momy, Energy, gamma, vol)\n",
        "\n",
        "        # get time step (CFL) = dx / max signal speed\n",
        "        dt = courant_fac * np.min(dx / (np.sqrt(gamma*P/rho) + np.sqrt(vx**2+vy**2)))\n",
        "        plotThisTurn = False\n",
        "        if t + dt > outputCount*tOut:\n",
        "            dt = outputCount*tOut - t\n",
        "            plotThisTurn = True\n",
        "\n",
        "        # Add Source (half-step)\n",
        "        Mass, Momx, Momy, Energy = addSourceTerm(Mass, Momx, Momy, Energy, g, dt/2)\n",
        "\n",
        "        # get Primitive variables\n",
        "        rho, vx, vy, P = getPrimitive(Mass, Momx, Momy, Energy, gamma, vol)\n",
        "\n",
        "        # calculate gradients\n",
        "        rho_dx, rho_dy = getGradient(rho, dx)\n",
        "        vx_dx,  vx_dy  = getGradient(vx,  dx)\n",
        "        vy_dx,  vy_dy  = getGradient(vy,  dx)\n",
        "        P_dx,   P_dy   = getGradient(P,   dx)\n",
        "\n",
        "        # slope limit gradients\n",
        "        if useSlopeLimiting:\n",
        "            rho_dx, rho_dy = slopeLimit(rho, dx, rho_dx, rho_dy)\n",
        "            vx_dx,  vx_dy  = slopeLimit(vx , dx, vx_dx,  vx_dy )\n",
        "            vy_dx,  vy_dy  = slopeLimit(vy , dx, vy_dx,  vy_dy )\n",
        "            P_dx,   P_dy   = slopeLimit(P  , dx, P_dx,   P_dy  )\n",
        "\n",
        "        # extrapolate half-step in time\n",
        "        rho_prime = rho - 0.5*dt * ( vx * rho_dx + rho * vx_dx + vy * rho_dy + rho * vy_dy)\n",
        "        vx_prime  = vx  - 0.5*dt * ( vx * vx_dx + vy * vx_dy + (1/rho) * P_dx )\n",
        "        vy_prime  = vy  - 0.5*dt * ( vx * vy_dx + vy * vy_dy + (1/rho) * P_dy )\n",
        "        P_prime   = P   - 0.5*dt * ( gamma*P * (vx_dx + vy_dy)  + vx * P_dx + vy * P_dy )\n",
        "\n",
        "        # extrapolate in space to face centers\n",
        "        rho_XL, rho_XR, rho_YL, rho_YR = extrapolateInSpaceToFace(rho_prime, rho_dx, rho_dy, dx)\n",
        "        vx_XL,  vx_XR,  vx_YL,  vx_YR  = extrapolateInSpaceToFace(vx_prime,  vx_dx,  vx_dy,  dx)\n",
        "        vy_XL,  vy_XR,  vy_YL,  vy_YR  = extrapolateInSpaceToFace(vy_prime,  vy_dx,  vy_dy,  dx)\n",
        "        P_XL,   P_XR,   P_YL,   P_YR   = extrapolateInSpaceToFace(P_prime,   P_dx,   P_dy,   dx)\n",
        "\n",
        "        # compute fluxes (local Lax-Friedrichs/Rusanov)\n",
        "        flux_Mass_X, flux_Momx_X, flux_Momy_X, flux_Energy_X = getFlux(rho_XL, rho_XR, vx_XL, vx_XR, vy_XL, vy_XR, P_XL, P_XR, gamma)\n",
        "        flux_Mass_Y, flux_Momy_Y, flux_Momx_Y, flux_Energy_Y = getFlux(rho_YL, rho_YR, vy_YL, vy_YR, vx_YL, vx_YR, P_YL, P_YR, gamma)\n",
        "\n",
        "        # update solution\n",
        "        Mass   = applyFluxes(Mass, flux_Mass_X, flux_Mass_Y, dx, dt)\n",
        "        Momx   = applyFluxes(Momx, flux_Momx_X, flux_Momx_Y, dx, dt)\n",
        "        Momy   = applyFluxes(Momy, flux_Momy_X, flux_Momy_Y, dx, dt)\n",
        "        Energy = applyFluxes(Energy, flux_Energy_X, flux_Energy_Y, dx, dt)\n",
        "\n",
        "        # Add Source (half-step)\n",
        "        Mass, Momx, Momy, Energy = addSourceTerm(Mass, Momx, Momy, Energy, g, dt/2)\n",
        "\n",
        "        # update time\n",
        "        t += dt\n",
        "\n",
        "        # Save frame if we need to plot\n",
        "        if plotThisTurn or (t >= tEnd):\n",
        "            plt.cla()\n",
        "            plt.imshow(rho.T)\n",
        "            plt.clim(0.4, 2.0)\n",
        "            ax = plt.gca()\n",
        "            ax.invert_yaxis()\n",
        "            ax.get_xaxis().set_visible(False)\n",
        "            ax.get_yaxis().set_visible(False)\n",
        "            ax.set_aspect('equal')\n",
        "\n",
        "            # Save current frame as image\n",
        "            plt.savefig(f'frames/frame_{outputCount:04d}.png')\n",
        "            outputCount += 1\n",
        "\n",
        "    # Create GIF from frames\n",
        "    with imageio.get_writer('simulation.gif', mode='I', duration=0.1) as writer:\n",
        "        for i in range(1, outputCount):\n",
        "            image = imageio.imread(f'frames/frame_{i:04d}.png')\n",
        "            writer.append_data(image)\n",
        "\n",
        "    # Cleanup by removing the frames directory\n",
        "    for i in range(1, outputCount):\n",
        "        os.remove(f'frames/frame_{i:04d}.png')\n",
        "    os.rmdir('frames')\n",
        "\n",
        "    print(\"GIF has been created and saved as 'simulation.gif'\")\n",
        "    return 0\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()\n"
      ],
      "metadata": {
        "id": "jCxMz-k_Jpo5",
        "outputId": "2fdcc47d-a796-4bca-9f4e-8373710193a3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 477
        }
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "<ipython-input-3-06ad4fc47ae8>:126: DeprecationWarning: Starting with ImageIO v3 the behavior of this function will switch to that of iio.v3.imread. To keep the current behavior (and make this warning disappear) use `import imageio.v2 as imageio` or call `imageio.v2.imread` directly.\n",
            "  image = imageio.imread(f'frames/frame_{i:04d}.png')\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "GIF has been created and saved as 'simulation.gif'\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}