Finite Volumen Wand.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Aufgabe 4.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "np.set_printoptions(linewidth=200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aufgabe 4.2.1 - 4.2.3\n",
    "\n",
    "Zelle, Mesh und Solver sowie RBen\n",
    "\n",
    "Der Solver kümmert sich automatisch zwischen den Übergang zwischen den Platten - kappa ist stückweise definiert und die Breite der Zellen ist in den Zellen enthalten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class cell:\n",
    "    normals = np.array([(0, 1, 0), (1, 0, 0), (0, -1, 0), (-1, 0, 0), (0, 0, -1), (0, 0, 1)])\n",
    "    \n",
    "    def __init__(self, position, dimensions):\n",
    "        self.position = np.array(position)\n",
    "        self.dimensions = np.array(dimensions)\n",
    "        # N, E, S, W, V, H\n",
    "        areas = [(np.abs(n) - 1)* dimensions for n in self.normals]\n",
    "        self.areas = [(1 if i[0] == 0 else i[0]) * (1 if i[1] == 0 else i[1]) * (1 if i[2] == 0 else i[2]) for i in areas]\n",
    "class equidistant1DMesh:\n",
    "    def __init__(self, width, dimensions, start_x):\n",
    "        delta_x, delta_y, delta_z = dimensions\n",
    "        n_x = int(width / delta_x)\n",
    "        cells = []\n",
    "        for x in np.linspace(start_x, width + start_x, n_x, endpoint=False):\n",
    "            center = x + delta_x / 2\n",
    "            newcell = cell((center, 0, 0), dimensions)\n",
    "            #print(newcell.position)\n",
    "            cells += [newcell]\n",
    "        self.cells = cells\n",
    "        self.length = len(self.cells)\n",
    "    def join(self, other):\n",
    "        self.cells += other.cells\n",
    "        self.length = len(self.cells)\n",
    "    def getLeft(self, n):\n",
    "        return n-1\n",
    "    def hasLeft(self, n):\n",
    "        return n != 0\n",
    "    def getRight(self, n):\n",
    "        return n+1\n",
    "    def hasRight(self, n):\n",
    "        return n != len(self.cells) - 1\n",
    "class solver:\n",
    "    def __init__(self, mesh):\n",
    "        self.mesh = mesh\n",
    "    def assemble(self, kappa):\n",
    "        self.A = np.zeros((self.mesh.length, self.mesh.length))\n",
    "        self.rhs = np.zeros((self.mesh.length))\n",
    "        for i in range(self.mesh.length):\n",
    "            if self.mesh.hasLeft(i) and self.mesh.hasRight(i):\n",
    "                delta_x_w = (self.mesh.cells[i].position - self.mesh.cells[self.mesh.getLeft(i)].position)[0]\n",
    "                delta_x_e = (self.mesh.cells[self.mesh.getRight(i)].position - self.mesh.cells[i].position)[0]\n",
    "                k_w = kappa(self.mesh.cells[i].position[0] - delta_x_w / 2)\n",
    "                k_e = kappa(self.mesh.cells[i].position[0] + delta_x_e / 2)\n",
    "                A_w = self.mesh.cells[i].areas[3]\n",
    "                A_e = self.mesh.cells[i].areas[1]\n",
    "                n_w = cell.normals[3][0]\n",
    "                n_e = cell.normals[1][0]\n",
    "                self.A[i, self.mesh.getLeft(i)] += - k_w * A_w * n_w / delta_x_w\n",
    "                self.A[i, i] += k_w * A_w * n_w / delta_x_w - k_e * A_e * n_e / delta_x_e\n",
    "                self.A[i, self.mesh.getRight(i)] += k_e * A_e * n_e / delta_x_e\n",
    "    def solve(self, rbs):\n",
    "        for rb in rbs:\n",
    "            rb.apply(self.A, self.rhs)\n",
    "        return np.linalg.solve(self.A, self.rhs)\n",
    "class rb():\n",
    "    position = 10\n",
    "    def __init__(self, position):\n",
    "        self.position = position\n",
    "    def apply(self, systemmatrix, rhs):\n",
    "        pass\n",
    "class neumann(rb):\n",
    "    waermestrom = 5\n",
    "    def __init__(self, position, waermestrom, delta_x):\n",
    "        super(neumann,self).__init__(position)\n",
    "        self.waermestrom = waermestrom\n",
    "        self.delta_x = delta_x\n",
    "    def apply(self, systemmatrix, rhs):\n",
    "        if (self.position == 0):\n",
    "            # Vorwärtsdifferenz\n",
    "            systemmatrix[self.position, 0:2] = (1, -1)\n",
    "        elif (self.position < len(rhs)):\n",
    "            # Rückwärtsdifferenz\n",
    "            systemmatrix[self.position, self.position-1:self.position+1] = (-1, 1)\n",
    "        else:\n",
    "            raise ValueError(\"Out of bounds\")\n",
    "        rhs[self.position] = rhs[self.position] + self.waermestrom * self.delta_x\n",
    "class dirichlet(rb):\n",
    "    temperatur = 5\n",
    "    def __init__(self, position, temperatur):\n",
    "        super(dirichlet,self).__init__(position)\n",
    "        self.temperatur = temperatur\n",
    "    def apply(self, systemmatrix, rhs):\n",
    "        if (self.position > len(rhs)):\n",
    "            raise ValueError(\"Out of bounds\")\n",
    "        systemmatrix[self.position, self.position] = 1\n",
    "        rhs[self.position] = rhs[self.position] + self.temperatur"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aufgabe 4.2.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_x1 = 0.1\n",
    "delta_x2 = 0.02\n",
    "delta_y = 0.6\n",
    "delta_z = 0.7\n",
    "width_1 = 0.8\n",
    "width_2 = 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "m = equidistant1DMesh(width_1, (delta_x1, delta_y, delta_z), 0)\n",
    "m2 = equidistant1DMesh(width_2, (delta_x2, delta_y, delta_z), width_1)\n",
    "m.join(m2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = solver(m)\n",
    "kappa1 = 20\n",
    "kappa2 = 10\n",
    "def kappa(x):\n",
    "    if x <= width_1:\n",
    "        return kappa1\n",
    "    else:\n",
    "        return kappa2\n",
    "s.assemble(kappa)\n",
    "rb1 = dirichlet(0, 300)\n",
    "rb2 = neumann(m.length - 1, -50, delta_x2)\n",
    "result = s.solve([rb1, rb2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([i.position[0] for i in m.cells], result, \".-\")\n",
    "plt.grid()\n",
    "plt.title(\"Temperaturverlauf\")\n",
    "plt.ylabel(\"Temperatur [K]\")\n",
    "plt.xlabel(\"Länge [m]\")\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}