blockMeshGrading.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compound grading for blockMesh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting the expansion Ratio of cells in blockMesh\n",
    "\n",
    "$R$ is the final to first cell size ratio. \n",
    "$r$ is the first to second expansion ratio.\n",
    "$n$ is the number of cells.\n",
    "$\\delta x_s$ is the smallest cell size.\n",
    "$l$ is the total length. Then\n",
    "$$r = R^{\\frac{1}{n-1}} = \\frac{l-\\delta x_s}{l - (R \\times \\delta x_s)}$$\n",
    "$$\\delta x_s = l \\frac{r-1}{\\alpha r - 1}$$\n",
    "and\n",
    "$$ \\alpha = R \\ for \\ R>1$$\n",
    "\n",
    "\\begin{equation*}\n",
    "\t\\alpha = 1-r^{-n} + r^{-1} \\ for \\ R<1\n",
    "\\end{equation*}\n",
    "\n",
    "\n",
    "$$n = \\frac{\\ln R}{\\ln r}+1$$\n",
    "\n",
    "Setting the double expansion ratio given as\n",
    "\n",
    "(0.05 0.11 10)    // 5% x-dir, 11% cells, expansion = 10 \n",
    "\n",
    "(0.90 0.78 1.0)    // 90% x-dir, 78% cells, expansion = 1 \n",
    "\n",
    "(0.05 0.11 0.1) // 5% x-dir, 11% cells, expansion = 0.1 (1/10) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def getNumberOfCellsAndExpansionRatio(L,xmin,xmax):\n",
    "    \"\"\" Get number of cells and expansion ratio given the Length of domain, min and max cell size \"\"\"\n",
    "\n",
    "#   FirstToLastCellExpansionRatio\n",
    "    R = xmax/xmin\n",
    "    \n",
    "#   CellToCellExpansionRatio\n",
    "    r = (L-xmin)/(L-(xmin*R))\n",
    "    \n",
    "#   Number of cells\n",
    "    if xmin==xmax:\n",
    "        N = np.ceil(L/xmin)\n",
    "    else:\n",
    "        N = np.ceil(np.log(R)/np.log(r) + 1)\n",
    "    \n",
    "    return N, R, r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R [4.961311]\n",
      "x 0.357\n",
      "x 0.4\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from scipy.optimize import fsolve\n",
    "def getExpansionRatioFromCellsAndLength(L,xmin,N):\n",
    "    \"\"\" Get expansion ratio given the Length of domain, number of cells, and min cell size \"\"\"\n",
    "\n",
    "    def func(R):\n",
    "        return  np.log(R)/np.log((L-xmin)/(L-(xmin*R))) + 1 - N\n",
    "    \n",
    "    R = fsolve(func, 1.01)\n",
    "    r = R**(1/(N-1))\n",
    "    return R, r\n",
    "\n",
    "R,r = getExpansionRatioFromCellsAndLength(50,1,20)\n",
    "print (\"R\",R)\n",
    "\n",
    "def setFormat(x,formatIn=\".3f\"):\n",
    "    return str('{0:'+formatIn+'}').format(x)\n",
    "\n",
    "x = 0.356536\n",
    "print(\"x\", setFormat(x))\n",
    "print(\"x\", setFormat(x, formatIn=\".1f\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L 0.0240 Ls 0.0120 Lc 0.0096 Le 0.0024\n",
      "Ns = start cells: 31 ; rs = start expansion ratio: 0.983 ; Rs: 0.600\n",
      "Nc = centre cells: 69 ; rc = centre expansion ratio: 0.974 ; Rs: 0.167\n",
      "Ne = end cells: 58 ; re = end expansion ratio: 0.994 ; Re: 0.700\n",
      "Nt = Total Cells: 158\n",
      "Cell Ratio (Start Centre End ) = ( 0.196, 0.437, 0.367 )\n",
      "Length Ratio (Left Center Right ) = ( 0.500, 0.400, 0.100 )\n",
      "Final grading for cell edge\n",
      "(\n",
      "  ( 0.500   0.196   0.600 ) \n",
      "  ( 0.400   0.437   0.167 ) \n",
      "  ( 0.100   0.367   0.700 ) \n",
      " )\n"
     ]
    }
   ],
   "source": [
    "## Three different gradings, also possible to have same grading for two sections\n",
    "#                      |-----|---------|----|\n",
    "# cell size:           x1    x2        x3   x4\n",
    "# cell total length    |<--------L--------->|\n",
    "# start,centre, end L  | Ls  |  Lc     | Le |  \n",
    "x1 = 50e-5\n",
    "x2 = 30e-5\n",
    "x3 = 5e-5\n",
    "x4 = 3.5e-5\n",
    "\n",
    "# lenght of cell\n",
    "L = 24e-3\n",
    "\n",
    "# start section length\n",
    "Ls = L*50/100\n",
    "# end section length\n",
    "Le = L*10/100\n",
    "# centre section length\n",
    "Lc = L-Ls-Le\n",
    "\n",
    "print(\"L\", '{0:.4f}'.format(L), \"Ls\", '{0:.4f}'.format(Ls), \"Lc\", '{0:.4f}'.format(Lc), \"Le\", '{0:.4f}'.format(Le))\n",
    "\n",
    "# find cell count and expansion ratio for Ls\n",
    "Ns, Rs, rs = getNumberOfCellsAndExpansionRatio(Ls,x1,x2)\n",
    "print (\"Ns = start cells:\", '{0:.0f}'.format(Ns), \";\", \"rs = start expansion ratio:\", '{0:.3f}'.format(rs), \";\", \"Rs:\", '{0:.3f}'.format(Rs))\n",
    "\n",
    "# find cell count and expansion ratio for Lc\n",
    "Nc, Rc, rc = getNumberOfCellsAndExpansionRatio(Lc,x2,x3)\n",
    "print (\"Nc = centre cells:\", '{0:.0f}'.format(Nc), \";\", \"rc = centre expansion ratio:\", '{0:.3f}'.format(rc), \";\", \"Rs:\", '{0:.3f}'.format(Rc))\n",
    "\n",
    "# find cell count and expansion ratio for Le\n",
    "Ne, Re, re = getNumberOfCellsAndExpansionRatio(Le,x3,x4)\n",
    "print (\"Ne = end cells:\", '{0:.0f}'.format(Ne), \";\", \"re = end expansion ratio:\", '{0:.3f}'.format(re), \";\", \"Re:\", '{0:.3f}'.format(Re))\n",
    "\n",
    "# total cells\n",
    "Nt = Ns + Nc + Ne # for full edge\n",
    "print (\"Nt = Total Cells:\", setFormat(Nt, formatIn=\".0f\"))\n",
    "\n",
    "cellRatioStartCenterEnd = [setFormat(Ns/Nt), setFormat(Nc/Nt), setFormat(Ne/Nt)]\n",
    "print (\"Cell Ratio (Start Centre End ) =\", \"(\",', '.join(map(str, cellRatioStartCenterEnd)) , \")\")\n",
    "\n",
    "lengthRatioStartCenterEnd = [setFormat(Ls/L), setFormat(Lc/L), setFormat(Le/L)]\n",
    "print (\"Length Ratio (Left Center Right ) =\", \"(\",', '.join(map(str, lengthRatioStartCenterEnd)) , \")\")\n",
    "\n",
    "print (\"Final grading for cell edge\")\n",
    "\n",
    "print ( \"(\\n\",  \" (\", setFormat(Ls/L), \" \", setFormat(Ns/Nt),  \" \",  setFormat(Rs),      \")\", \"\\n\", \\\n",
    "              \" (\", setFormat(Lc/L), \" \", setFormat(Nc/Nt),   \" \",  setFormat(Rc),     \")\", \"\\n\", \\\n",
    "              \" (\", setFormat(Le/L), \" \", setFormat(Ne/Nt),  \" \",   setFormat(Re),     \")\",\"\\n\",\")\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L 0.0200 Ls 0.0100 Lc 0.0050 Le 0.0050\n",
      "Ns = start cells: 286 ; rs = start expansion ratio: 1.000 ; Rs: 1.000\n",
      "Nc = centre cells: 46 ; rc = centre expansion ratio: 1.045 ; Rs: 7.143\n",
      "Ne = end cells: 14 ; re = end expansion ratio: 1.056 ; Re: 2.000\n",
      "Nt = Total Cells: 346\n",
      "Cell Ratio (Start Centre End ) = ( 0.827, 0.133, 0.040 )\n",
      "Length Ratio (Left Center Right ) = ( 0.500, 0.250, 0.250 )\n",
      "Final grading for cell edge\n",
      "(\n",
      "  ( 0.500   0.827   1.000 ) \n",
      "  ( 0.250   0.133   7.143 ) \n",
      "  ( 0.250   0.040   2.000 ) \n",
      " )\n"
     ]
    }
   ],
   "source": [
    "## Three different gradings, also possible to have same grading for two sections\n",
    "#                      |-----|---------|----|\n",
    "# cell size:           x1    x2        x3   x4\n",
    "# cell total length    |<--------L--------->|\n",
    "# start,centre, end L  | Ls  |  Lc     | Le |  \n",
    "x1 = 3.5e-5\n",
    "x2 = 3.5e-5\n",
    "x3 = 25e-5\n",
    "x4 = 50e-5\n",
    "\n",
    "# lenght of cell\n",
    "L = 20e-3\n",
    "\n",
    "# start section length\n",
    "Ls = L*50/100\n",
    "# end section length\n",
    "Le = L*25/100\n",
    "# centre section length\n",
    "Lc = L-Ls-Le\n",
    "\n",
    "print(\"L\", '{0:.4f}'.format(L), \"Ls\", '{0:.4f}'.format(Ls), \"Lc\", '{0:.4f}'.format(Lc), \"Le\", '{0:.4f}'.format(Le))\n",
    "\n",
    "# find cell count and expansion ratio for Ls\n",
    "Ns, Rs, rs = getNumberOfCellsAndExpansionRatio(Ls,x1,x2)\n",
    "print (\"Ns = start cells:\", '{0:.0f}'.format(Ns), \";\", \"rs = start expansion ratio:\", '{0:.3f}'.format(rs), \";\", \"Rs:\", '{0:.3f}'.format(Rs))\n",
    "\n",
    "# find cell count and expansion ratio for Lc\n",
    "Nc, Rc, rc = getNumberOfCellsAndExpansionRatio(Lc,x2,x3)\n",
    "print (\"Nc = centre cells:\", '{0:.0f}'.format(Nc), \";\", \"rc = centre expansion ratio:\", '{0:.3f}'.format(rc), \";\", \"Rs:\", '{0:.3f}'.format(Rc))\n",
    "\n",
    "# find cell count and expansion ratio for Le\n",
    "Ne, Re, re = getNumberOfCellsAndExpansionRatio(Le,x3,x4)\n",
    "print (\"Ne = end cells:\", '{0:.0f}'.format(Ne), \";\", \"re = end expansion ratio:\", '{0:.3f}'.format(re), \";\", \"Re:\", '{0:.3f}'.format(Re))\n",
    "\n",
    "# total cells\n",
    "Nt = Ns + Nc + Ne # for full edge\n",
    "print (\"Nt = Total Cells:\", setFormat(Nt, formatIn=\".0f\"))\n",
    "\n",
    "cellRatioStartCenterEnd = [setFormat(Ns/Nt), setFormat(Nc/Nt), setFormat(Ne/Nt)]\n",
    "print (\"Cell Ratio (Start Centre End ) =\", \"(\",', '.join(map(str, cellRatioStartCenterEnd)) , \")\")\n",
    "\n",
    "lengthRatioStartCenterEnd = [setFormat(Ls/L), setFormat(Lc/L), setFormat(Le/L)]\n",
    "print (\"Length Ratio (Left Center Right ) =\", \"(\",', '.join(map(str, lengthRatioStartCenterEnd)) , \")\")\n",
    "\n",
    "print (\"Final grading for cell edge\")\n",
    "\n",
    "print ( \"(\\n\",  \" (\", setFormat(Ls/L), \" \", setFormat(Ns/Nt),  \" \",  setFormat(Rs),      \")\", \"\\n\", \\\n",
    "              \" (\", setFormat(Lc/L), \" \", setFormat(Nc/Nt),   \" \",  setFormat(Rc),     \")\", \"\\n\", \\\n",
    "              \" (\", setFormat(Le/L), \" \", setFormat(Ne/Nt),  \" \",   setFormat(Re),     \")\",\"\\n\",\")\")"
   ]
  },
  {
   "attachments": {
    "grid.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualizing results using blockMesh\n",
    "See the attached folder \"compoundGradedMesh\" edit system/blockMeshDict and run\n",
    "blockMesh (requires workiing openfoam installation, Tested on version 5.0). The resulting grid is shown below \n",
    "![grid.png](attachment:grid.png)\n"
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}