ABLScaling_function.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a66e50ec",
   "metadata": {},
   "source": [
    "# RANS ABL Mesh mapping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "68bbfb7c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51e75816",
   "metadata": {},
   "source": [
    "\n",
    "Implemented in `eval_coord()`:\n",
    "$$\n",
    "x(\\xi) = \\frac{\\Delta_0}{r}  \\frac{1-r^{\\xi+1}}{1-r} - \\frac{\\Delta_0}{r}\n",
    "$$\n",
    "\n",
    "Implemented in `eval_fac()`:\n",
    "$$\n",
    "\\frac{dx}{d\\xi} = \\frac{\\Delta_0}{r} \\frac{\\xi+1}{r-1} r^\\xi \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "63215fc1",
   "metadata": {},
   "outputs": [],
   "source": [
    "coord = lambda xi, delta0, r: delta0*(1-r**(xi+1))/(1-r)/r - delta0/r\n",
    "fac   = lambda xi, delta0, r: delta0*(r**xi)*log(r)\n",
    "\n",
    "def plotgrid(ax, xivec, coordfunc, *args, **kwargs):\n",
    "    for xi in xivec:\n",
    "        x = coordfunc(xi, *args)\n",
    "        #print(x)\n",
    "        ax.axhline(x,**kwargs)\n",
    "    return\n",
    "\n",
    "def printgrid(xivec, coordfunc, *args):\n",
    "    print('%-4s %8s %8s %s'%('xi','real x','cellsize','stretching'))\n",
    "    for i, xi in enumerate(xivec):\n",
    "        x = coordfunc(xi, *args)\n",
    "        cellsize = 0.0 if i==0 else x - coordfunc(xivec[i-1], *args)\n",
    "        sratio   = 0.0 if i<2  else cellsize/(coordfunc(xivec[i-1], *args)-coordfunc(xivec[i-2], *args))\n",
    "        print('%-4i %8.4f %8.4f %8.4f'%(xi, x, cellsize, sratio))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "29abdcee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "xi     real x cellsize stretching\n",
      "0      0.0000   0.0000   0.0000\n",
      "1      0.1000   0.1000   0.0000\n",
      "2      0.2100   0.1100   1.1000\n",
      "3      0.3310   0.1210   1.1000\n",
      "4      0.4641   0.1331   1.1000\n",
      "5      0.6105   0.1464   1.1000\n",
      "6      0.7716   0.1611   1.1000\n",
      "7      0.9487   0.1772   1.1000\n",
      "8      1.1436   0.1949   1.1000\n",
      "9      1.3579   0.2144   1.1000\n"
     ]
    }
   ],
   "source": [
    "Nxi    = 10\n",
    "xi     = np.linspace(0,Nxi-1,Nxi)\n",
    "delta0 = 0.1\n",
    "r      = 1.1\n",
    "#print(coord(0, delta0, r))\n",
    "#print(coord(1, delta0, r))\n",
    "#print(xi[0],delta0*((r**0) - r))\n",
    "printgrid(xi, coord, delta0, r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "20b21f4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 750x750 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plot the grid\n",
    "fig, ax = plt.subplots(1,1, figsize=(5,5), dpi=150)\n",
    "plotgrid(ax, xi, coord, delta0, r)\n",
    "plotgrid(ax, xi+0.5, coord, delta0, r, color='r', ls=':')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16f6c9ab",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}