demo_stencils.ipynb 79.5 KB
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{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbsphinx": "hidden"
   },
   "outputs": [],
   "source": [
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    "from lbmpy.session import *\n",
    "from lbmpy.stencils import get_stencil"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Demo: Stencils\n",
    "\n",
    "A stencils is a tuple of directions, where each direction is again a tuple with as many entries as there are dimensions. Technically a stencil is only a nested tuple.\n",
    "The *stencils* submodule already has a predefined set of commonly used stencils.\n",
    "A common notation for stencils in the lattice Boltzmann literature is the *DxQy* notation, where *x* is the dimension of the space, and *y* the number of directions. For example *D2Q9* is a two-dimensional stencil with 9 directions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( \\left( 0, \\  0\\right), \\  \\left( 0, \\  1\\right), \\  \\left( 0, \\  -1\\right), \\  \\left( -1, \\  0\\right), \\  \\left( 1, \\  0\\right), \\  \\left( -1, \\  1\\right), \\  \\left( 1, \\  1\\right), \\  \\left( -1, \\  -1\\right), \\  \\left( 1, \\  -1\\right)\\right)$"
      ],
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      "text/plain": [
       "((0, 0), (0, 1), (0, -1), (-1, 0), (1, 0), (-1, 1), (1, 1), (-1, -1), (1, -1))"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stencil = get_stencil(\"D2Q9\")\n",
    "stencil"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "image/png": 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3stx39wJvmXBofZ/x+r0//8j1QjoiYoCYMSbjF2g1tsLTL376RCGvVuWFa/0HnYbmA05cEk5jKywNzeOcvO6ixlY4GpqHuXFxU42tMDQ0j3LzCsIam/00NA/ywmW6NTZ7aWge44XIkjQ2+2hoHuKlyJI0NntoaB7hxciSNLbB09A8wMuRJWlsg6OhucwPkSVpbPnT0Fzkp8iSNLb8aGgu8WNkSRpb7jQ0F/g5siSNLTcamsOCEFmSxpY9Dc1BQYosSWPLjobmkCBGlqSxDUxDc0CQI0vS2DLT0AqsGCJL0tjS09AKqJgiS9LY+qehFUgxRpaksfWloRVAMUeWpLGl0tBsppF109i6aWg20sj60tgsGppNNLL0NDYNzRYa2cCKPTYNbZA0suwVc2wa2iBoZLkr1tg0tDxpZPkrxtg0tDxoZINXbLFpaDnSyOxTTLFpaDnQyOxXLLFpaFnSyAqnGGLT0LKgkRVe0GPT0AagkTknyLFpaBloZM4LamwaWhoamXuCGJuG1g+NzH1Bi01D60Uj844gxaah9aCReU9QYtPQEjQy7wpCbBoaGpkf+D22og9NI/MPP8dW1KFpZP7j19iKNjSNzL/8GFtRhqaR+Z/fYiu60DSy4PBTbEUVmkYWPH6JrWhC08iCyw+xFUVoGlnweT22wIemkRUPL8cW6NA0suLj1dgCG5pGVry8GFsgQ9PIlNdiC1xoGplK8lJsgQpNI1O9eSW2wISmkal0vBBbIELTyNRA3I7N96FpZCpbbsbmq9BEpERESnv8rpGpnGSKTURKRUQKcb++CS0R2AbgUREp18hUvvqLTUQqgOXAWhGxvQvxy/4pIp8FlmI9OLwFHIZG1kfiEXl84teNib/3T/y9WbdVt8S22g0MAV4FDgbiwJnGmKdsvS+/bHcReQE4qtfiCmPMXjfm41UiMhd4DOvRuiaxOLkzhe3egfwu8UzW0Wvxs8aYWXbejy8OHUVkOvAvvRbvAZaJSLkLU/KyVcBeuiMj8fNe4BVXZuRRich+j/Wg1NORIjLVzvvyRWjA14DeQQ0B5gJHOD8d7zLGbAOe6b0YeMIYE3VhSl52NPBpoKrX8lLgGjvvyNFDR4lEPwJMBcoyrBYD1plw6B8AIjIM2IoVFlhP8wZ4CvgB8KK+7gCJRGuxHnRqefrXM3jxyW/QFbe2WUlpO8d85iZmnbEaaAZeMuFQq4vT9YTEa7RjgOuB2VhPPBWJ/7wH2M8Y0yKRqAAzgAlYEaaTsu+m3JcT+2hiJ7gbODSHYauB+Zwyaj5WUO1Ygd0O3G6M2Wr7RH1KItHPAwtJPusbA+9vmEJX3NopSkpjNBywju53rjuB/zDh0O+cn603icgE4ArgUkCwnuWuZvmO3wD3ApNzuLnVwHwTDu1KLnDq0PFScosM4KPAlcCxwDrgcmC0MebfNbJuEomOBL5Lz0NrEaip24mIQcQwtH4nqR8PVQA3SSRa5+xsvcsYs8kY8w1gDNZ+twGYCVxHbpGBte8u6Lkg0yGcnY7Pc9xMIAzE9fAwraPp73Cmpr6J1l0jrZ/rmvsZV5YY+0QhJ+c3xpg24F4R+SXWdn0pz5ua2fMXp0LL95FzmDEmZutMgqf/bVtWFqeiag8ihtKyeJqx9YWblr8ZY4xEoskPtvORsm2dCq0gp7UoINO2HTVuS95jla2cCq2v0/c/MOX3zg7hpLN3cdV/b3dpRsHR2S7ceuVoVr9QQ2tzKWMmdHLedVGO+cxut6cWCFvWlbH42jGsfX0IZeWGI+e0cMWi7ZSl/0jXvdCWbVyz7+c9rcK506dy3Gktrs0nSGIxCI2N8YNHN9IwMcbzj9dwy+VjOWD6esZN1kPxwVp87RjqR8Z54B/v0rKzhOvPmMAjdwxj3oJd6YZ44wPrFQ/XUjsixqHH9/6EXuWjeqhh/sJGxk2OUVIKM0/dzaixnby9qvcHsyofOzaXc9ypLVQOMYTGxplx3G42vl2ZaYg3Qnvm4TqOP60Z+0+aVgCN75eybWMFk6Z3uj2VQJh70U6eXVZL227hg01lvLayhsNPzHhY7v6e/f6GMt5aVc2c8/p7C1oN1t5O+P6XGzju1GYmHaKh2WHGzDY2rankC1MO5MLDJjP5o+3MOj3jmTbuh/bk/XUcNKON8VP0LHy7dcXhe/MbKCs3LLjtA7enEwhdcbjh7PEcdXILj2xYw9I319LaVMKd14/KNMz90J5dVs/sLzS5PY3AMV3wo0v3oylaxsIHtlJeMfAYNbCmxlI+/KCMMy7bRUWVYdioLk46u5lXn834eZu7ob3+XBU7t5cxe56+22i3RVeMYfO7Fdz40GaqqvWsGrsMHx0nNG4vv7trGLG90PxhCU8/VMf+03p/py2Fe2/vA/zxwXr+9VMt1NTpjmCnrevLeOahesoqDOce0v29qktu2sbJ5+mD2mB96+dbuetbo3n0ZyMoKTF85Ig2Lvthxs9/3Q3ta3fo64ZCGDspxvId77g9jcCadngHP35iUy5D3H+NplQRcCq0fN9R1HciBzaYMz10+2bWlfiTj5Rt61Robzs8rpgMZhvp9s3AhEMGyPcQPGWcU6Hdj3UZr1x0AUsKMJegeS3xJ1d/M+HQarsnE0D35TGmC/hVzwWOXTNEItEjgLPI7poh64GHTDj0Fyfm5ncSiQ4FvoT1bfRa0n/9xQAtwHPAfSYc0rP5syCR6InA6VjXx8x0zZA41tUAHjbh0PMpt6FfXFaq8PRdR6UcoKEp5QANTSkHaGhKOUBDU8oBGppSDtDQlHLA/wMrT6+gWnWOVAAAAABJRU5ErkJggg==\n",
59
      "text/plain": [
60
       "<Figure size 216x216 with 1 Axes>"
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      ]
     },
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     "metadata": {
      "needs_background": "light"
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
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    "plt.figure(figsize=(3, 3))\n",
    "ps.stencil.plot(stencil)"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the literature there is no agreement or convention of the direction ordering. \n",
    "Thus the ``getStencil`` function takes an optional parameter defining the ordering."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
89
      "image/png": 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\n",
90
      "text/plain": [
91
       "<Figure size 216x216 with 1 Axes>"
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      ]
     },
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     "metadata": {
      "needs_background": "light"
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
    "stencil = get_stencil(\"D2Q9\", ordering='counterclockwise')\n",
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    "plt.figure(figsize=(3, 3))\n",
    "ps.stencil.plot(stencil)"
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   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare this to the visualization above and note that only the direction order has changed.\n",
    "The LBM method is independent of the stencil ordering, as long as one order is consistently used everywhere."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The visualization routines take an optional ``data`` parameter, which has to be a sequence of information to attach to each direction. This info is then shown as labels instead of the direction index.\n",
    "\n",
    "There are two ways to visualize 3D stencils - either as a 3D plot, or as three 2D plots:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
130
      "image/png": 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\n",
131
      "text/plain": [
132
       "<Figure size 1152x432 with 1 Axes>"
133
134
      ]
     },
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     "metadata": {
      "needs_background": "light"
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
142
    "ps.stencil.plot(get_stencil(\"D3Q19\"), data=list(range(19)))"
143
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146
   ]
  },
  {
   "cell_type": "code",
147
   "execution_count": 6,
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   "metadata": {},
   "outputs": [
    {
     "data": {
152
      "image/png": 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\n",
153
      "text/plain": [
154
       "<Figure size 1152x432 with 3 Axes>"
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      ]
     },
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     "metadata": {
      "needs_background": "light"
     },
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     "output_type": "display_data"
    }
   ],
   "source": [
164
    "ps.stencil.plot(get_stencil(\"D3Q19\"), slice=True, sliceAxis=2)"
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   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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",
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   "version": "3.8.2"
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  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}