{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ "from lbmpy.session import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Demo: Stencils\n", "\n", "A stencil is a class which holds internally a tuple of directions, where each direction is again a tuple with as many entries as there are dimensions. The stencil class behaves like a nested tuple.\n", "Internally it 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. The available DxQy stencils can be obtained via the Stencil enum which is in the enum submodule of lbmpy:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", " \n", " \n", " \n", " \n", "\n", "
Nr.Direction NameDirection
$0$$\\mathtt{\\text{C}}$$\\left( 0, \\ 0\\right)$
$1$$\\mathtt{\\text{N}}$$\\left( 0, \\ 1\\right)$
$2$$\\mathtt{\\text{S}}$$\\left( 0, \\ -1\\right)$
$3$$\\mathtt{\\text{W}}$$\\left( -1, \\ 0\\right)$
$4$$\\mathtt{\\text{E}}$$\\left( 1, \\ 0\\right)$
$5$$\\mathtt{\\text{NW}}$$\\left( -1, \\ 1\\right)$
$6$$\\mathtt{\\text{NE}}$$\\left( 1, \\ 1\\right)$
$7$$\\mathtt{\\text{SW}}$$\\left( -1, \\ -1\\right)$
$8$$\\mathtt{\\text{SE}}$$\\left( 1, \\ -1\\right)$
\n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stencil = LBStencil(Stencil.D2Q9)\n", "stencil" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(3, 3))\n", "stencil.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the literature there is no agreement or convention of the direction ordering. \n", "Thus the ``LBStencil`` class takes an optional parameter defining the ordering." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "stencil = LBStencil(Stencil.D2Q9, ordering='counterclockwise')\n", "plt.figure(figsize=(3, 3))\n", "stencil.plot()" ] }, { "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": { "image/png": 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\n", 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\n", 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