{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from lbmpy.session import *\n", "from lbmpy.chapman_enskog import ChapmanEnskogAnalysis\n", "sp.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Demo: Automatic Chapman Enskog Analysis \n", "\n", "\n", "First, we create a SRT lattice Boltzmann method. It is defined as the set of moments, together with one relaxation rate per moment." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
\n", " Moment-Based Method\n", " Stencil: D3Q19Zero-Centered Storage: ✗Force Model: None
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\n", " Continuous Hydrodynamic Maxwellian Equilibrium\n", " \n", " $f (\\rho, \\left( u_{0}, \\ u_{1}, \\ u_{2}\\right), \\left( v_{0}, \\ v_{1}, \\ v_{2}\\right)) \n", " = \\frac{3 \\sqrt{6} \\delta_{\\rho} e^{- \\frac{3 v_{0}^{2}}{2} - \\frac{3 v_{1}^{2}}{2} - \\frac{3 v_{2}^{2}}{2}}}{4 \\pi^{\\frac{3}{2}}} + \\frac{3 \\sqrt{6} e^{- \\frac{3 \\left(- u_{0} + v_{0}\\right)^{2}}{2} - \\frac{3 \\left(- u_{1} + v_{1}\\right)^{2}}{2} - \\frac{3 \\left(- u_{2} + v_{2}\\right)^{2}}{2}}}{4 \\pi^{\\frac{3}{2}}}$\n", "
Compressible: ✗Deviation Only: ✗Order: 2
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Relaxation Info
MomentEq. Value Relaxation Rate
$1$$\\rho$$\\omega$
$x$$u_{0}$$\\omega$
$y$$u_{1}$$\\omega$
$z$$u_{2}$$\\omega$
$x^{2}$$\\frac{\\rho}{3} + u_{0}^{2}$$\\omega$
$y^{2}$$\\frac{\\rho}{3} + u_{1}^{2}$$\\omega$
$z^{2}$$\\frac{\\rho}{3} + u_{2}^{2}$$\\omega$
$x y$$u_{0} u_{1}$$\\omega$
$x z$$u_{0} u_{2}$$\\omega$
$y z$$u_{1} u_{2}$$\\omega$
$x^{2} y$$\\frac{u_{1}}{3}$$\\omega$
$x^{2} z$$\\frac{u_{2}}{3}$$\\omega$
$x y^{2}$$\\frac{u_{0}}{3}$$\\omega$
$x z^{2}$$\\frac{u_{0}}{3}$$\\omega$
$y^{2} z$$\\frac{u_{2}}{3}$$\\omega$
$y z^{2}$$\\frac{u_{1}}{3}$$\\omega$
$x^{2} y^{2}$$\\frac{\\rho}{9} + \\frac{u_{0}^{2}}{3} + \\frac{u_{1}^{2}}{3}$$\\omega$
$x^{2} z^{2}$$\\frac{\\rho}{9} + \\frac{u_{0}^{2}}{3} + \\frac{u_{2}^{2}}{3}$$\\omega$
$y^{2} z^{2}$$\\frac{\\rho}{9} + \\frac{u_{1}^{2}}{3} + \\frac{u_{2}^{2}}{3}$$\\omega$
" ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lb_config = LBMConfig(method=Method.TRT, stencil=Stencil.D3Q19, compressible=False, zero_centered=False)\n", "method = create_lb_method(lbm_config=lb_config)\n", "method" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, the Chapman Enskog analysis object is created. This may take a while..." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "analysis = ChapmanEnskogAnalysis(method)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This object now information about the method, e.g. the relation of relaxation rate to viscosities, if the method approximates the compressible or incompressible continuity equation ..." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "False" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "analysis.compressible" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[ \\frac{\\rho}{3}\\right]$" ], "text/plain": [ "⎡ρ⎤\n", "⎢─⎥\n", "⎣3⎦" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "analysis.pressure_equation" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{\\omega - 2}{6 \\omega}$" ], "text/plain": [ "-(ω - 2) \n", "─────────\n", " 6⋅ω " ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "analysis.get_kinematic_viscosity()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle - \\frac{1}{9} + \\frac{2}{9 \\omega}$" ], "text/plain": [ " 1 2 \n", "- ─ + ───\n", " 9 9⋅ω" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "analysis.get_bulk_viscosity()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But also details of the analysis are available:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}{\\partial_{t} \\rho} + {\\partial_{0} u_{0}} + {\\partial_{1} u_{1}} + {\\partial_{2} u_{2}}\\\\- \\frac{\\epsilon \\omega {\\partial_{0} {\\Pi_{00}^{(1)}}}}{2} - \\frac{\\epsilon \\omega {\\partial_{1} {\\Pi_{01}^{(1)}}}}{2} - \\frac{\\epsilon \\omega {\\partial_{2} {\\Pi_{02}^{(1)}}}}{2} + \\epsilon {\\partial_{0} {\\Pi_{00}^{(1)}}} + \\epsilon {\\partial_{1} {\\Pi_{01}^{(1)}}} + \\epsilon {\\partial_{2} {\\Pi_{02}^{(1)}}} + \\frac{{\\partial_{0} \\rho}}{3} + {\\partial_{t} u_{0}} + {\\partial_{0} (u_{0}^{2}) } + {\\partial_{1} (u_{0} u_{1}) } + {\\partial_{2} (u_{0} u_{2}) }\\\\- \\frac{\\epsilon \\omega {\\partial_{0} {\\Pi_{01}^{(1)}}}}{2} - \\frac{\\epsilon \\omega {\\partial_{1} {\\Pi_{11}^{(1)}}}}{2} - \\frac{\\epsilon \\omega {\\partial_{2} {\\Pi_{12}^{(1)}}}}{2} + \\epsilon {\\partial_{0} {\\Pi_{01}^{(1)}}} + \\epsilon {\\partial_{1} {\\Pi_{11}^{(1)}}} + \\epsilon {\\partial_{2} {\\Pi_{12}^{(1)}}} + \\frac{{\\partial_{1} \\rho}}{3} + {\\partial_{t} u_{1}} + {\\partial_{1} (u_{1}^{2}) } + {\\partial_{0} (u_{0} u_{1}) } + {\\partial_{2} (u_{1} u_{2}) }\\\\- \\frac{\\epsilon \\omega {\\partial_{0} {\\Pi_{02}^{(1)}}}}{2} - \\frac{\\epsilon \\omega {\\partial_{1} {\\Pi_{12}^{(1)}}}}{2} - \\frac{\\epsilon \\omega {\\partial_{2} {\\Pi_{22}^{(1)}}}}{2} + \\epsilon {\\partial_{0} {\\Pi_{02}^{(1)}}} + \\epsilon {\\partial_{1} {\\Pi_{12}^{(1)}}} + \\epsilon {\\partial_{2} {\\Pi_{22}^{(1)}}} + \\frac{{\\partial_{2} \\rho}}{3} + {\\partial_{t} u_{2}} + {\\partial_{2} (u_{2}^{2}) } + {\\partial_{0} (u_{0} u_{2}) } + {\\partial_{1} (u_{1} u_{2}) }\\end{matrix}\\right]$" ], "text/plain": [ "⎡ \n", "⎢ \n", "⎢ ε⋅ω⋅D(\\Pi_(1)_(2, 0, 0)) ε⋅ω⋅D(\\Pi_(1)_(1, 1, 0)) ε⋅ω⋅D(\\Pi_(1)_(1, 0, \n", "⎢- ──────────────────────── - ──────────────────────── - ─────────────────────\n", "⎢ 2 2 2 \n", "⎢ \n", "⎢ ε⋅ω⋅D(\\Pi_(1)_(1, 1, 0)) ε⋅ω⋅D(\\Pi_(1)_(0, 2, 0)) ε⋅ω⋅D(\\Pi_(1)_(0, 1, \n", "⎢- ──────────────────────── - ──────────────────────── - ─────────────────────\n", "⎢ 2 2 2 \n", "⎢ \n", "⎢ ε⋅ω⋅D(\\Pi_(1)_(1, 0, 1)) ε⋅ω⋅D(\\Pi_(1)_(0, 1, 1)) ε⋅ω⋅D(\\Pi_(1)_(0, 0, \n", "⎢- ──────────────────────── - ──────────────────────── - ─────────────────────\n", "⎣ 2 2 2 \n", "\n", " D(rho) + D(u_0) + D(u_1) + D(u_2) \n", " \n", "1)) \n", "─── + ε⋅D(\\Pi_(1)_(2, 0, 0)) + ε⋅D(\\Pi_(1)_(1, 1, 0)) + ε⋅D(\\Pi_(1)_(1, 0, 1))\n", " \n", " \n", "1)) \n", "─── + ε⋅D(\\Pi_(1)_(1, 1, 0)) + ε⋅D(\\Pi_(1)_(0, 2, 0)) + ε⋅D(\\Pi_(1)_(0, 1, 1))\n", " \n", " \n", "2)) \n", "─── + ε⋅D(\\Pi_(1)_(1, 0, 1)) + ε⋅D(\\Pi_(1)_(0, 1, 1)) + ε⋅D(\\Pi_(1)_(0, 0, 2))\n", " \n", "\n", " ⎤\n", " ⎥\n", " D(rho) ⎥\n", " + ────── + D(u_0) + D(u_0**2) + D(u_0*u_1) + D(u_0*u_2)⎥\n", " 3 ⎥\n", " ⎥\n", " D(rho) ⎥\n", " + ────── + D(u_1) + D(u_1**2) + D(u_0*u_1) + D(u_1*u_2)⎥\n", " 3 ⎥\n", " ⎥\n", " D(rho) ⎥\n", " + ────── + D(u_2) + D(u_2**2) + D(u_0*u_2) + D(u_1*u_2)⎥\n", " 3 ⎦" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sp.Matrix(analysis.get_macroscopic_equations())" ] } ], "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": "3.8.2" } }, "nbformat": 4, "nbformat_minor": 2 }