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Commit 6c1a0d26 authored by Radek Fučík's avatar Radek Fučík
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new structure (fixed)

parent 9039e5f3
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src/d1q3_ade/Makefile 0 → 100644
View file @ 6c1a0d26
defaults: all
all:
@+../scripts/build.sh
clean:
@rm -rf output* compare* latex simplify
purge: clean
@rm -rf *.pdf
src/d1q3_ade/supp_d1q3_ade.tex 0 → 100644
View file @ 6c1a0d26
\input{latex/header}
\titler{D1Q3}{ADE}
\def\model{d1q3}
\def\pde{ade}
\def\path{latex}
\input{\path/\model_defs}
\begin{document}
\maketitle
\tableofcontents
\section{Global definitions}
\input{\path/supp_\model_defs}
\section{Spatial EPDEs}
\subsection{SRT}
\def\colmod{srt}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}
\subsubsection{Conservation of mass equation}
\attachtxt{output_\model_\pde_\colmod_symbolic_pde_00.txt}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsection{MRT}
\def\colmod{mrt1}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}
\subsubsection{Conservation of mass equation}
\attachtxt{output_\model_\pde_\colmod_symbolic_pde_00.txt}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsection{CLBM}
\def\colmod{clbm1}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}
\subsubsection{Conservation of mass equation}
\attachtxt{output_\model_\pde_\colmod_symbolic_pde_00.txt}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\section{Comparison of SRT, MRT, and CLBM}
\subsection{Conservation of mass equation}
\input{compare_output_\model_\pde/pde_00}
\bibliography{\path/ref.bib}
\end{document}
src/d1q3_nse/Makefile 0 → 100644
View file @ 6c1a0d26
defaults: all
all:
@+../scripts/build.sh
clean:
@rm -rf output* compare* latex simplify
purge: clean
@rm -rf *.pdf
src/d1q3_nse/compare_output_d1q3_nse/pde_00.tex 0 → 100644
View file @ 6c1a0d26
\begin{flushleft}
\noindent
${\color{blue}\frac{ \partial \rho}{\partial t}}$
$+$
$\ou\frac{\dl}{\dt}{\color{blue}\frac{ \partial \rho}{\partial \x}}$
$+$
$\rho\frac{\dl}{\dt}{\color{blue}\frac{ \partial \ou}{\partial \x}}$
$+$
$ ( -1+\ou^{2}+3 c_s^{2} ) \frac{\ou}{12}\frac{\dl^{3}}{\dt}{\color{blue}\frac{ \partial^3 \rho}{\partial \x^{3}}}$
$+$
$ ( -1+3 \ou^{2}+c_s^{2} ) \frac{\rho}{12}\frac{\dl^{3}}{\dt}{\color{blue}\frac{ \partial^3 \ou}{\partial \x^{3}}}$
$+$
${\color{darkgreen}\hyperref[Ccompare_0_compare_output_d1q3_nse_1]{C_{{\D_x^{4}\rho}}^{(0)\modelq}}}\frac{\dl^{4}}{\dt}{\color{blue}\frac{ \partial^4 \rho}{\partial \x^{4}}}$
{\phantomsection\label{Ecompare_0_compare_output_d1q3_nse_1}}
$+$
${\color{darkgreen}\hyperref[Ccompare_0_compare_output_d1q3_nse_2]{C_{{\D_x^{4}\ou}}^{(0)\modelq}}}\frac{\dl^{4}}{\dt}{\color{blue}\frac{ \partial^4 \ou}{\partial \x^{4}}}$
{\phantomsection\label{Ecompare_0_compare_output_d1q3_nse_2}}
$=0,$
\vskip 1em
where:\end{flushleft}
\begin{flushleft}
\scriptsize
\noindent
\phantomsection\label{Ccompare_0_compare_output_d1q3_nse_1}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(0)\modelq}}$ at \hyperref[Ecompare_0_compare_output_d1q3_nse_1]{${\color{blue}\frac{ \partial^4 \rho}{\partial \x^{4}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(0),\modelqc\mathrm{SRT}}} =
( c_s^{2} \omega-3 \ou^{4} \omega+2 c_s^{4}-6 \ou^{2}+24 \ou^{2} c_s^{2}+3 \ou^{2} \omega+6 \ou^{4}-2 c_s^{2}-12 \ou^{2} c_s^{2} \omega- c_s^{4} \omega ) \frac{1}{24 \omega}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(0),\modelqc\mathrm{MRT1}}} =
( -3 \ou^{4} \omega_{3}+2 c_s^{4}-6 \ou^{2}+24 \ou^{2} c_s^{2}+ \omega_{3} c_s^{2}+6 \ou^{4}-2 c_s^{2}- \omega_{3} c_s^{4}+3 \ou^{2} \omega_{3}-12 \ou^{2} \omega_{3} c_s^{2} ) \frac{1}{24 \omega_{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(0),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{4}\rho}}^{(0),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_0_compare_output_d1q3_nse_2}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(0)\modelq}}$ at \hyperref[Ecompare_0_compare_output_d1q3_nse_2]{${\color{blue}\frac{ \partial^4 \ou}{\partial \x^{4}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(0),\modelqc\mathrm{SRT}}} =
( -4-3 c_s^{2} \omega+10 \ou^{2}-5 \ou^{2} \omega+6 c_s^{2}+2 \omega ) \frac{ \ou \rho}{12 \omega}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(0),\modelqc\mathrm{MRT1}}} =
( -4+2 \omega_{3}+10 \ou^{2}-3 \omega_{3} c_s^{2}+6 c_s^{2}-5 \ou^{2} \omega_{3} ) \frac{ \ou \rho}{12 \omega_{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(0),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{4}\ou}}^{(0),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\end{flushleft}
src/d1q3_nse/compare_output_d1q3_nse/pde_01.tex 0 → 100644
View file @ 6c1a0d26
\begin{flushleft}
\noindent
$\ou{\color{blue}\frac{ \partial \rho}{\partial t}}$
$+$
$\rho{\color{blue}\frac{ \partial \ou}{\partial t}}$
$+$
$( \ou^{2}+c_s^{2} )\frac{\dl}{\dt}{\color{blue}\frac{ \partial \rho}{\partial \x}}$
$+$
$2 \ou \rho\frac{\dl}{\dt}{\color{blue}\frac{ \partial \ou}{\partial \x}}$
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_1]{C_{{\D_x\rho},{\D_x\ou}}^{(1)\modelq}}}\frac{\dl^{2}}{\dt}{\color{blue}\frac{ \partial \rho}{\partial \x} \frac{ \partial \ou}{\partial \x}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_1}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_2]{C_{{\D_x\ou},{\D_x\ou}}^{(1)\modelq}}}\frac{\dl^{2}}{\dt}\left({\color{blue}\frac{ \partial \ou}{\partial \x}}\right)^2$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_2}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_3]{C_{{\D_x^{2}\rho}}^{(1)\modelq}}}\frac{\dl^{2}}{\dt}{\color{blue}\frac{ \partial^2 \rho}{\partial \x^{2}}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_3}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_4]{C_{{\D_x^{2}\ou}}^{(1)\modelq}}}\frac{\dl^{2}}{\dt}{\color{blue}\frac{ \partial^2 \ou}{\partial \x^{2}}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_4}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_5]{C_{{\D_x^{3}\rho}}^{(1)\modelq}}}\frac{\dl^{3}}{\dt}{\color{blue}\frac{ \partial^3 \rho}{\partial \x^{3}}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_5}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_6]{C_{{\D_x^{3}\ou}}^{(1)\modelq}}}\frac{\dl^{3}}{\dt}{\color{blue}\frac{ \partial^3 \ou}{\partial \x^{3}}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_6}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_7]{C_{{\D_x^{4}\rho}}^{(1)\modelq}}}\frac{\dl^{4}}{\dt}{\color{blue}\frac{ \partial^4 \rho}{\partial \x^{4}}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_7}}
$+$
${\color{darkgreen}\hyperref[Ccompare_1_compare_output_d1q3_nse_8]{C_{{\D_x^{4}\ou}}^{(1)\modelq}}}\frac{\dl^{4}}{\dt}{\color{blue}\frac{ \partial^4 \ou}{\partial \x^{4}}}$
{\phantomsection\label{Ecompare_1_compare_output_d1q3_nse_8}}
$=0,$
\vskip 1em
where:\end{flushleft}
\begin{flushleft}
\scriptsize
\noindent
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_1}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x\rho},{\D_x\ou}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_1]{${\color{blue}\frac{ \partial \rho}{\partial \x} \frac{ \partial \ou}{\partial \x}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x\rho},{\D_x\ou}}^{(1),\modelqc\mathrm{SRT}}} =
( -2-2 c_s^{2} \omega+6 \ou^{2}-3 \ou^{2} \omega+4 c_s^{2}+\omega ) \frac{1}{\omega}$
\vskip 1em
${\color{darkgreen}C_{{\D_x\rho},{\D_x\ou}}^{(1),\modelqc\mathrm{MRT1}}} =
( -2+\omega_{3}+6 \ou^{2}-2 \omega_{3} c_s^{2}+4 c_s^{2}-3 \ou^{2} \omega_{3} ) \frac{1}{\omega_{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x\rho},{\D_x\ou}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x\rho},{\D_x\ou}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_2}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x\ou},{\D_x\ou}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_2]{$\left({\color{blue}\frac{ \partial \ou}{\partial \x}}\right)^2$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x\ou},{\D_x\ou}}^{(1),\modelqc\mathrm{SRT}}} =
( 2-\omega ) \frac{3 \ou \rho}{\omega}$
\vskip 1em
${\color{darkgreen}C_{{\D_x\ou},{\D_x\ou}}^{(1),\modelqc\mathrm{MRT1}}} =
( 2-\omega_{3} ) \frac{3 \ou \rho}{\omega_{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x\ou},{\D_x\ou}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x\ou},{\D_x\ou}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_3}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{2}\rho}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_3]{${\color{blue}\frac{ \partial^2 \rho}{\partial \x^{2}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{2}\rho}}^{(1),\modelqc\mathrm{SRT}}} =
( -2-3 c_s^{2} \omega+2 \ou^{2}- \ou^{2} \omega+6 c_s^{2}+\omega ) \frac{\ou}{2 \omega}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{2}\rho}}^{(1),\modelqc\mathrm{MRT1}}} =
( -2+\omega_{3}+2 \ou^{2}-3 \omega_{3} c_s^{2}+6 c_s^{2}- \ou^{2} \omega_{3} ) \frac{\ou}{2 \omega_{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{2}\rho}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{2}\rho}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_4}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{2}\ou}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_4]{${\color{blue}\frac{ \partial^2 \ou}{\partial \x^{2}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{2}\ou}}^{(1),\modelqc\mathrm{SRT}}} =
( -2- c_s^{2} \omega+6 \ou^{2}-3 \ou^{2} \omega+2 c_s^{2}+\omega ) \frac{\rho}{2 \omega}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{2}\ou}}^{(1),\modelqc\mathrm{MRT1}}} =
( -2+\omega_{3}+6 \ou^{2}- \omega_{3} c_s^{2}+2 c_s^{2}-3 \ou^{2} \omega_{3} ) \frac{\rho}{2 \omega_{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{2}\ou}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{2}\ou}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_5}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{3}\rho}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_5]{${\color{blue}\frac{ \partial^3 \rho}{\partial \x^{3}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{3}\rho}}^{(1),\modelqc\mathrm{SRT}}} =
( 12 c_s^{2} \omega-36 \ou^{4} \omega+12 c_s^{4}+7 \ou^{4} \omega^{2}-36 \ou^{2}+144 \ou^{2} c_s^{2}- c_s^{2} \omega^{2}+36 \ou^{2} \omega+36 \ou^{4}-12 c_s^{2}-144 \ou^{2} c_s^{2} \omega-12 c_s^{4} \omega+ c_s^{4} \omega^{2}+24 \ou^{2} c_s^{2} \omega^{2}-7 \ou^{2} \omega^{2} ) \frac{1}{12 \omega^{2}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{3}\rho}}^{(1),\modelqc\mathrm{MRT1}}} =
( -36 \ou^{4} \omega_{3}+24 \ou^{2} \omega_{3}^{2} c_s^{2}+ \omega_{3}^{2} c_s^{4}+12 c_s^{4}-36 \ou^{2}+144 \ou^{2} c_s^{2}+12 \omega_{3} c_s^{2}+7 \ou^{4} \omega_{3}^{2}+36 \ou^{4}- \omega_{3}^{2} c_s^{2}-12 c_s^{2}-12 \omega_{3} c_s^{4}+36 \ou^{2} \omega_{3}-7 \ou^{2} \omega_{3}^{2}-144 \ou^{2} \omega_{3} c_s^{2} ) \frac{1}{12 \omega_{3}^{2}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{3}\rho}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{3}\rho}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_6}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{3}\ou}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_6]{${\color{blue}\frac{ \partial^3 \ou}{\partial \x^{3}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{3}\ou}}^{(1),\modelqc\mathrm{SRT}}} =
( -24-4 \omega^{2}-36 c_s^{2} \omega+60 \ou^{2}+5 c_s^{2} \omega^{2}-60 \ou^{2} \omega+36 c_s^{2}+24 \omega+11 \ou^{2} \omega^{2} ) \frac{ \ou \rho}{6 \omega^{2}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{3}\ou}}^{(1),\modelqc\mathrm{MRT1}}} =
( -24-4 \omega_{3}^{2}+24 \omega_{3}+60 \ou^{2}-36 \omega_{3} c_s^{2}+5 \omega_{3}^{2} c_s^{2}+36 c_s^{2}-60 \ou^{2} \omega_{3}+11 \ou^{2} \omega_{3}^{2} ) \frac{ \ou \rho}{6 \omega_{3}^{2}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{3}\ou}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{3}\ou}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_7}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_7]{${\color{blue}\frac{ \partial^4 \rho}{\partial \x^{4}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(1),\modelqc\mathrm{SRT}}} =
( 12+8 \omega^{2}+198 c_s^{2} \omega-216 \ou^{4} \omega-\omega^{3}+144 c_s^{4}+6 c_s^{2} \omega^{3}+90 \ou^{4} \omega^{2}-156 \ou^{2}+672 \ou^{2} c_s^{2}-9 \ou^{4} \omega^{3}-78 c_s^{2} \omega^{2}+234 \ou^{2} \omega+144 \ou^{4}-132 c_s^{2}-1008 \ou^{2} c_s^{2} \omega-216 c_s^{4} \omega-18 \omega-34 \ou^{2} c_s^{2} \omega^{3}+10 \ou^{2} \omega^{3}+82 c_s^{4} \omega^{2}+404 \ou^{2} c_s^{2} \omega^{2}-5 c_s^{4} \omega^{3}-98 \ou^{2} \omega^{2} ) \frac{\ou}{12 \omega^{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(1),\modelqc\mathrm{MRT1}}} =
( 12-216 \ou^{4} \omega_{3}+404 \ou^{2} \omega_{3}^{2} c_s^{2}-\omega_{3}^{3}-5 \omega_{3}^{3} c_s^{4}+8 \omega_{3}^{2}-18 \omega_{3}+82 \omega_{3}^{2} c_s^{4}+144 c_s^{4}-9 \ou^{4} \omega_{3}^{3}-156 \ou^{2}-34 \ou^{2} \omega_{3}^{3} c_s^{2}+672 \ou^{2} c_s^{2}+198 \omega_{3} c_s^{2}+90 \ou^{4} \omega_{3}^{2}+144 \ou^{4}-78 \omega_{3}^{2} c_s^{2}-132 c_s^{2}-216 \omega_{3} c_s^{4}+234 \ou^{2} \omega_{3}+6 \omega_{3}^{3} c_s^{2}-98 \ou^{2} \omega_{3}^{2}-1008 \ou^{2} \omega_{3} c_s^{2}+10 \ou^{2} \omega_{3}^{3} ) \frac{\ou}{12 \omega_{3}^{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\rho}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{4}\rho}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\phantomsection\label{Ccompare_1_compare_output_d1q3_nse_8}
\noindent\textbf{coefficient ${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(1)\modelq}}$ at \hyperref[Ecompare_1_compare_output_d1q3_nse_8]{${\color{blue}\frac{ \partial^4 \ou}{\partial \x^{4}}}$}:}
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(1),\modelqc\mathrm{SRT}}} =
( 12+8 \omega^{2}+54 c_s^{2} \omega-756 \ou^{4} \omega-\omega^{3}+24 c_s^{4}+2 c_s^{2} \omega^{3}+310 \ou^{4} \omega^{2}-252 \ou^{2}+432 \ou^{2} c_s^{2}-29 \ou^{4} \omega^{3}-22 c_s^{2} \omega^{2}+378 \ou^{2} \omega+504 \ou^{4}-36 c_s^{2}-648 \ou^{2} c_s^{2} \omega-36 c_s^{4} \omega-18 \omega-18 \ou^{2} c_s^{2} \omega^{3}+14 \ou^{2} \omega^{3}+14 c_s^{4} \omega^{2}+252 \ou^{2} c_s^{2} \omega^{2}- c_s^{4} \omega^{3}-154 \ou^{2} \omega^{2} ) \frac{\rho}{12 \omega^{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(1),\modelqc\mathrm{MRT1}}} =
( 12-756 \ou^{4} \omega_{3}+252 \ou^{2} \omega_{3}^{2} c_s^{2}-\omega_{3}^{3}- \omega_{3}^{3} c_s^{4}+8 \omega_{3}^{2}-18 \omega_{3}+14 \omega_{3}^{2} c_s^{4}+24 c_s^{4}-29 \ou^{4} \omega_{3}^{3}-252 \ou^{2}-18 \ou^{2} \omega_{3}^{3} c_s^{2}+432 \ou^{2} c_s^{2}+54 \omega_{3} c_s^{2}+310 \ou^{4} \omega_{3}^{2}+504 \ou^{4}-22 \omega_{3}^{2} c_s^{2}-36 c_s^{2}-36 \omega_{3} c_s^{4}+378 \ou^{2} \omega_{3}+2 \omega_{3}^{3} c_s^{2}-154 \ou^{2} \omega_{3}^{2}-648 \ou^{2} \omega_{3} c_s^{2}+14 \ou^{2} \omega_{3}^{3} ) \frac{\rho}{12 \omega_{3}^{3}}$
\vskip 1em
${\color{darkgreen}C_{{\D_x^{4}\ou}}^{(1),\modelqc\mathrm{CLBM1}}} =
C_{{\D_x^{4}\ou}}^{(1),\modelqc\mathrm{MRT1}}
$
\vskip 1em
\end{flushleft}
src/d1q3_nse/latex 0 → 120000
View file @ 6c1a0d26
../latex
\ No newline at end of file
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/log_95348 0 → 100644
View file @ 6c1a0d26
[ 0.2s] [mem: 8 MB peak: 8 MB] LBMAT: d=1 q=3 order=4 mfco=4 model=d1q3_clbm1 M=M1 pde_type=NSE do_subs=yes pid=95348
[ 0.2s] [mem: 8 MB peak: 8 MB] compute NSE
[ 0.2s] [mem: 8 MB peak: 8 MB] step 0: allocate conserved and nonconserved quantities
[ 0.2s] [mem: 12 MB peak: 12 MB] step 1: assemble initial PDE
[ 0.2s] [mem: 12 MB peak: 12 MB] step 2: eliminate zero-th order derivatives
[ 0.2s] [mem: 12 MB peak: 12 MB] assemble W2 matrix
[ 0.2s] [mem: 12 MB peak: 12 MB] inversion of W2
[ 0.2s] [mem: 12 MB peak: 12 MB] multiply -W2i*abs_rhs
[ 0.3s] [mem: 13 MB peak: 13 MB] replace coefs by symbolic variables
[ 0.3s] [mem: 13 MB peak: 13 MB] step 3: Gaussian elimination of nonconserved quantities
[ 0.3s] [mem: 13 MB peak: 13 MB] Gaussian elimination: diagonal: row=0: loop_restart (0)
[ 0.3s] [mem: 13 MB peak: 13 MB] row=0 der=(1,0,0,0) order=1
[ 0.3s] [mem: 15 MB peak: 15 MB] Gaussian elimination: diagonal: row=0: loop_restart (1)
[ 0.3s] [mem: 15 MB peak: 15 MB] row=0 der=(0,2,0,0) order=2
[ 0.3s] [mem: 14 MB peak: 15 MB] row=0 der=(2,0,0,0) order=2
[ 0.4s] [mem: 14 MB peak: 15 MB] Gaussian elimination: diagonal: row=0: loop_restart (2)
[ 0.4s] [mem: 14 MB peak: 15 MB] row=0 der=(1,2,0,0) order=3
[ 0.4s] [mem: 14 MB peak: 15 MB] row=0 der=(3,0,0,0) order=3
[ 0.4s] [mem: 14 MB peak: 15 MB] Gaussian elimination: diagonal: row=0: loop_restart (3)
[ 0.4s] [mem: 14 MB peak: 15 MB] row=0 der=(0,4,0,0) order=4
[ 0.5s] [mem: 14 MB peak: 15 MB] row=0 der=(2,2,0,0) order=4
[ 0.5s] [mem: 14 MB peak: 15 MB] row=0 der=(4,0,0,0) order=4
[ 0.6s] [mem: 14 MB peak: 15 MB] Gaussian elimination: diagonal: row=0: loop_restart (4)
[ 0.6s] [mem: 14 MB peak: 15 MB] Gaussian elimination: below diagonal: row=0: eliminating from 1 to 0: loop_restart (0)
[ 0.6s] [mem: 14 MB peak: 15 MB] Gaussian elimination: above diagonal: row=0: loop_restart (0)
[ 0.6s] [mem: 14 MB peak: 15 MB] step 4: elimination of higher order derivatives of conserved quantities
[ 0.6s] [mem: 14 MB peak: 15 MB] row=0 der=(0,1,0,0) order=1
[ 0.6s] [mem: 15 MB peak: 15 MB] row=0 der=(0,2,0,0) order=2
[ 0.6s] [mem: 14 MB peak: 15 MB] row=0 der=(1,1,0,0) order=2
[ 0.6s] [mem: 14 MB peak: 15 MB] row=0 der=(0,3,0,0) order=3
[ 0.7s] [mem: 14 MB peak: 15 MB] row=0 der=(1,2,0,0) order=3
[ 0.7s] [mem: 14 MB peak: 15 MB] row=0 der=(2,1,0,0) order=3
[ 0.7s] [mem: 15 MB peak: 15 MB] row=0 der=(0,4,0,0) order=4
[ 0.8s] [mem: 15 MB peak: 15 MB] row=0 der=(1,3,0,0) order=4
[ 0.8s] [mem: 15 MB peak: 15 MB] row=0 der=(2,2,0,0) order=4
[ 0.8s] [mem: 15 MB peak: 15 MB] row=0 der=(3,1,0,0) order=4
[ 0.9s] [mem: 15 MB peak: 15 MB] step 5: elimination of higher order derivatives of conserved quantities
[ 0.9s] [mem: 15 MB peak: 15 MB] assemble matrix W and its inverse
[ 0.9s] [mem: 15 MB peak: 15 MB] multiply -Wi*pde
[ 1.0s] [mem: 17 MB peak: 17 MB] step 6: eliminate all spatial derivatives up to time order=1
[ 1.0s] [mem: 17 MB peak: 17 MB] iter=0: lowest time derivative order: basindex=0 der=(1,0,0,0) time_order=0
[ 1.0s] [mem: 18 MB peak: 18 MB] iter=1: lowest time derivative order: basindex=0 der=(1,1,0,0) time_order=0
[ 1.0s] [mem: 18 MB peak: 18 MB] iter=2: lowest time derivative order: basindex=0 der=(1,1,0,0) time_order=0
[ 1.0s] [mem: 18 MB peak: 18 MB] iter=3: lowest time derivative order: basindex=0 der=(1,2,0,0) time_order=0
[ 1.0s] [mem: 18 MB peak: 18 MB] iter=4: lowest time derivative order: basindex=0 der=(1,3,0,0) time_order=0
[ 1.0s] [mem: 18 MB peak: 18 MB] iter=5: lowest time derivative order: basindex=0 der=(2,0,0,0) time_order=0
[ 1.1s] [mem: 17 MB peak: 18 MB] iter=0: lowest time derivative order: basindex=0 der=(1,0,0,0) time_order=0
[ 1.1s] [mem: 18 MB peak: 18 MB] iter=1: lowest time derivative order: basindex=0 der=(1,1,0,0) time_order=0
[ 1.1s] [mem: 18 MB peak: 18 MB] iter=2: lowest time derivative order: basindex=0 der=(1,2,0,0) time_order=0
[ 1.1s] [mem: 18 MB peak: 18 MB] iter=3: lowest time derivative order: basindex=0 der=(1,3,0,0) time_order=0
[ 1.1s] [mem: 18 MB peak: 18 MB] iter=4: lowest time derivative order: basindex=0 der=(2,0,0,0) time_order=0
[ 1.1s] [mem: 17 MB peak: 18 MB] iter=0: lowest time derivative order: basindex=1 der=(1,0,0,0) time_order=0
[ 1.2s] [mem: 18 MB peak: 18 MB] iter=1: lowest time derivative order: basindex=1 der=(1,1,0,0) time_order=0
[ 1.2s] [mem: 18 MB peak: 18 MB] iter=2: lowest time derivative order: basindex=1 der=(1,1,0,0) time_order=0
[ 1.2s] [mem: 18 MB peak: 18 MB] iter=3: lowest time derivative order: basindex=1 der=(1,2,0,0) time_order=0
[ 1.3s] [mem: 18 MB peak: 18 MB] iter=4: lowest time derivative order: basindex=1 der=(1,3,0,0) time_order=0
[ 1.3s] [mem: 18 MB peak: 18 MB] iter=5: lowest time derivative order: basindex=1 der=(2,0,0,0) time_order=0
[ 1.4s] [mem: 18 MB peak: 18 MB] iter=0: lowest time derivative order: basindex=1 der=(1,0,0,0) time_order=0
[ 1.4s] [mem: 18 MB peak: 18 MB] iter=1: lowest time derivative order: basindex=1 der=(1,1,0,0) time_order=0
[ 1.4s] [mem: 19 MB peak: 19 MB] iter=2: lowest time derivative order: basindex=1 der=(1,2,0,0) time_order=0
[ 1.5s] [mem: 19 MB peak: 19 MB] iter=3: lowest time derivative order: basindex=1 der=(1,3,0,0) time_order=0
[ 1.5s] [mem: 19 MB peak: 19 MB] iter=4: lowest time derivative order: basindex=1 der=(2,0,0,0) time_order=0
[ 1.6s] [mem: 18 MB peak: 19 MB] step 7: eliminate all spatial derivatives of time derivatives of order=1
[ 2.1s] [mem: 22 MB peak: 22 MB] eliminate all spatial derivatives up to time order=2
[ 2.1s] [mem: 22 MB peak: 22 MB] iter=0: lowest time derivative order: basindex=0 der=(2,0,0,0) time_order=1
[ 2.1s] [mem: 24 MB peak: 24 MB] iter=1: lowest time derivative order: basindex=0 der=(2,1,0,0) time_order=1
[ 2.1s] [mem: 23 MB peak: 24 MB] iter=2: lowest time derivative order: basindex=0 der=(2,1,0,0) time_order=1
[ 2.1s] [mem: 23 MB peak: 24 MB] iter=3: lowest time derivative order: basindex=0 der=(2,2,0,0) time_order=1
[ 2.2s] [mem: 23 MB peak: 24 MB] iter=4: lowest time derivative order: basindex=0 der=(3,0,0,0) time_order=1
[ 2.2s] [mem: 22 MB peak: 24 MB] iter=0: lowest time derivative order: basindex=0 der=(2,0,0,0) time_order=1
[ 2.2s] [mem: 24 MB peak: 24 MB] iter=1: lowest time derivative order: basindex=0 der=(2,1,0,0) time_order=1
[ 2.2s] [mem: 23 MB peak: 24 MB] iter=2: lowest time derivative order: basindex=0 der=(2,2,0,0) time_order=1
[ 2.2s] [mem: 23 MB peak: 24 MB] iter=3: lowest time derivative order: basindex=0 der=(3,0,0,0) time_order=1
[ 2.2s] [mem: 22 MB peak: 24 MB] iter=0: lowest time derivative order: basindex=1 der=(2,0,0,0) time_order=1
[ 2.2s] [mem: 24 MB peak: 24 MB] iter=1: lowest time derivative order: basindex=1 der=(2,1,0,0) time_order=1
[ 2.3s] [mem: 23 MB peak: 24 MB] iter=2: lowest time derivative order: basindex=1 der=(2,1,0,0) time_order=1
[ 2.3s] [mem: 23 MB peak: 24 MB] iter=3: lowest time derivative order: basindex=1 der=(2,2,0,0) time_order=1
[ 2.3s] [mem: 23 MB peak: 24 MB] iter=4: lowest time derivative order: basindex=1 der=(3,0,0,0) time_order=1
[ 2.3s] [mem: 22 MB peak: 24 MB] iter=0: lowest time derivative order: basindex=1 der=(2,0,0,0) time_order=1
[ 2.3s] [mem: 23 MB peak: 24 MB] iter=1: lowest time derivative order: basindex=1 der=(2,1,0,0) time_order=1
[ 2.4s] [mem: 23 MB peak: 24 MB] iter=2: lowest time derivative order: basindex=1 der=(2,2,0,0) time_order=1
[ 2.4s] [mem: 23 MB peak: 24 MB] iter=3: lowest time derivative order: basindex=1 der=(3,0,0,0) time_order=1
[ 2.4s] [mem: 22 MB peak: 24 MB] backward substitution
[ 2.7s] [mem: 22 MB peak: 24 MB] step 8: eliminate all spatial derivatives of time derivatives of order=2
[ 3.2s] [mem: 26 MB peak: 26 MB] eliminate all spatial derivatives up to time order=3
[ 3.2s] [mem: 26 MB peak: 26 MB] iter=0: lowest time derivative order: basindex=0 der=(4,0,0,0) time_order=2
[ 3.2s] [mem: 26 MB peak: 26 MB] iter=0: lowest time derivative order: basindex=1 der=(4,0,0,0) time_order=2
[ 3.2s] [mem: 26 MB peak: 26 MB] backward substitution
[ 3.5s] [mem: 27 MB peak: 27 MB] step 9: output and save
[ 3.7s] [mem: 9 MB peak: 27 MB] Finished
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_x__X__frho(t,x,y,z)_xxx 0 → 100644
View file @ 6c1a0d26
1/3*o_3^(-1)*dl^4*c_s^4*dt^(-1)*rho^(-1)-1/6*dl^4*c_s^4*dt^(-1)*rho^(-1)
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_x__X__fu(t,x,y,z)_xxx 0 → 100644
View file @ 6c1a0d26
10/3*o_3^(-1)*dl^4*dt^(-1)*u^3-5/3*dl^4*dt^(-1)*u^3+2/3*dl^4*dt^(-1)*u-4/3*o_3^(-1)*dl^4*dt^(-1)*u-3/2*dl^4*c_s^2*dt^(-1)*u+3*o_3^(-1)*dl^4*c_s^2*dt^(-1)*u
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_xx__X__frho(t,x,y,z)_xx 0 → 100644
View file @ 6c1a0d26
1/3*o_3^(-1)*dl^4*c_s^4*dt^(-1)*rho^(-1)-1/6*dl^4*c_s^4*dt^(-1)*rho^(-1)
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_xx__X__fu(t,x,y,z)_xx 0 → 100644
View file @ 6c1a0d26
31/6*o_3^(-1)*dl^4*dt^(-1)*u^3-31/12*dl^4*dt^(-1)*u^3+13/12*dl^4*dt^(-1)*u-13/6*o_3^(-1)*dl^4*dt^(-1)*u-13/4*dl^4*c_s^2*dt^(-1)*u+13/2*o_3^(-1)*dl^4*c_s^2*dt^(-1)*u
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_xxx 0 → 100644
View file @ 6c1a0d26
1/4*u*dl^3*c_s^2*dt^(-1)+1/12*u^3*dl^3*dt^(-1)-1/12*u*dl^3*dt^(-1)
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_xxx__X__fu(t,x,y,z)_x 0 → 100644
View file @ 6c1a0d26
-5/3*o_3^(-1)*u*dl^4*dt^(-1)+5/6*u*dl^4*dt^(-1)-11/6*u^3*dl^4*dt^(-1)+11/3*o_3^(-1)*u^3*dl^4*dt^(-1)+6*o_3^(-1)*u*dl^4*c_s^2*dt^(-1)-3*u*dl^4*c_s^2*dt^(-1)
src/d1q3_nse/output_d1q3_nse_clbm1_symbolic/pde_00/coef_frho(t,x,y,z)_xxxx 0 → 100644
View file @ 6c1a0d26
o_3^(-1)*u^2*dl^4*c_s^2*dt^(-1)+1/12*o_3^(-1)*dl^4*c_s^4*dt^(-1)-1/24*dl^4*c_s^4*dt^(-1)-1/2*u^2*dl^4*c_s^2*dt^(-1)+1/4*o_3^(-1)*u^4*dl^4*dt^(-1)-1/8*u^4*dl^4*dt^(-1)-1/12*o_3^(-1)*dl^4*c_s^2*dt^(-1)+1/24*dl^4*c_s^2*dt^(-1)-1/4*o_3^(-1)*u^2*dl^4*dt^(-1)+1/8*u^2*dl^4*dt^(-1)
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