Commit 6c1a0d26 authored by Radek Fučík's avatar Radek Fučík
Browse files

new structure (fixed)

parent 9039e5f3

src/d1q3_ade/Makefile

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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

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\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

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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

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\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

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\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}