\input{latex/header}

\titler{D3Q27}{NSE}
\def\model{d3q27}
\def\pde{nse}
\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: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\subsection{MRT}
\def\colmod{mrt1}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}

\subsubsection{Conservation of mass: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\subsection{MRT2}
\def\colmod{mrt2}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}

\subsubsection{Conservation of mass: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\subsection{CLBM1}
\def\colmod{clbm1}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}

\subsubsection{Conservation of mass: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\subsection{CLBM2}
\def\colmod{clbm2}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}

\subsubsection{Conservation of mass: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\subsection{CuLBM1}
\def\colmod{culbm1}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}

\subsubsection{Conservation of mass: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\subsection{CuLBM2}
\def\colmod{culbm2}
\subsubsection{Definitions}
\input{\path/supp_\model_\colmod_defs}

\subsubsection{Conservation of mass: $\rho$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_00}
\subsubsection{Conservation of momentum: $\rho \ou$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_01}
\subsubsection{Conservation of momentum: $\rho \ov$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_02}
\subsubsection{Conservation of momentum: $\rho \ow$}
\input{output_\model_\pde_\colmod_symbolic/spatial_EPDE/pde_03}

\section{Comparison of SRT, MRT, CLBM, and CuLBM}

\subsection{Conservation of mass: $\rho$}
\input{compare_output_\model_\pde/pde_00}

\subsection{Conservation of momentum: $\rho \ou$}
\input{compare_output_\model_\pde/pde_01}

\subsection{Conservation of momentum: $\rho \ov$}
\input{compare_output_\model_\pde/pde_02}

\subsection{Conservation of momentum: $\rho \ow$}
\input{compare_output_\model_\pde/pde_03}

\bibliography{\path/ref.bib}

\end{document}
