Collision operator  $\vec{C}$:
\begin{equation*}
\vec{C}\left(\vec{f} \right) = \matr{K}^{-1} \matr{S} \left(\vec{\kappa}^{(eq)} - \matr{K}\vec{f} \right),
\end{equation*}
where
$$
	\matr{S} = \mathrm{diag}(\oA,\oB,\oC,\oD,\oE),
$$
$\oA,\oB,\dots,\oE \in \left(0,2\right).$ 

%Matrix $\matr{K}$ corresponds to the transformation matrix to the central moment basis defined by
Matrix $\matr{K}$ corresponds to the transformation matrix to the central moment basis defined by
\begin{equation*}
\vec{\kappa} = \Big( k_{(0,0)}, k_{(1,0)}, k_{(0,1)}, k_{(2,0)}, k_{(0,2)} \Big)^T,
\end{equation*}
and is given by
%Thus, the transformation matrix $\matr{K}$ satisfies
\input{\path/d2q5_clbm1_matK}

The equilibrium central moments are defined by
\begin{equation*}
\vec{\kappa}^{(eq)} = \matr{K}\matr{M}^{-1} \vec{\mu}^{(eq)},
\end{equation*}
i.e.,
\input{\path/d2q5_clbm1_eq}




%\noindent
%Matrix $\matr{B}$:
%\input{\path/d2q5m5_matB_per_els}
