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
$$
	\matr{S} = \mathrm{diag}(\oA,\oB,\oC),
$$
$\oA,\oB,\oC \in \left(0,2\right).$ 

Matrix $\matr{K}$ corresponds to the transformation matrix to the central moment basis defined by
\begin{equation*}
\vec{\kappa} = \Big(	k_{(0)}, k_{(1)}, k_{(2)} \Big)^T
\end{equation*}
and is given by
\input{\path/d1q3_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/d1q3_clbm1_eq}
