LBM section - added brief description of the collision operator

\subsubsection{Collision operator}

The term $\mathcal C_q$ in \cref{eq:lbm:LBE} denotes the discrete collision operator; in this paper we use the cumulant operator proposed in~\cite{geier2015cumulant} with the relaxation rates set as suggested therein and including the approximations of the spatial velocity derivatives to reduce the artifacts due to the absence of higher-order cumulants~\cite{geier2017a,geier2017b}.

\inline{Link between LBE and NSE (from the analysis): $\hat\nu = c_s^2 \left( \hat\tau - \frac{1}{2} \right)$, $\nu = \hat\nu \frac{\delta_x^2}{\delta_t}$ but this is for SRT, the cumulant operator has different/more relaxation parameters}

The term $\mathcal C_q$ in \cref{eq:lbm:LBE} denotes the discrete collision operator; in this paper we use the cumulant operator proposed in~\cite{geier2015cumulant}.

The operator has several parameters that drive the relaxation rates of different cumulants towards their equilibria.

The first relaxation rate, $\omega_1$, is linked to the kinematic viscosity $\nu$ in the Navier--Stokes equations via

\begin{equation}

    \nu = c_s^2 \left( \frac{1}{\omega_1} - \frac{1}{2} \right).

\end{equation}

The other relaxation rates are set as suggested by the authors of the original paper.

Furthermore, the approximations of the spatial velocity derivatives to reduce the artifacts due to the absence of higher-order cumulants are also incorporated in the collision operator according to \cite{geier2017a,geier2017b}.

\subsubsection{Equilibrium function}

\inline{describe the discrete equilibrium function based on equilibrium cumulants that we use in the code}

\inline[nolist]{Dotaz na PE: jak bys strucne popsal to co máme implementované v \ic{d3q27_eq_inv_cum.h}? Je to primo v nejakem clanku? Nebo je to matematicky ekvivalentni te "standardni" funkci kterou mame v \ic{d3q27_eq.h}, jenom jinak implementovane?}

\subsubsection{Boundary conditions}