Linear stability and isotropy properties of athermal regularized lattice Boltzmann methods.

The present work proposes a general methodology to study stability and isotropy properties of lattice Boltzmann (LB) schemes. As a first investigation, such a methodology is applied to better understand these properties in the context of regularized approaches. To this extent, linear stability analyses of two-dimensional models are proposed: the standard Bhatnagar-Gross-Krook collision model, the original precollision regularization, and the recursive regularized model, where off-equilibrium distributions are partially computed thanks to a recursive formula.

Consistent vortex initialization for the athermal lattice Boltzmann method.

A barotropic counterpart of the well-known convected vortex test case is rigorously derived from the Euler equations along with an athermal equation of state. Starting from a given velocity distribution corresponding to an intended flow recirculation, the athermal counterpart of the Euler equations are solved to obtain a consistent density field. The present initialization is assessed on a standard lattice Boltzmann solver based on the D2Q9 lattice.

Recursive regularization step for high-order lattice Boltzmann methods.

A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second- (and higher-) order nonhydrodynamic contributions in under-resolved conditions.