Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters

We describe how regularization of lattice Boltzmann methods can be achieved by modifying dissipation. Classes of techniques used to try to improve regularization of LBMs include flux limiters, enforcing the exact correct production of entropy and manipulating non-hydrodynamic modes of the system in relaxation. Each of these techniques corresponds to an additional modification of dissipation compared with the standard LBGK model. Using some standard 1D and 2D benchmarks including the shock tube and lid driven cavity, we explore the effectiveness of these classes of methods.

Keywords: Lattice Boltzmann, Dissipation, Stability, Entropy, Filtering, Multiple Relaxation Times (MRT), Shock Tube, Lid-Driven Cavity.