Improving the stability of multiple-relaxation lattice Boltzmann methods with central moments

In this work we seek lattice Boltzmann methods (LBM) with improved stability that retain accuracy. Using von Neumann stability analysis to extract dispersion and diffusion errors, we compare the D2Q9 lattice scheme with three collision operators: the single relaxation time (BGK), the multiple-relaxation time with raw moments (MRT-RM) and with central moments (MRT-CM). First, we observe that the MRT-CM shows favorable properties when compared to the other two schemes. This method provides low errors, enhanced stability and enables the modification of free parameters. Second, we optimize these free parameters to increase dissipation only for high under-resolved wavenumbers, leaving low wavenumbers (well resolved scales) unchanged. In particular, we show that the optimized MRT-CM can cope with lower viscosities, higher velocities and coarser meshes that their predecessors. Finally, the optimized MRT-CM is tested for a shear layers flow to illustrate the enhanced stability and accuracy of the proposed technique.