Recovering the full Navier Stokes equations with lattice Boltzmann schemes

We consider multi relaxation times lattice Boltzmann scheme with two particle distributions for the thermal Navier Stokes equations formulated with conservation of mass and momentum and dissipation of volumic entropy. Linear stability is taken into consideration to determine a coupling between two coefficients of dissipation. We present interesting numerical results for one-dimensional strong nonlinear acoustic waves with shocks.