Stabilization of the lattice Boltzmann method by the H theorem:: A numerical test

For a one-dimensional benchmark shock tube problem, we implement the lattice Boltzmann method based on the H theorem [I. Karlin, A. Ferrante, and H. C. Ottinger, Europhys. Lett. 47, 182 (1999)]. Results of simulation demonstrate significant improvement of stability, as compared to realizations without explicit entropic estimations.