Nonlinear stability of compressible thermal lattice BGK models

The nonlinear stability of thermal lattice BGK models is examined by means of computer simulation for the case of one- and two-dimensional compressible flows. It is shown that in one dimension (1D) the method is stable on a sizeable range of flow speeds and temperatures. In two dimensions (2D) the method is stable even in the presence of negative distribution functions, but on a smaller stability domain. The computational efficiency of the method compares favorably with classical algorithms for compressible flows, such as the lambda-scheme and the Lax-Wendroff scheme.