Abstract
In the presented paper the stability of the solutions of kinetic equations, which formed the models of ideal compressible gases at arbitrary heat ratio, is investigated. Models are widely used in applications of the lattice Boltzmann method, presented in the literature. The stability analysis is based on the considering of linear approximation and on the transition to the system of ordinary differential equations with complex coefficients. After the computations the stability criteria of the models are formulated for the cases of fixed values of relaxation time. The stability analysis is an important stage of the modelling process, because it may realize some help in choosing of the proper model for using in practical simulations.
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