Regularized Equations for Numerical Simulation of Flows of Homogeneous Binary Mixtures of Viscous Compressible Gases

Computational Mathematics and Mathematical Physics. 2019. Vol. 59. No. 11. P. 1832–1847.

Elizarova T. G., Zlotnik A.A., Shil’nikov E. V.

Translator: I. Ruzanova

Regularized equations for binary mixtures of viscous compressible gases (in the absence of chemical reactions) are considered. Two new simpler systems of equations are constructed for the case of a homogeneous mixture, when the velocities and temperatures of the components coincide. In the case of moderately rarefied gases, such a system is obtained by aggregating previously derived general equations for binary mixtures of polyatomic gases. In the case of relatively dense gases, the regularizing terms in these equations are subjected to a further substantial modification. For both cases, balance equations for the total mass, kinetic, and internal energy and new balance equations for total entropy are derived from the constructed equations; additionally, the entropy production is proved to be nonnegative. As an example of successful use of the new equations, the two-dimensional Rayleigh–Taylor instability of relatively dense gas mixtures is numerically simulated in a wide range of Atwood numbers.

Keywords: the entropy balance equation, homogeneous binary mixture of compressible gases, regularized equations, Rayleigh–Taylor instability