On quasi-gasdynamic and quasi-hydrodynamic equations for binary gas mixtures

Abstract

The quasigasdynamic (QGD) approach makes it possible to construct convenient and reliable differ� ence schemes for the numerical solution of various gasdynamic problems. Its description can be found in (1-3). More specifically, in (2, Chapter 9) (see also (4)), the Boltzmann kinetic equation for a mixture of monatomic gases (5) is used to derive and test QGD equations for binary mixtures of nonreactive ideal polytropic gases. In this paper, we analyze and expand the capabili� ties of the QGD approach in this area. The original equations from (2) are rewritten as conservation laws, which are more conventional in viscous gas dynamics and convenient for discretization. Additionally, an external force and a heat source are taken into account. We briefly discuss the parabolicity of the sys� tem in the sense of Petrovskii, which ensures that the system is well defined. An entropy balance equation is derived, and the entropy production for a gas mixture is shown to be nonnegative, which ensures that the sys� tem is physically consistent (but does not hold in all available descriptions of gas mixtures). Importantly, to achieve the latter property, the expressions for the exchange terms in the total energy balance equation (initially derived only for monatomic gas mixtures) are properly generalized. Additionally, we introduce a simplification of the QGD system for binary mixtures, which is referred to as a quasihydrodynamic system and is used for the numerical simulation of weakly compressible suband transonic flows. At the end of this paper, we present simplified barotropic versions of both systems and derive a corresponding energy bal� ance equation with nonpositive energy production. The QGD system for binary gas mixtures a and b (see (2)) consists of the following mass balance, momentum, and total energy equations for the gas α: