期刊
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
卷 57, 期 4, 页码 706-725出版社
MAIK NAUKA/INTERPERIODICA/SPRINGER
DOI: 10.1134/S0965542517020166
关键词
Navier-Stokes equations for viscous compressible heat-conducting gases; quasi-gasdynamic system of equations; spatial discretization; conservativeness; law of nondecreasing entropy
资金
- Russian Foundation for Basic Research [16-01-00048]
The multidimensional quasi-gasdynamic system written in the form of mass, momentum, and total energy balance equations for a perfect polytropic gas with allowance for a body force and a heat source is considered. A new conservative symmetric spatial discretization of these equations on a nonuniform rectangular grid is constructed (with the basic unknown functions-density, velocity, and temperature-defined on a common grid and with fluxes and viscous stresses defined on staggered grids). Primary attention is given to the analysis of entropy behavior: the discretization is specially constructed so that the total entropy does not decrease. This is achieved via a substantial revision of the standard discretization and applying numerous original features. A simplification of the constructed discretization serves as a conservative discretization with nondecreasing total entropy for the simpler quasi-hydrodynamic system of equations. In the absence of regularizing terms, the results also hold for the Navier-Stokes equations of a viscous compressible heat-conducting gas.
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