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On new spatial discretization of the multidimensional quasi-gasdynamic system of equations with nondecreasing total entropy. (English. Russian original) Zbl 1354.35121
Dokl. Math. 94, No. 1, 423-429 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 469, No. 4, 402-408 (2016).
Summary: The multidimensional quasi-gasdynamic system of equations 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 on a nonuniform rectangular grid is constructed for this system. The basic unknown functions (density, velocity, and temperature) are defined on a common grid, while the fluxes and viscous stresses, on staggered grids. The discretization is specially constructed so that the total entropy does not decrease, which is achieved by applying numerous original features.
MSC:
35Q35 PDEs in connection with fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics, general
76M20 Finite difference methods applied to problems in fluid mechanics
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References:
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