Geodesic
Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 710-729 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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A. A. Zlotnik. Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 710-729. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a10/

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