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
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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.
@article{ZVMMF_2017_57_4_a10,
author = {A. A. Zlotnik},
title = {Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {710--729},
publisher = {mathdoc},
volume = {57},
number = {4},
year = {2017},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a10/}
}
TY - JOUR AU - A. A. Zlotnik TI - Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2017 SP - 710 EP - 729 VL - 57 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a10/ LA - ru ID - ZVMMF_2017_57_4_a10 ER -
%0 Journal Article %A A. A. Zlotnik %T Entropy-conservative spatial discretization of the multidimensional quasi-gasdynamic system of equations %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2017 %P 710-729 %V 57 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a10/ %G ru %F ZVMMF_2017_57_4_a10
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/