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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2016, Volume 56, Number 2, Pages 301–317
DOI: https://doi.org/10.7868/S0044466916020186
(Mi zvmmf10346)
 

This article is cited in 23 scientific papers (total in 23 papers)

On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force

A. A. Zlotnik

Department of Mathematics, Faculty of Economics Sciences, National Research University Higher School of Economics, Myasnitskaya ul. 20, Moscow, 101000, Russia
References:
Abstract: A multidimensional barotropic quasi-gasdynamic system of equations in the form of mass and momentum conservation laws with a general gas equation of state $p=p(\rho)$ with $p'(\rho)>0$ and a potential body force is considered. For this system, two new symmetric spatial discretizations on nonuniform rectangular grids are constructed (in which the density and velocity are defined on the basic grid, while the components of the regularized mass flux and the viscous stress tensor are defined on staggered grids). These discretizations involve nonstandard approximations for $\nabla p(\rho)$, $\mathrm{div}(\rho\mathbf{u})$, and $\rho$. As a result, a discrete total mass conservation law and a discrete energy inequality guaranteeing that the total energy does not grow with time can be derived. Importantly, these discretizations have the additional property of being well-balanced for equilibrium solutions. Another conservative discretization is discussed in which all mass flux components and viscous stresses are defined on the same grid. For the simpler barotropic quasi-hydrodynamic system of equations, the corresponding simplifications of the constructed discretizations have similar properties.
Key words: viscous compressible Navier–Stokes equations, quasi-gasdynamic system of equations, potential body force, spatial discretization, energy balance equation, well balanced property.
Funding agency Grant number
National Research University Higher School of Economics 15-09-0266
Russian Foundation for Basic Research 13-01-00703_а
14-01-90009-Бел_а
Received: 02.06.2015
English version:
Computational Mathematics and Mathematical Physics, 2016, Volume 56, Issue 2, Pages 303–319
DOI: https://doi.org/10.1134/S0965542516020160
Bibliographic databases:
Document Type: Article
UDC: 517.958:533.7
Language: Russian
Citation: A. A. Zlotnik, “On conservative spatial discretizations of the barotropic quasi-gasdynamic system of equations with a potential body force”, Zh. Vychisl. Mat. Mat. Fiz., 56:2 (2016), 301–317; Comput. Math. Math. Phys., 56:2 (2016), 303–319
Citation in format AMSBIB
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  • This publication is cited in the following 23 articles:
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