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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 2, Pages 267–284
DOI: https://doi.org/10.7868/S004446691502009X (Mi zvmmf10156) 		 
This article is cited in 9 scientific papers (total in 9 papers)

On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance

V. A. Gavrilina, A. A. Zlotnikb

a Department of Mathematical Modeling, Moscow Power Engineering Institute, Technical University, Krasnokazarmennaya ul. 14, Moscow, 111250, Russia
b Department of Higher Mathematics, Faculty of Economics, National Research University Higher School of Economics, Myasnitskaya ul. 20, Moscow, 101000, Russia
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DOI: https://doi.org/10.7868/S004446691502009X
Abstract: The one-dimensional quasi-gasdynamic system of equations in the form of mass, momentum, and total energy conservation laws with general gas equations of state is considered. A family of three-point symmetric spatial discretizations of this system is studied for which the internal energy equation has a suitable form (without imbalance terms). An entropy balance equation is derived, and the influence exerted by the choice of discretizations of various terms on the form of difference imbalance terms in this equation is determined. Special discretizations are presented for which the corresponding nondivergence imbalance terms are zero. The Euler system of equations is solved numerically in the cases of a perfect polytropic gas, stiffened gas, and the van der Waals equations of state.
Key words: gas dynamics, general equations of state, quasi-gasdynamic system of equations, entropy balance equation, spatial discretization.
Funding agency Grant number
National Research University Higher School of Economics 14-09-0189
Russian Foundation for Basic Research 13-01-00703
14-01-90009-Бел
Received: 11.03.2014
Revised: 25.09.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 2, Pages 264–281
DOI: https://doi.org/10.1134/S0965542515020098
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
Citation: V. A. Gavrilin, A. A. Zlotnik, “On spatial discretization of the one-dimensional quasi-gasdynamic system of equations with general equations of state and entropy balance”, Zh. Vychisl. Mat. Mat. Fiz., 55:2 (2015), 267–284; Comput. Math. Math. Phys., 55:2 (2015), 264–281
Citation in format AMSBIB
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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