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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 8, Pages 1391–1404 (Mi zvmmf10253)  

The Riemann problem in the quasi-one-dimensional approximation

M. V. Abakumova, Yu. P. Popovb, P. V. Rodionova

a Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991, Russia
b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

Abstract: The classical one-dimensional Riemann problem is generalized to the quasi-one-dimensional case. A plane slotted channel with a discontinuous cross section is considered. The resulting exact self-similar solution is compared with numerical results obtained for a system of quasi-onedimensional and two-dimensional equations. It is shown that they are in good qualitative agreement and, for certain parameters, also agree well quantitatively.

Key words: Riemann problem, quasi-one-dimensional approximation, flow in channels of variable cross section, self-similar solution, computational gas dynamics.

DOI: https://doi.org/10.7868/S0044466915080025

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:8, 1356–1369

Bibliographic databases:

UDC: 519.634
Received: 26.02.2015

Citation: M. V. Abakumov, Yu. P. Popov, P. V. Rodionov, “The Riemann problem in the quasi-one-dimensional approximation”, Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015), 1391–1404; Comput. Math. Math. Phys., 55:8 (2015), 1356–1369

Citation in format AMSBIB
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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