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Matem. Mod., 2016, Volume 28, Number 12, Pages 33–55 (Mi mm3794)  

Exact and approximate Riemann solvers for compressible two-phase flows

Igor Menshovab

a Keldysh Institute of Applied Mathematics RAS
b VNIIA «ROSATOM»

Abstract: A numerical method for solving the two-phase hydrodynamics equations that describe the flow of dispersed solid and gas mixture is considered. The Godunov method is applied to approximate numerical fluxes with implementing solutions to the Riemann problem. The formulations of these problems for the solid and gas phases are given, their exact analytical solutions are described and possible simplified approximate solutions are discussed. The obtained theoretical results are applied to construction of the discrete model which leads to extension of well-known Godunov-type and Rusanov-type methods to the system of Baer–Nunziato equations for non-equilibrium twophase flows. Numerical results concern the method verification on generalized Sod problems with analytical self-similar solutions of two-phase equations.

Keywords: two-phase flow, non-conservative Euler equations, Riemann problem, numerical methods of Godunov and Rusanov.

Funding Agency Grant Number
Russian Science Foundation 15-11-00021


Full text: PDF file (522 kB)
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English version:
Mathematical Models and Computer Simulations, 2017, 9:4, 405–422

Received: 26.11.2015

Citation: Igor Menshov, “Exact and approximate Riemann solvers for compressible two-phase flows”, Matem. Mod., 28:12 (2016), 33–55; Math. Models Comput. Simul., 9:4 (2017), 405–422

Citation in format AMSBIB
\Bibitem{Men16}
\by Igor~Menshov
\paper Exact and approximate Riemann solvers for compressible two-phase flows
\jour Matem. Mod.
\yr 2016
\vol 28
\issue 12
\pages 33--55
\mathnet{http://mi.mathnet.ru/mm3794}
\elib{https://elibrary.ru/item.asp?id=28119134}
\transl
\jour Math. Models Comput. Simul.
\yr 2017
\vol 9
\issue 4
\pages 405--422
\crossref{https://doi.org/10.1134/S2070048217040093}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85024392469}


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