Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Conservative formulation for compressible multiphase flows


Authors: Evgeniy Romenski, Alexander A. Belozerov and Ilya M. Peshkov
Journal: Quart. Appl. Math. 74 (2016), 113-136
MSC (2010): Primary 35L65, 76T99
DOI: https://doi.org/10.1090/qam/1409
Published electronically: December 3, 2015
MathSciNet review: 3472522
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Abstract: Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The resulting governing equations of the formulated model belong to the class of hyperbolic systems of conservation laws. In order to examine the reliability of the model, the one-dimensional Riemann problem for the four-phase flow is studied numerically with the use of the MUSCL-Hancock method in conjunction with the GFORCE flux.


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Additional Information

Evgeniy Romenski
Affiliation: Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
Email: evrom@math.nsc.ru

Alexander A. Belozerov
Affiliation: Novosibirsk State University, Novosibirsk, 630090, Russian Federation
Email: belozerov314@gmail.com

Ilya M. Peshkov
Affiliation: Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
Address at time of publication: Aix-Marseille Université, CNRS, IUSTI UMR 7343, Marseille, France
Email: peshkov@math.nsc.ru

DOI: https://doi.org/10.1090/qam/1409
Keywords: Hyperbolic system of conservation laws, multiphase compressible flow, four phase flow, finite-volume method, Riemann problem
Received by editor(s): May 15, 2014
Received by editor(s) in revised form: July 3, 2014
Published electronically: December 3, 2015
Additional Notes: The financial support from the Russian Foundation for Basic Research (grants 13-05-00076 and 13-05-12051), Presidium of Russian Academy of Sciences (Programme of Fundamental Research No. 15, project 121), and the Siberian Branch of Russian Academy of Sciences (Integration Projects No. 127 and No. 30) is greatly acknowledged.
The financial support from the Labex MEC (ANR-10-LABX-0092) and A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Ave nir” French government program managed by the French National Research Agency (ANR) is acknowledged
Article copyright: © Copyright 2015 Brown University


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