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Practical Techniques in Ghost Fluid Method for Compressible Multi-Medium Flows

Part of: Two-phase and multiphase flows Probabilistic methods, simulation and stochastic differential equations Hyperbolic equations and systems

Published online by Cambridge University Press:  31 August 2016

Liang Xu ,
Chengliang Feng  and
Tiegang Liu
Liang Xu*
Affiliation:
China Academy of Aerospace Aerodynamics, Beijing 100074, P.R. China
Chengliang Feng*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
Tiegang Liu*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, P.R. China
*
*Corresponding author. Email addresses:xul@buaa.edu.cn (L. Xu), fengchengliang@163.com (C. Feng), liutg@buaa.edu.cn (T. Liu)
*Corresponding author. Email addresses:xul@buaa.edu.cn (L. Xu), fengchengliang@163.com (C. Feng), liutg@buaa.edu.cn (T. Liu)
*Corresponding author. Email addresses:xul@buaa.edu.cn (L. Xu), fengchengliang@163.com (C. Feng), liutg@buaa.edu.cn (T. Liu)
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Abstract

The modified ghost fluid method (MGFM), due to its reasonable treatment for ghost fluid state, has been shown to be robust and efficient when applied to compressible multi-medium flows. Other feasible definitions of the ghost fluid state, however, have yet to be systematically presented. By analyzing all possible wave structures and relations for a multi-medium Riemann problem, we derive all the conditions to define the ghost fluid state. Under these conditions, the solution in the real fluid region can be obtained exactly, regardless of the wave pattern in the ghost fluid region. According to the analysis herein, a practical ghost fluid method (PGFM) is proposed to simulate compressible multi-medium flows. In contrast with the MGFM where three degrees of freedomat the interface are required to define the ghost fluid state, only one degree of freedomis required in this treatment. However, when these methods proved correct in theory are used in computations for the multi-medium Riemann problem, numerical errors at the material interface may be inevitable. We show that these errors are mainly induced by the single-medium numerical scheme in essence, rather than the ghost fluid method itself. Equipped with some density-correction techniques, the PGFM is found to be able to suppress these unphysical solutions dramatically.

Keywords

Modified ghost fluid methodghost fluid statemulti-medium Riemann problemgeneral equation of statecompressible multi-medium flow

MSC classification

Secondary: 35L45: Initial value problems for first-order hyperbolic systems 65C20: Models, numerical methods 76T10: Liquid-gas two-phase flows, bubbly flows
Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 3 , September 2016 , pp. 619 - 659
Copyright
Copyright © Global-Science Press 2016 

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