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A simple method for compressible multiphase mixtures and interfaces
Author(s) -
Andrianov Nikolai,
Saurel Richard,
Warnecke Gerald
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.424
Subject(s) - godunov's scheme , compressibility , simple (philosophy) , robustness (evolution) , compressible flow , mathematics , upwind scheme , partial differential equation , numerical analysis , mathematical analysis , mechanics , physics , philosophy , biochemistry , chemistry , epistemology , discretization , gene
We develop a Godunov‐type scheme for a non‐conservative, unconditional hyperbolic multiphase model. It involves a set of seven partial differential equations and has the ability to solve interface problems between pure materials as well as compressible multiphase mixtures with two velocities and non‐equilibrium thermodynamics (two pressures, two temperatures, two densities, etc.).Its numerical resolution poses several difficulties. The model possesses a large number of acoustic and convective waves (seven waves) and it is not easy to upwind all these waves accurately and simply. Also, the system is non‐conservative, and the numerical approximations of the corresponding terms need to be provided. In this paper, we focus on a method, based on a characteristic decomposition which solves these problems in a simple way and with good accuracy. The robustness, accuracy and versatility of the method is clearly demonstrated on several test problems with exact solutions. Copyright © 2003 John Wiley & Sons, Ltd.