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Numerical approximation of a degenerated non‐conservative multifluid model: relaxation scheme
Author(s) -
Berthon C.,
Braconnier B.,
Nkonga B.
Publication year - 2005
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.933
Subject(s) - relaxation (psychology) , mathematics , computation , shock wave , stability (learning theory) , scheme (mathematics) , flow (mathematics) , numerical approximation , work (physics) , shock (circulatory) , numerical analysis , mathematical analysis , mechanics , computer science , geometry , physics , algorithm , thermodynamics , medicine , psychology , social psychology , machine learning
The present work is devoted to the numerical approximation of a system which arises when modelling a two‐phase flow in a pipeline. Two particular difficulties are of special interest, the non‐conservativity and the weakly hyperbolicity of this system. Some elementary waves are characterized and a relaxation system, unconditionally hyperbolic, is proposed. The stability criteria of the resulting relaxation method are achieved by a Chapmann–Enskog‐like expansion. A numerical scheme based on the relaxation system is proposed and computations are performed on a shock tube. Validation is performed by comparison with the exact solution and also to the solution from a modified HLL scheme. Copyright © 2005 John Wiley & Sons, Ltd.