Numerical approximation of a degenerated non‐conservative multifluid model: relaxation scheme | Zendy

Berthon C. | Zendy; Braconnier B. | Zendy; Nkonga B. | Zendy

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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.

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