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A Riemann solver and upwind methods for a two‐phase flow model in non‐conservative form
Author(s) -
Castro C. E.,
Toro E. F.
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.1055
Subject(s) - riemann solver , upwind scheme , mathematics , riemann problem , godunov's scheme , flow (mathematics) , riemann hypothesis , roe solver , solver , mathematical analysis , calculus (dental) , mathematical optimization , discretization , numerical analysis , geometry , finite volume method , mechanics , physics , medicine , dentistry
We present a theoretical solution for the Riemann problem for the five‐equation two‐phase non‐conservative model of Saurel and Abgrall. This solution is then utilized in the construction of upwind non‐conservative methods to solve the general initial‐boundary value problem for the two‐phase flow model in non‐conservative form. The basic upwind scheme constructed is the non‐conservative analogue of the Godunov first‐order upwind method. Second‐order methods in space and time are then constructed via the MUSCL and ADER approaches. The methods are systematically assessed via a series of test problems with theoretical solutions. Copyright © 2005 John Wiley & Sons, Ltd.