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On Riemann solvers for compressible liquids
Author(s) -
Ivings M. J.,
Causon D. M.,
Toro E. F.
Publication year - 1998
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/(sici)1097-0363(19980915)28:3<395::aid-fld718>3.0.co;2-s
Subject(s) - riemann solver , riemann problem , roe solver , godunov's scheme , riemann hypothesis , solver , mathematics , compressible flow , riemann's differential equation , compressibility , mathematical analysis , riemann xi function , physics , numerical analysis , mechanics , mathematical optimization , finite volume method
A number of Riemann solvers are proposed for the solution of the Riemann problem in a compressible liquid. Both the Tait and Tammann equations of state are used to describe the liquid. Along with exact Riemann solvers, a detailed description of a primitive variable Riemann solver, a two‐shock Riemann solver, a two‐rarefaction Riemann solver and an extension to the HLL Riemann solver, namely the HLLC Riemann solver, are presented. It is shown how these Riemann solvers may be implemented into Godunov‐type numerical methods. The appropriateness of each of the Riemann solvers for a number of flow situations is demonstrated by applying Godunov's method to some revealing shock tube test problems. © 1998 John Wiley & Sons, Ltd.