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Flux difference splitting for the Euler equations in one spatial co‐ordinate with area variation
Author(s) -
Glaister P.
Publication year - 1988
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.1650080109
Subject(s) - riemann solver , euler equations , ordinate , riemann problem , shock (circulatory) , euler's formula , roe solver , mathematics , mathematical analysis , flux (metallurgy) , geometry , solver , riemann hypothesis , total variation diminishing , physics , mechanics , mathematical optimization , finite volume method , medicine , materials science , metallurgy
An approximate (linearized) Riemann solver is presented for the solution of the Euler equations of gas dynamics in one spatial co‐ordinate. This includes cylindrically and spherically symmetric geometries and also applies to narrow ducts with area variation. The method is Roe's flux difference splitting with a technique for dealing with source terms. The results of two problems, a spherically divergent infinite shock and a converging cylindrical shock, are presented. The numerical results compare favourably with those of Noh's recent survey and also with those of Ben‐Artzi and Falcovitz using a more complicated Riemann solver.