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Performance of numerical methods on the non‐unique solution to the Riemann problem for the shallow water equations
Author(s) -
Andrianov Nikolai
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.846
Subject(s) - exact solutions in general relativity , riemann problem , mathematics , riemann solver , numerical analysis , shallow water equations , riemann hypothesis , waves and shallow water , mathematical analysis , mechanics , physics , finite volume method , thermodynamics
For certain initial conditions, the exact solution to the Riemann problem for the shallow water equations is not unique. We test the performance of several numerical methods on such initial data and establish that the numerical solution can pick out different exact solutions. Moreover, the numerical solution does not necessarily converge towards the picked‐out exact solution. Copyright © 2005 John Wiley & Sons, Ltd.