Performance of numerical methods on the non-unique solution to the Riemann problem for the shallow water equations

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19 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)825-831
Number of pages7
JournalInternational Journal for Numerical Methods in Fluids
Volume47
Issue number8-9
DOIs
Publication statusPublished - 20 Mar 2005
Externally publishedYes
Event8th ICFD Conference on Numerical Methods for Fluid Dynamics - Oxford, United Kingdom
Duration: 29 Mar 20041 Apr 2004
Conference number: 8

Keywords

  • Non-strictly hyperbolic non-conservative system
  • Riemann problem
  • Shallow water equations
  • Test cases

Programme Area

  • Programme Area 2: Water Resources

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