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Research Article
Performance of numerical methods on the non-unique solution to the Riemann problem for the shallow water equations
Article first published online: 4 MAR 2005
DOI: 10.1002/fld.846
Copyright © 2005 John Wiley & Sons, Ltd.
Issue
1097-0363/asset/cover.gif?v=1&s=4f4c032b9f06da7e1e8ac4e112013c5bf916f2e7 "International Journal for Numerical Methods in Fluids")
International Journal for Numerical Methods in Fluids
Special Issue: 8th ICFD Conference on Numerical Methods for Fluid Dynamics
Volume 47, Issue 8-9, pages 825–831, 20 - 30 March 2005
Additional Information
How to Cite
Andrianov, N. (2005), Performance of numerical methods on the non-unique solution to the Riemann problem for the shallow water equations. Int. J. Numer. Meth. Fluids, 47: 825–831. doi: 10.1002/fld.846
Publication History
- Issue published online: 4 MAR 2005
- Article first published online: 4 MAR 2005
- Manuscript Accepted: 26 JUL 2004
- Manuscript Revised: 22 JUL 2004
- Manuscript Received: 27 APR 2004
Funded by
- HYKE. Grant Number: HPRN-CT-2002-00282
- Abstract
- References
- Cited By
Keywords:
- shallow water equations;
- Riemann problem;
- non-strictly hyperbolic non-conservative system;
- test cases
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. Copyright © 2005 John Wiley & Sons, Ltd.