On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations

Authors:
Yulong Xing;Chi-Wang Shu;Sebastian Noelle
Affiliations:
Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, USA 37831 and Department of Mathematics, University of Tennessee, Knoxville, USA 37996;Division of Applied Mathematics, Brown University, Providence, USA 02912;Institute for Geometry and Applied Mathematics, RWTH Aachen University, Aachen, Germany 52056
Venue:
Journal of Scientific Computing
Year:
2011

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Abstract

This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate significant spurious oscillations, unless an extremely refined mesh is used. On the other hand, moving-water well-balanced methods perform well in these tests. The numerical examples in this note clearly demonstrate the importance of utilizing moving-water well-balanced methods for solutions near a moving-water equilibrium.