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.
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C.-W. Shu’s research is supported by AFOSR grant FA9550-09-1-0126 and NSF grant DMS-0809086. S. Noelle’s research is supported by DFG grant GK 775.
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Xing, Y., Shu, CW. & Noelle, S. On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations. J Sci Comput 48, 339–349 (2011). https://doi.org/10.1007/s10915-010-9377-y
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DOI: https://doi.org/10.1007/s10915-010-9377-y