On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations

Journal Article · Sat Jan 01 00:00:00 EST 2011 · Journal of Scientific Computing

DOI:https://doi.org/10.1007/s10915-010-9377-y· OSTI ID:1018577

Xing, Yulong ^[1]; Shu, Chi-wang ^[2]; Noelle, Sebastian ^[3]

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1. ORNL
2. Brown University
3. Institut fur Physikalische Chemie der RWTH

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.

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC); Work for Others (WFO)
• DOE Contract Number: DE-AC05-00OR22725
• OSTI ID: 1018577
• Journal Information: Journal of Scientific Computing, Vol. 48, Issue 1-3; ISSN 0885--7474
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ACCURACY
OSCILLATIONS
WATER