315 | IGPM315.pdf December 2010 |
TITLE | On the Advantage of Well-Balanced Schemes for Moving-Water Equilibria of the Shallow Water Equations |
AUTHORS | Yulong Xing, Chi-Wang Shu, Sebastian Noelle |
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. |
KEYWORDS | Shallow water equation, still water, moving water equilibrium, high order accuracy, well balanced scheme. |
DOI | 10.1007/s10915-010-9377-y |
PUBLICATION | Journal of scientific computing 48(1/3), 339-349 (2011) |