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

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, movingwater 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.

• Type: Journal
• Year: 2011
• Where: JSCIC
• Authors: Yulong Xing, Chi-Wang Shu, Sebastian Noelle
• Keywords: JSCIC 2011, Moving Water, Shallow Water Equations, Spurious Oscillations