Reducing Numerical Artifacts by Sacrificing Well-Balance for Rotating Shallow-Water Flow

Abstract

We consider the problem of rotational shallow-water flow for which non-trivial rotating steady-state solutions are of great importance. In particular, we investigate a high-resolution central-upwind scheme that is well-balanced for a subset of these stationary solutions and show that the well-balanced design is the source of numerical artifacts when applied to more general problems. We propose an alternative flux evaluation that sacrifices the well-balanced property and demonstrate that this gives qualitatively better results for relevant test cases and real-world oceanographic simulations.