Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere

Abstract

The paper develops high order accurate Runge-Kutta discontinuous local evolution Galerkin (RKDLEG) methods on the cubed-sphere grid for the shallow water equations (SWEs). Instead of using the dimensional splitting method or solving one-dimensional Riemann problem in the direction normal to the cell interface, the RKDLEG methods are built on genuinely multi-dimensional approximate local evolution operator of the locally linearized SWEs on a sphere by considering all bicharacteristic directions. Several numerical experiments are conducted to demonstrate the accuracy and performance of our RKDLEG methods, in comparison to the Runge-Kutta discontinuous Galerkin method with Godunov's flux etc.

46 pages,24 figures

References in corpus (2)

• A Comparison of Two Shallow Water Models with Non-Conforming Adaptive Grids: classical tests
• Well-balanced finite volume evolution Galerkin methods for the shallow water equations

Cited by in corpus (1)

• High-order accurate well-balanced energy stable adaptive moving mesh finite difference schemes for the shallow water equations with non-flat bottom topography