Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid

摘要

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.