Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid. Issue 2 (9th May 2017)

• Record Type: Journal Article
• Authors: Kuang, Yangyu; Wu, Kailiang; Tang, Huazhong
• Is Part Of: Numerical mathematics. Volume 10:Issue 2(2017)
• Page Start: 373
• Page End: 419
• Publication Date: 2017-05-09
• Subjects: 65M25, -- 76M10; RKDLEG method, -- evolution operator, -- genuinely multi-dimensional method, -- shallow water equations, -- cubed-sphere grid; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2017.s09
• Languages: English
• ISSNs: 1004-8979

Abstract

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.