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

Part of: Basic methods in fluid mechanics Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  09 May 2017

Yangyu Kuang ,
Kailiang Wu  and
Huazhong Tang
Yangyu Kuang*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
Kailiang Wu*
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, OH 43210, USA
Huazhong Tang*
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, China
*
*Corresponding author. Email addresses:kyy@pku.edu.cn (Y. Y. Kuang), wukl@pku.edu.cn (K. L. Wu), hztang@math.pku.edu.cn (H. Z. Tang)
*Corresponding author. Email addresses:kyy@pku.edu.cn (Y. Y. Kuang), wukl@pku.edu.cn (K. L. Wu), hztang@math.pku.edu.cn (H. Z. Tang)
*Corresponding author. Email addresses:kyy@pku.edu.cn (Y. Y. Kuang), wukl@pku.edu.cn (K. L. Wu), hztang@math.pku.edu.cn (H. Z. Tang)
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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.

Keywords

RKDLEG methodevolution operatorgenuinely multi-dimensional methodshallow water equationscubed-sphere grid

MSC classification

Secondary: 65M25: Method of characteristics 76M10: Finite element methods
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 2 , May 2017 , pp. 373 - 419
Copyright
Copyright © Global-Science Press 2017 

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