期刊
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
卷 10, 期 2, 页码 373-419出版社
CAMBRIDGE UNIV PRESS
DOI: 10.4208/nmtma.2017.s09
关键词
RKDLEG method; evolution operator; genuinely multi-dimensional method; shallow water equations; cubed-sphere grid
资金
- National Natural Science Foundation of China [91330205, 11421101, 91630310]
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.
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