Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid
2017 ◽
Vol 10
(2)
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pp. 373-419
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Keyword(s):
AbstractThe 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.
2009 ◽
Vol 198
(21-26)
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pp. 1766-1774
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2019 ◽
Vol 80
(3)
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pp. 1936-1956
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2020 ◽
Vol 35
(6)
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pp. 355-366
2013 ◽
Vol 57
(1)
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pp. 19-41
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2011 ◽
Vol 235
(18)
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pp. 5357-5366
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2008 ◽
Vol 134
(2)
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pp. 243-255
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2014 ◽
Vol 257
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pp. 536-553
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