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

  • Yangyu Kuang (a1), Kailiang Wu (a2) and Huazhong Tang (a1)

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.

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Corresponding author

*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)

References

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

  • Yangyu Kuang (a1), Kailiang Wu (a2) and Huazhong Tang (a1)

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