@Article{NMTMA-10-373,
author = {Yangyu Kuang, Kailiang Wu and Huazhong Tang},
title = {Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2017},
volume = {10},
number = {2},
pages = {373--419},
abstract = {<p style="text-align: justify;">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&#39;s flux etc.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.s09},
url = {http://global-sci.org/intro/article_detail/nmtma/12351.html}
}