TY - JOUR
T1 - Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid
AU - Yangyu Kuang, Kailiang Wu & Huazhong Tang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 2
SP - 373
EP - 419
PY - 2017
DA - 2017/10
SN - 10
DO - http://doi.org/10.4208/nmtma.2017.s09
UR - https://global-sci.org/intro/article_detail/nmtma/12351.html
KW - 
AB - <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>