Article ID Journal Published Year Pages File Type
499075 Computer Methods in Applied Mechanics and Engineering 2009 9 Pages PDF
Abstract

In this paper, dynamic p-adaptive Runge–Kutta discontinuous Galerkin (RKDG) methods for the two-dimensional shallow water equations (SWE) are investigated. The p-adaptive algorithm that is implemented dynamically adjusts the order of the elements of an unstructured triangular grid based on a simple measure of the local flow properties of the numerical solution. Time discretization is accomplished using optimal strong-stability-preserving (SSP) RK methods. The methods are tested on two idealized problems of coastal ocean modeling interest with complex bathymetry – namely, the idealization of a continental shelf break and a coastal inlet. Numerical results indicate the stability, robustness, and accuracy of the algorithm, and it is shown that the use of dynamic p-adaptive grids offers savings in CPU time relative to grids with elements of a fixed order p that use either local h-refinement or global p-refinement to adequately resolve the solution while offering comparable accuracy.

Related Topics
Physical Sciences and Engineering Computer Science Computer Science Applications
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