hp Discontinuous Galerkin Methods for Advection Dominated Problems in Shallow Water Flow
In this paper, we discuss the development, verification, and application of an hp discontinuous Galerkin (DG) finite element model for solving the shallow water equations (SWE) on unstructured triangular grids. The h and p convergence properties of the method are demonstrated for both linear and highly nonlinear problems with advection dominance. Standard h-refinement for a fixed p leads to p + 1 convergence rates, while exponential convergence is observed for p-refinement for a fixed h. It is also demonstrated that the use of p-refinement is more efficient for problems exhibiting smooth solutions. Additionally, the ability of p-refinement to adequately resolve complex, two-dimensional flow structures is demonstrated in the context of a coastal inlet problem.
Publisher - Elsevier
Subjects - Water, Modelling
Collection: Section 2: Water Quality (2014)
Citation: Kubatko EJ, Westerink JJ, Dawson C. 2006. hp Discontinuous Galerkin Methods for Advection Dominated Problems in Shallow Water Flow. Computer Methods in Applied Mechanics and Engineering; 196(1-3):437-451 http://dx.doi.org/10.1016/j.cma.2006.05.002