Modeling and Computations of Shallow-Water Coastal Flows

Development of a Coastal Inundation Model using a Triangular Discontinuous Galerkin Method

Shiva Gopalakrishnan

Naval Postgraduate School
[SLIDES]

The use of unstructured triangular meshes provides an opportunity to accurately model coastlines which will aid in the study of tsunamis and storm surges. Discontinuous Galerkin methods employing triangular elements applied to shallow water equations have been developed by Giraldo and co-workers [1,2]. The attractive features of the discontinuous Galerkin method over the finite element and the finite volume methods are the higher order accuracies and the local conservation properties. The local nature of the discontinuous Galerkin method inherently lends itself to efficient parallelization on massively parallel processing computers. A coastal inundation model applied in the triangular discontinuous Galerkin framework willbe discussed in this presentation. Standardized test cases existing in the literature will be verified and possible higher order methods for wetting and drying will be discussed.

Adaptive mesh techniques will enable the optimal use of computational resources while providing higher resolutions in regions of interest. A combination of proposed R-refinement and H-refinement schemes for triangular grids applied to the DG method will also be presented in the talk. An eventual goal is to combine wind forcing data from mesoscale atmospheric models to simulate storm surges.

References
[1] F.X. Giraldo and T. Warburton, "A high-order triangular discontinuous Galerkin oceanic shallow water model", International Journal for Numerical Methods in Fluids, v.56, p.899-925, 2008
[2] F.X. Giraldo and M. Restelli, "High-order semi-implicit time-integrators for a triangular discontinuous Galerkin oceanic shallow water model", International Journal for Numerical Methods in Fluids, v.63, p.1077-1102, 2009