A Performance Comparison of Continuous and Discontinuous Finite Element Shallow Water Models

Authors:
Ethan J. Kubatko;Shintaro Bunya;Clint Dawson;Joannes J. Westerink;Chris Mirabito
Affiliations:
Department of Civil and Environmental Engineering and Geodetic Science, The Ohio State University, Columbus, USA 43210;Department of Systems Innovation, The University of Tokyo, Tokyo, Japan 113-8656;Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA 78712;Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, USA 46556;Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, USA 78712
Venue:
Journal of Scientific Computing
Year:
2009

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Abstract

We present a comparative study of two finite element shallow water equation (SWE) models: a generalized wave continuity equation based continuous Galerkin (CG) model--an approach used by several existing SWE models--and a recently developed discontinuous Galerkin (DG) model. While DG methods are known to possess a number of favorable properties, such as local mass conservation, one commonly cited disadvantage is the larger number of degrees of freedom associated with the methods, which naturally translates into a greater computational cost compared to CG methods. However, in a series of numerical tests, we demonstrate that the DG SWE model is generally more efficient than the CG model (i) in terms of achieving a specified error level for a given computational cost and (ii) on large-scale parallel machines because of the inherently local structure of the method. Both models are verified on a series of analytic test cases and validated on a field-scale application.