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

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.