Wave Propagation Characteristics of Continuous and Discontinuous Galerkin Finite Element Algorithms for the Shallow Water Equations

摘要

Domains for shallow water simulation have become more complicated in recent years and many of the existing solution algorithms are being stretched beyond their inherent limitations. One proposed solution to this problem is to use a coupled algorithm that employs more than one discretization technique within the domain. As a first step in studying such coupled algorithms, this paper examines the properties of existing continuous and discontinuous Galerkin finite element algorithms to determine their individual abilities to propagate waves. Fourier and dispersion analyses indicate that the generalized wave continuity and discontinuous Galerkin approaches are promising candidates for such a coupled solution technique, as they both exhibit similar phase behavior. In particular, they show minimal phase error and do not overly damp the solution.