Discontinuous Galerkin methods for dispersive shallow water models in closed basins: Spurious eddies and their removal using curved boundary methods

• Published in: Ocean modelling (Oxford) Vol. 107; pp. 112 - 124
• Main Authors: Steinmoeller, D.T., Stastna, M., Lamb, K.G.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2016
• Subjects: Boussinesq equations; Computer simulation; Dispersion (wave); Eddies; Fluid dynamics; Galerkin methods; Marine; Mathematical models; Methodology; Obstacles; Ocean basins; Ocean models; Shallow water equations; Water waves; Wave dispersion; Canada, Ontario, Pinehurst L; Canada, Alberta; Water waves; Shallow water equations; Mathematical models; Boussinesq equations; Fluid dynamics; Wave dispersion
• ISSN: 1463-5003; 1463-5011
• DOI: 10.1016/j.ocemod.2016.10.007

•A moderateorder method is used to solve model equations for dispersive waves.•We illustrate that straightsided elements can generate spurious eddies.•It is shown that the use of curvilinear elements suppresses the spurious eddies.•The model is shown to be useful in 2D simulations in realworld lake geometries. Discontinuous Galerkin methods offer a promising methodology for treating nearly hyperbolic systems such as dispersion-modified shallow water equations in complicated basins. Use of straight-edged triangular elements can lead to the generation of spurious eddies when wave fronts propagate around sharp, re-entrant obstacles such as headlands. While these eddies may be removed by adding strong artificial dissipation (e.g., eddy viscosity), for nearly inviscid simulations that focus on wave phenomena this approach is not reasonable. We demonstrate that the moderate order Discontinuous Galerkin methodology may be extended to curved triangular elements provided that the integral formulations are computed with high-order quadrature and cubature rules. Simulations with the new technique do not exhibit spurious eddy generation in idealized complex domains or real-world basins as exemplified by Pinehurst Lake, Alberta, Canada.