zbMATH — the first resource for mathematics

Discontinuous Galerkin spectral/\(hp\) element modelling of dispersive shallow water systems. (English) Zbl 1067.76057
From the summary: We consider the unstructured spectral/\(hp\) discontinuous Galerkin formulation of weakly nonlinear dispersive Boussinesq equations and nonlinear shallow water equations (a subset of the Boussinesq equations). Discretization of the Boussinesq equations involves resolving third-order mixed derivatives. To efficiently handle these high-order terms, we present a new scalar formulation based on the divergence of the momentum equations. Numerical computations illustrate the exponential convergence with regard to expansion order. Finally, we simulate solitary wave solutions.

76M10 Finite element methods applied to problems in fluid mechanics
76M22 Spectral methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76B25 Solitary waves for incompressible inviscid fluids
Full Text: DOI
[10] Dupont, F. (2001). Comparison of Numerical Methods for Modelling Ocean Circulation in Basins with Irregular Coasts, Ph.D. Thesis, McGill University.
[13] Eskilsson, C., and Sherwin, S. J. A triangular spectral/hp discontinuous Galerkin method for modelling two-dimensional shallow water equations. Int. J. Numeric. Meth. Fluids, in press. · Zbl 1085.76544
[14] Giraldo, F. X. (1998). A spectral element semi-Lagrangian method for the shallow water equations on unstructured grids. Proceeding of the Fourth World Congress on Computational Mechanics.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.