Spectral/hp discontinuous Galerkin methods for modelling 2D Boussinesq equations

  • Authors:

  • Claes Eskilsson;Spencer J. Sherwin

  • Affiliations:

  • Department of Civil and Environmental Engineering, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden;Department of Aeronautics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

We present spectral/hp discontinuous Galerkin methods for modelling weakly nonlinear and dispersive water waves, described by a set of depth-integrated Boussinesq equations, on unstructured triangular meshes. When solving the equations two different formulations are considered: directly solving the coupled momentum equations and the 'scalar method', in which a wave continuity equation is solved as an intermediate step. We demonstrate that the approaches are fully equivalent and give identical results in terms of accuracy, convergence and restriction on the time step. However, the scalar method is shown to be more CPU efficient for high order expansions, in addition to requiring less storage.