A pseudo-spectral discontinuous multidomain penalty method model for the simulation of geophysical flows

We report our latest results in the development of a pseudo-spectral discontinuous multidomain penalty method model for high Reynolds number incompressible flows. The target flow for simulation by this model is the shoaling of nonlinear internal waves over gentle slopes. The governing equations are discretized in time with three fractional steps. Spatial discretization is based on Legendre polynomials in quadrilateral subdomains. Nonlinear terms are advanced explicitly, while the pressure (Poisson) and viscous (Helmholtz) terms are handled implicitly through the implementation of particular preconditioning techniques. Numerical stability is ensured through the implementation of a penalty scheme based on the energy integral method and spectral filtering. The effectiveness of the model in the treatment of non- linearities is compared with analytical solutions for the Burgers and shallow water equations. For the latter case a comparison with discontinuous Galerkin Method will be presented.