Simulating Tsunamis in the Indian Ocean with real bathymetry by using a high-order triangular Discontinuous Galerkin oceanic shallow water model
Giraldo. Francis X.
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The validation of the atmospheric model has been done considering standard tests from Williamson et al. [D.L. Williamson, J.B. Drake, J.J. Hack, R. Jakob, P.N. Swarztrauber, A standard test set for numerical approximations to the shallow water equations in spherical geometry, J. Comput. Phys. 102 (1992) 211–224], unsteady analytical solutions of the nonlinear shallow water equations and a barotropic instability caused by an initial perturbation of a jet stream. A convergence rate of OðDxkþ1Þ was observed in the model experiments. Furthermore, a numerical experiment is presented, for which the third-order time-integration method lim- its the model error. Thus, the time step Dt is restricted by both the CFL-condition and accuracy demands. Conservation of mass was shown up to machine precision and energy conservation converges for both increasing grid resolution and increasing polynomial order k.
The Discontinuous Galerkin Coastal Ocean Model (DGCOM) is a two-dimensional shallow water model for simulating coastal ocean processes.SIAM CSE Talk, March 2009