Simulating Tsunamis in the Indian Ocean with real bathymetry by using a high-order triangular Discontinuous Galerkin oceanic shallow water model

Abstract

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.