In this talk, I will focus on the importance of the classical problem of the global ocean tides and the necessary numerical framework for its modelling. The development of models of the ocean tides with higher resolution near coastlines and courser resolution offshore, has been required to account for the significant impacts of coastline configuration and bathymetry (associated with sea level rise) on both the amplitude and phase of tidal constituents. This capability becomes especially important in the context of tidal analyses at times in the past when sea levels are known to have differed significantly from present.

Here I present a novel global model based on the discontinuous Galerkin disretization of the shallow water equations that employs 3rd order Runge-Kutta time stepping on unstructured triangular grids. The model has been efficiently parallelized and is thereby shown to achieve essentially perfect linear scaling which makes it suitable for the generation of extremely high resolution results in local regions of interest. I will also present the results of several benchmarking tests and tidal simulations.