Abstract

Korea Institute of Atmospheric Prediction Systems (KIAPS) is a new organization founded to develop the next generation operational numerical weather prediction (NWP) model for Korea Meteorological Administration (KMA). With the increasing demand for global high-resolution simulation, scalability becomes an important issue and highly scalable numerical methods such as spectral element (continuous Galerkin, CG) or discontinuous Galerkin (DG) methods are gaining interest. Although conventional finite difference (FD) or finite volume (FV) methods offer excellent efficiency, it is difficult to formulate high order schemes on nonorthogonal grid structures which is needed to avoid grid singularities. On the other hand, CG/DG methods are not constrained to lower order on unstructured, nonorthogonal grids. We present high order convergence properties of CG/DG methods for advection, shallow water equations on structured and/or unstructured grids in one and/or two dimensions. In order t o match the high order spatial truncation error, an explicit general order m-stage m1 order strong stability preserving (SSP) Runge-Kutta time integrator is used. With this setup, we can obtain arbitrary order convergence rates.