Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations
- 1Center for Coastal Margin Observation & Prediction, Oregon Health & Science University, Portland, OR, USA
- 2Department of Mathematics, Imperial College London, London, UK
- 3Department of Earth Science and Engineering, Imperial College London, London, UK
- 4Department of Computing, Imperial College London, London, UK
- apresent address: Finnish Meteorological Institute, Helsinki, Finland
- bpresent address: Department of Computer Science, Durham University, Durham, UK
Abstract. Unstructured grid ocean models are advantageous for simulating the coastal ocean and river–estuary–plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive, which limits their applicability to real-life problems. In this paper, we describe a novel discontinuous Galerkin (DG) finite element discretization for the hydrostatic equations. The formulation is fully conservative and second-order accurate in space and time. Monotonicity of the advection scheme is ensured by using a strong stability-preserving time integration method and slope limiters. Compared to previous DG models, advantages include a more accurate mode splitting method, revised viscosity formulation, and new second-order time integration scheme. We demonstrate that the model is capable of simulating baroclinic flows in the eddying regime with a suite of test cases. Numerical dissipation is well-controlled, being comparable or lower than in existing state-of-the-art structured grid models.