Thetis coastal ocean model: discontinuous Galerkin discretization for the three-dimensional hydrostatic equations

TL;DR

This paper introduces a novel discontinuous Galerkin finite element discretization for 3D hydrostatic ocean equations, improving accuracy and efficiency for coastal and estuarine simulations.

Contribution

It presents a fully conservative, second-order accurate DG discretization with enhanced mode splitting, viscosity formulation, and time integration, suitable for complex coastal flows.

Findings

Capable of simulating baroclinic eddying flows

Numerical dissipation comparable or lower than existing models

Enhanced accuracy and stability in unstructured grid ocean modeling

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.