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

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.

Submitted to Geoscientific Model Development

References in corpus (8)

• Firedrake: automating the finite element method by composing abstractions
• Automated derivation of the adjoint of high-level transient finite element programs
• A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling
• TSFC: a structure-preserving form compiler
• Automated generation and symbolic manipulation of tensor product finite elements
• Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements
• A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake
• An algorithm for the optimization of finite element integration loops

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• CFL Optimized Forward-Backward Runge-Kutta Schemes for the Shallow Water Equations