A Semi-implicit Semi-Lagrangian Finite-Element Shallow-Water Ocean Model

Abstract The finite-element, semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangular meshes. Triangular finite elements are attractive for ocean modeling because of their flexibility for representing irregular boundaries and for local mesh refinement. A kriging interpolator is used for the semi-Lagrangian advection, leading to an accurate representation of the slow Rossby modes. The terms that govern fast gravitational oscillations are discretized using the semi-implicit scheme, thereby circumventing a severe time step restriction. A low-order velocity–surface-elevation finite-element basis-function pair is used for the spatial discretization. Results of test problems to simulate slowly propagating Rossby modes illustrate the promise of the proposed approach for ocean modeling.

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