A semi-implicit semi-Lagrangian finite-element shallow-water ocean model

The finite-element. semi-implicit, and semi-Lagrangian methods are combined together to solve the shallow-water equations using unstructured triangula r meshes. Triangular finite elements are attractive for ocean modeling beca use of their flexibility for representing irregular boundaries and for loca l mesh refinement. A kriging interpolator is used for the semi-Lagrangian a dvection. leading to an accurate representation of the slow Rossby modes. T he terms that govern fast gravitational oscillations are discretized using the semi-implicit scheme, thereby circumventing a severe time step restrict ion. A low-order velocity-surface-elevation finite-element basis-function p air is used for the spatial discretization. Results of test problems to sim ulate slowly propagating Rossby modes illustrate the promise of the propose d approach for ocean modeling.