Abstract
AbstractThe finiteâelement, semiâimplicit, and semiâLagrangian methods are used on unstructured meshes to solve the nonlinear shallowâwater system. Several đ1 approximation schemes are developed for an accurate treatment of the advection terms. The employed finiteâelement discretization schemes are the PâP1 and P2âP1 pairs. Triangular finite elements are attractive because of their flexibility for representing irregular boundaries and for local mesh refinement. By tracking the characteristics backward from both the interpolation and quadrature nodes and using đ1 interpolating schemes, an accurate treatment of the nonlinear terms and, hence, of Rossby waves is obtained. Results of test problems to simulate slowly propagating Rossby modes illustrate the promise of the proposed approach in ocean modelling. Copyright © 2007 John Wiley & Sons, Ltd.
Published Version
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