High-order C{sup}1 finite-element interpolating schemes - Part II: Nonlinear semi-Lagrangian shallow-water models

摘要

The finite-element, semi-implicit, and semi-Lagrangian methods are used on unstructured meshes to solve the nonlinear shallow-water system. Several C{sup}1 approximation schemes are developed for an accurate treatment of the advection terms. The employed finite-element discretization schemes are the (P{sub}1){sup}(NC)-P{sub}1 and P{sub}2-P{sub}1 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 C{sup}1 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.