A hybrid numerical method for the shallow water equations with source term

Abstract

In coastal oceanography there is interest in problems modeled by the shallow water equations, where variations in channel depth are accounted for by the presence of source terms. A numerical treatment for the solution of such problems is presented here, in terms of a hybrid approach, which combines a second-order TVD scheme for conservation law equations (assuming no source terms) with an eigenvector projection scheme that incorporates the effects of nonzero source terms (in regions where the bottom is not flat). For the case where an initially sharp wave profile is assumed, the progress of a wave as it traverses an estuary whose channel depth varies is calculated. Excellent numerical results are obtained.