A GRP Scheme for 2D Shallow Water Equations with Source Terms

摘要

The aim of this paper is to apply the FVM to the solution of thern2D shallow water equations (SWEs) with source terms byrnadopting the Generalized Riemann Problem (GRP) scheme forrnthe advection terms. The upwind scheme will be used for thernbottom sloping terms in order to minimize the discrepancyrnbetween the sloping term and the static pressure term involvedrnin the advection terms, which is especially necessary for slowlyvaryingrnstatus variables. The model is applied to simulating therntide process in the water area near Tianjin Port. The simulatedrnresults of velocity by the proposed new model show significantrnimprovement compared with the results by the model withoutrnintroducing the GRP scheme and the upwind scheme for thernsloping term. Comparison of the numerical results of waterrnsurface elevation and velocity with the measurements is carriedrnout, which show basic agreements.