Semi‐implicit finite element methods applied to the solution of the shallow water equations

Abstract

Semi‐implicit time integration schemes have been combined with finite element space discretization in developing a numerical scheme for the solution of the classical shallow water equations. The principal advantages of this approach are twofold: first, a highly variable gridding capability that allows selective regions of high resolution to be constructed within the computing domain, and second, the use of large time steps chosen on the basis of accuracy rather than by a Courant‐type restriction on their magnitude. The method will be useful in computing the low‐frequency–long wave motions driven by tides and wind on continental shelves and in marginal seas where higher grid resolution is necessary to describe adequately the nearshore dynamics. Application of the methodology is demonstrated by the calculation of the currents and sea surface heights in a hypothetical shelf domain that is driven by a single consituent deep ocean tide.