An improved regularization for time-staggered discretization and its link to the semi-implicit method

Abstract

A regularized time-staggered discretization of the shallow-water equations has recently been proposed. Here, a new form of the regularization operator is presented. This form addresses a weakness in the original formulation so that now the discretization preserves the analytic forced response. Because the reformulation takes account of the forcing terms in the equations, if the unregularized equations are in balance, in the sense that ∇.(Du/Dt) vanishes, then the regularized equations maintain this balance. Copyright © 2006 Royal Meteorological Society.