Generalized energy and potential enstrophy conserving finite difference schemes for the shallow water equations

Abstract

The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method for deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second order schemes and pseudo-fourth order schemes. The simplest B-grid pseudo-fourth-order schemes are presented. -Author