A cascadic conjugate gradient algorithm for mass conservative, semi-implicit discretization of the shallow water equations on locally refined structured grids

A semi-implicit, mass conservative discretization scheme is applied to the two-dimensional shallow water equations on a hierarchy of structured, locally refined Cartesian grids. Different resolution grids are fully interacting and the discrete Helmholtz equation obtained from the semi-implicit discretization is solved by the cascadic conjugate gradient method. A flux correction is applied at the interface between the coarser and finer discretization grids, so as to ensure discrete mass conservation, along with symmetry and diagonal dominance of the resulting matrix. Two-dimensional idealized simulations are presented, showing the accuracy and the efficiency of the resulting method. Copyright (C) 2002 John Wiley Sons, Ltd.