A semi-Lagrangian approach to the shallow water equations

J. R. Bates

National Aeronautics and Space Administration, Goddard Laboratory for Atmospheres, Greenbelt, MD, 20771

Stephen F. McCormick and John Ruge

Computational Math Group, Campus Box 170, University of Colorado at Denver, PO Box 173363, Denver, CO, 80217-3364

David S. Sholl

Program in Applied Mathematics, Campus Box 526, University of Colorado at Boulder Boulder, CO, 80309-0526

Irad Yavneh

Oceanography and GTP, National Center for Atmospheric Research, Boulder, CO, 80307-3000


Abstract

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.