The Hamiltonian particle-mesh method for the spherical shallow water equations

Abstract

The Hamiltonian particle-mesh (HPM) method is generalized to the spherical shallow-water equations, utilizing constrained particle dynamics on the sphere and Merilees pseudospectral method (complexity O(J2logJ) in the latitudinal gridsize) to approximate the inverse modified Helmholtz reeularization operator. The time step for the explicit, symplectic integrator depends only on a uniform physical smoothing length. Copyright © 2004 Royal Meteorological Society.