We introduce a Hamiltonian particle-mesh method for two-dimensional advection under incompressible flow fields. The method is applied to a simplified shallow-water model, called the weak-wave model, which combines slow nonlinear vortical motion with fast linear wave propagation. The advantages of the conservative particle-mesh method are demonstrated by means of the adiabatic energy exchange between vortical and wave motion. More generally, the proposed method is applicable to stable and efficient long-time simulations of other simplified geophysical fluid models. © 2003 IMACS. Published by Elsevier B.V. All rights reserved.
Cotter, C. J., & Reich, S. (2004). Geometric integration of a wave-vortex model. In Applied Numerical Mathematics (Vol. 48, pp. 293–305). https://doi.org/10.1016/j.apnum.2003.10.003