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
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doi.org/10.1002/asl.70
Atmospheric Science Letters
Computational Dynamics

Frank, J.E, & Reich, S. (2004). The Hamiltonian Particle-Mesh Method for the Spherical Shallow Water Equations. Atmospheric Science Letters, 5(5), 89–95. doi:10.1002/asl.70