A Particle-Mesh Method for the Shallow Water Equations near Geostrophic Balance
نویسندگان
چکیده
In this paper we outline a new particle-mesh method for rapidly rotating shallow-water ows, based on a set of regularized equations of motion. The time-stepping uses an operator splitting of the equations into an Eulerian gravity wave part and a Lagrangian advection part. An essential ingredient is the advection of absolute vorticity by means of translated radial basis functions. We show that this implies exact conservation of enstrophy. The method is tested on two model problems, based on qualitative features of the solutions obtained (i.e. dispersion or smoothness of PV contours) as well as increase in mean divergence level.
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