We describe the remapped particle-mesh advection method, a new mass-conserving method for solving the density equation which is suitable for combining with semi-Lagrangian methods for compressible flow applied to numerical weather prediction. In addition to the conservation property, the remapped particle-mesh method is computationally efficient and at least as accurate as current semi-Lagrangian methods based on cubic interpolation. We provide results of tests of the method in the plane, results from incorporating the advection method into a semi-Lagrangian method for the rotating shallow-water equations in planar geometry, and results from extending the method to the surface of a sphere.
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John Wiley & Sons
Quarterly Journal of the Royal Meteorological Society
Symplectic Integration of Atmospheric Dynamics: Long-term Statistical Accuracy for Ensemble Climate Simulations
Computational Dynamics

Cotter, C. J., Frank, J., & Reich, S. (2007). A remapped particle-mesh semi-Lagrangian advection scheme. Quarterly Journal of the Royal Meteorological Society, 133(622), 251–260. doi:10.1002/qj.11