The remapped particle-mesh advection scheme
  We describe the remapped particle-mesh 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. 
Colin J. Cotter and Jason Frank and Sebastian Reich