An explicit and conservative remapping strategy for semi-Lagrangian advection

Abstract

A conservative semi-Lagrangian advection scheme has recently been proposed by Cotter et al. in their article The remapped particle-mesh semi-Lagrangian advection scheme" publish in The Quarterly Journal of the Royal Meteorological Society (2007, volume 133, pages 251-260). It is based on a remapped particle-mesh implementation using bicubic B-spline as basis functions. It has been shown that the method is of comparable accuracy as standard bicubic semi-Lagrangian advection schemes. A potential drawback of the, so called, remapped particle-mesh send-Lagrangian (RPM SL) advection scheme is that it requires the solution of tridiagonal linear systems of equations. In this note, we demonstrate that the solution of linear equations can be avoided without sacrificing the conservation and accuracy properties of the original RPM SL method. Copyright © 2007 Royal Meteorological Society.