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" published 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 Bspline 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 semi-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.

Improvement of forecast skill for severe weather by merging radar-based extrapolation and storm-scale NWP corrected forecast

“…2. It uses a two-step Tracking Radar Echoes by Crosscorrelation (TREC) algorithm to estimate motion of a storm, and a mass-conserving, monotonic advection scheme based on the explicit remapped particle-mesh semi-Lagrangian (RPMSL) advection scheme for extrapolating reflectivity factor fields (Reich, 2007). The length step was chosen to be 5 min, corresponding to the temporal resolution of radar observations.…”

A simple and efficient locally mass conserving semi-Lagrangian transport scheme

“…The LMCSL scheme is quite similar to the so‐called ‘Remapped particle‐mesh semi‐Lagrangian advection scheme’ by Cotter et al (2007) and even more so to the modified version of this scheme by Reich (2007). The original scheme by Cotter et al (2007) involves solution of an implicit set of linear equations which is needed to obtain modified weights analogue to those in but for a downstream trajectory SL scheme.…”

“…The original scheme by Cotter et al (2007) involves solution of an implicit set of linear equations which is needed to obtain modified weights analogue to those in but for a downstream trajectory SL scheme. In the modified scheme by Reich (2007) an explicit modification of the downstream weights are introduced. It is even demonstrated that the methodology may be modified to handle the upstream SL approach as used in this paper, however, only for the non‐divergent passive advection equations.…”

“…A number of recent and less recent conservative SL—or ‘SL‐like’—methods (e.g. Laprise and Plante, 1995; Leslie and Purser, 1995; Rančić, 1995; Leonard et al, 1996; Lin and Rood, 1996; Nair and Machenhauer, 2002; Nair et al, 2002; Xiao et al, 2002; Zerroukat et al, 2002; Lin, 2004; Zerroukat et al, 2006; Lauritzen et al, 2006; Zerroukat et al, 2007; Cotter et al, 2007; Reich, 2007) have been suggested and tested in atmospheric models. These schemes not only benefit from the accuracy and numerical stability of the original interpolating grid point SL schemes but also have the conservation property advantages of their Eulerian counterparts.…”

A Charge Preserving Scheme for the Numerical Resolution of the Vlasov-Ampère Equations

“…This becomes problematic when low density or highly turbulent regions are studied. Hence, numerical methods which discretize the Vlasov equation on a grid of the phase space can offer a good alternative to PIC methods (see [7,16,17,34,6,12,28]). …”