A quasi-conservative version of the semi-Lagrangian advection scheme

Abstract

In this paper, the authors describe how to make the scheme quasi-conservative. Although the lack of conservation of the semi-Lagrangian method is not widely regarded as a serious problem, for climate studies, where many tens of thousands of time steps are needed, it could become so. The method proposed here is very cheap, and hence is a viable proposition for addition to existing semi-Lagrangian codes. Making the scheme conservative as well as monotone gives the scheme shock-capturing properties, thus making the method much more useful in application areas outside of meteorology. -from Author