A systematic method to enforce conservativity on semi-Lagrangian schemes

TL;DR

This paper introduces a systematic method to modify semi-Lagrangian schemes to ensure they are conservative, maintaining stability and accuracy while improving their physical fidelity in advection modeling.

Contribution

A novel systematic approach to enforce conservativity on semi-Lagrangian schemes without sacrificing stability or accuracy.

Findings

The method preserves the linear stability range.

It maintains the original order of accuracy.

It is effective with large CFL numbers and third-order schemes.

Abstract

Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a semi-Lagrangian advection scheme. This method is shown to generate conservative schemes with the same linear stability range and the same order of accuracy as the initial advection scheme from which they are derived. We used a criterion based on the column-balance property of the schemes to assess their conservativity property. We show that this approach can be used with large CFL numbers and third order schemes.