A simple mass conserving semi-Lagrangian scheme for transport problems

A mass conserving semi-Lagrangian (SL) scheme is achieved with a combination of a simple explicit smoothness-based mass correction and a standard non-conservative interpolating SL scheme. The resulting mass correction can be incorporated into any existing SL scheme with negligible extra cost. A more selective and less damping monotonicity filter by comparison to traditional filters is also presented. Results from various tests from the literature show that, in addition to mass conservation, the proposed scheme has negligible impact on the overall accuracy of the standard non-conservative SL scheme.