On simplifying 'incremental remap'-type transport schemes

The flux-form incremental remapping transport scheme introduced by Dukowicz and Baumgardner converts the transport problem into a remapping problem. This involves identifying overlap areas between quadrilateral flux-areas and regular square grid cells which is non-trivial and leads to some algorithm complexity. In the simpler swept area approach (originally introduced by Hirt et al.) the search for overlap areas is eliminated even if the flux-areas overlap several regular grid cells. The resulting simplified scheme leads to a much simpler and robust algorithm. We show that for sufficiently small Courant numbers (approximately CFL ≤ 1/2) the simplified (or swept area) scheme can be more accurate than the original incremental remapping scheme. This is demonstrated through a Von Neumann stability analysis, an error analysis and in idealized transport test cases on the sphere using the 'incremental remapping'-based scheme called FF-CSLAM (Flux-Form version of the Conservative Semi-Lagrangian Multi-tracer scheme) on the cubed-sphere.