On simplifying 'incremental remap'-type transport schemes
Lauritzen, P. H., Erath, C., & Mittal, R. (2011). On simplifying 'incremental remap'-type transport schemes. Journal Of Computational Physics, 230, 7957-7963. doi:10.1016/j.jcp.2011.06.030
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 algori... Show moreThe 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. Show less