A Flux-Form Semi-Lagrangian advection scheme for tracer transport on arbitrary meshes

A variant of the flux-form semi-Lagrangian (FFSL) advection scheme is presented suitable for use on arbitrary unstructured meshes. The time-step used with the scheme is not constrained by the Courant number, resulting in model run-times that may be many times faster than Courant-constrained schemes. The scheme also has the property of mass conservation. This makes the scheme a potential candidate for offline simulation of tracers in unstructured sediment transport, biogeochemical or atmospheric chemistry models. We describe the numerics of the scheme and apply it to a number of idealised and real applications to demonstrate its utility. In these test cases we compare results from the offline FFSL scheme with those generated by the original hydrodynamic model which uses high order conservative tracer transport. We assess the FFSL scheme for accuracy, conservation and computational efficiency. Additionally, traditional semi-Lagrangian advection schemes are included in assessments for comparison. Results indicate that the FFSL scheme produces closer agreement with tracer distributions generated by the hydrodynamic model than the semi-Lagrange scheme, and mass conservation was vastly superior. The FFSL scheme was also an order of magnitude faster than the hydrodynamic model in certain cases. The FFSL scheme presented here therefore offers a viable mass-conserving, computationally-efficient option for use in offline transport models on arbitrary unstructured meshes.