Comparative study of different advective schemes: Application to the MECCA model

A 3-D version of the MECCA model (Model of Estuarine and Coastal Circulation Assessment) is used to simulate the dynamics of the Eastern part of the English Channel. This area is characterized by a strong tidal turbulent regime and a frontal zone identified near the French coast by a low-salinity band. The model uses the upwind scheme to approximate the advective terms. Results show that the model overestimates the band width of the frontal zone and that this anomaly is definitely caused by the numerical diffusion introduced by the so-called upwind scheme (first-order approximation). In this paper, we study the flux-limiter schemes as an alternative to the upwind method in order to reduce this non-physical diffusion. To illustrate the improvements provided by this type of schemes, a comparison in 2-D schematic cases is made between the upwind and centered scheme with more recent higher-order schemes combined with limiter namely Minmod, Superbee, Van Leer and Monotonized Centered (MC) (called also MUSCL scheme). Respecting the CFL condition, our numerical simulations show that the flux-limiter schemes reduce the numerical diffusion and eliminate the oscillations caused by the non-limited higher-order schemes. For the schematic and realistic cases, the Superbee limiter is a good compromise between shape preservation and computational cost.