Flux-limiter schemes for oceanic tracers: application to the English Channel tidal model

A 2-D numerical model has been 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 l ow-salinity band. The model uses the characteristics method with a bi-cubic interpolation to approximate the advective terms. Results show that the mo del overestimates the band width of the frontal zone. This anomaly is cause d certainly by the numerical diffusion introduced by the interpolation proc edure used with the characteristics scheme. In order to reduce this non-phy sical diffusion, we investigate, in this study, the flux-limiter schemes as an alternative of the characteristics method. To illustrate the improvemen ts provided by this type of schemes, comparisons in 2-D model cases are mad e between the upwind and centred scheme with more recent higher order schem es combined with limiters namely Minmod, Superbee, Van Leer and Monotonized Centred (MC) (also called MUSCL scheme). Numerical simulations show that w hen the CFL condition is satisfied, the flux limiter schemes reduce the num erical diffusion and suppress the oscillations caused by the non-limited hi gher order schemes. For the model and realistic cases, the Superbee limiter was found to be a good compromise between shape preservation and computati onal cost. (C) 1999 Elsevier Science S.A. All rights reserved.