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 low-salinity band. The model uses the characteristics method with a bi-cubic interpolation to approximate the advective terms. Results show that the model overestimates the band width of the frontal zone. This anomaly is caused certainly by the numerical diffusion introduced by the interpolation procedure used with the characteristics scheme. In order to reduce this non-physical diffusion, we investigate, in this study, the flux-limiter schemes as an alternative of the characteristics method. To illustrate the improvements provided by this type of schemes, comparisons in 2-D model cases are made between the upwind and centred scheme with more recent higher order schemes combined with limiters namely Minmod, Superbee, Van Leer and Monotonized Centred (MC) (also called MUSCL scheme). Numerical simulations show that when the CFL condition is satisfied, the flux limiter schemes reduce the numerical diffusion and suppress the oscillations caused by the non-limited higher order schemes. For the model and realistic cases, the Superbee limiter was found to be a good compromise between shape preservation and computational cost.
flux-limiter english channel numerical diffusion tvd schemes tide coastal flow