École Nationale Supérieure de
Techniques Avancées

Résumé

In ocean modeling, the diffusion is an important physical phenomenon to analyze. Ocean numerical models, such as NEMO or CROCO, usually use the finite volume method with advection schemes to discretize transport terms on the computational grid. The schemes used for practical applications can be complex because they include certain positivity or nonlinear stability properties which are helpful for guaranteeing the robustness of numerical solutions. However, the advection schemes satisfying these properties introduce a numerical diffusion. To have a correct physical analysis of diffusive processes, it is necessary to quantify this numerical diffusion to make sure it doesn't exceed the diffusion applied for physical reasons. In this report I propose a mathematical framework for systematically evaluating the local numerical diffusion of any advection scheme. In particular, I checked that the method I propose gives results consistent with the previous analysis that had been made by hand. I illustrate these results with diagnostics on Total variation Diminishing (TVD) and Weighted Essentially Non-Oscillatory (WENO) schemes which are widely used in ocean modeling.