Developments and applications of numerical finite volumes methods for the description of oceanic flows

This report deals with numerical simulation of oceanic flows. In that context, we want to observe the behaviour of numerical methods that do not involve any restrictive hypothesis on modelization spatial scales. In order to do this, we have adapted and developed some resolution's techniques of Navier-Stokes incompressible equations based on finite volume methods. The first part of the study presents the numerical principle and modifications realized on this kind of technique and applied on structured meshes. Model's response concerns the three-dimensional behaviour of homogeneous or inhomogeneous uniform flow, in constant rotation, over isolated topography in a meso-scale basin. Results of a several sets of numerical simulations correctly fit to physical or other numerical descriptions available in literature. The second part deals with more significant extension of a finite volume method applied on unstructured meshes. Development of new two-dimensional elements leads to some horizontal homogeneous oceanic circulation's mechanisms occurring in large scales basins. Moreover, for transport's terms, the introduction of a type MUSCL scheme improves the quality of non-linear phenomena' results. This scheme is also successfully validated with an original two-dimensional analytic solution. Finally, current problems and conceivable alternatives relating to prospective three-dimensional applications of these discretization methods for numerical studies of oceanic flows are discussed. (author)