Towards the automatic design of compartment models for marine transport processes

In the context of solving marine problems, compartment models act as a complementary tool to the usual discretization methods such as finite difference or finite element methods: although they provide less accurate results, they allows for easier interpretation and faster simulations, hence providing the possibility for long-term model runs. However, the compartment model approach suffers from the fact that there is nowadays no automatic procedure to delineate the compartments and express the fluxes between them. As an attempt to fill the gap, a method towards automatic delineation of the compartments is proposed in this work. It is based on a community detection method from network theory, the stability method. The whole procedure is applied on a simple problem, showing satisfying results. Obviously, the problem considered is too simple to draw conclusions on the method proposed, but the encouraging results reached in this work show that further work is worthwhile. Alongside the presentations of the method and of the stability criterion for community detection, a whole chapter is dedicated to the theory of stochastic differential equations, leading to a Lagrangian numerical method for solving a two-dimensional advection- diffusion problem. Besides, a generic compartment model is build from the reactive transport equation, and its fundamental properties are shown. The only theoretical background needed to understand this work is to be familiar with the reactive transport equation. All the other theoretical tools are introduced and proved before they are used, making this work a standalone document.