A finite volume solver for the simulation of transport processes

The simulation of the tracer transport process is an increasingly important tool to predict the distribution of pollution released in coastal waters. The equation that governs the tracer transport is the advection-diffusion equation. Thanks to the tremendous developments in computer resources and in computing techniques, it has become possible to solve this equation for multi-dimensional problems and in complex domains. This thesis, devoted to this subject of tracer transport, consists of two main parts. The first deals with the existing 2-D transport solver and emphasizes notably on the improvements brought to this solver. Based on the finite volume method, the solver uses input data obtained from a separate flow solver. It was shown that a preprocessing step of the flow parameters according to newly developed techniques is required in order to ensure the positivity of the computed concentrations and the mass conservation of the overall solution. In order to be able to adopt a different time step in the transport solver than used for the flow computation, the usage of time integrated flow data has proven to be an efficient technique. The improvements brought to the 2-D solver were tested through the numerical application to a real-life case. The Dutch coastline case was chosen because of its importance from the environmental point of view. In the second part of the thesis, a 3-D version of the transport solver is developed. In the vertical direction, the physical domain is subdivided in a fixed number of layers, while in the horizontal direction, the domain is represented using an unstructured grid. The numerical estimation of the different fluxes of the adopted finite volume method are described in detail. The 3-D version requires also the preprocessing of the input flow data prior to their use in order to avoid the occurrence of unrealistic sources and sinks. The testing of the newly developed 3-D solver is achieved using two numerical applications. The first is a hypothetical test case consisting of simulating a tracer release in a river stretch and the second is a real-life application concerning the Dutch coastline. Different vertical profiles for the vertical diffusion coefficient were tested since this term plays an important role in the vertical mixing