This thesis is built around a biological and industrial problem: the simulation of the coupling of hydrodynamics and biology in the context of industrial microalgae culture in outdoor raceways. The numerical modeling is adressed with the use of a multilayer vertical discretization of hydrostatic Navier-Stokes equations coupled with a light sensitive Droop model. Numerically, kinetic schemes allow for the development of efficient, positivity preserving, well balanced and entropy satisfying schemes. Simulations are carried out in 2D and 3D. From a practical point of view, this model is capable of accounting for the utility of a paddlewheel and exhibits Lagrangian trajectories underwent by algae. Hence providing hints on the light history of algae in the pond, which is a key information to biologists, since it enables them to adapt their phytoplankton growth models to those particular, non natural conditions. In order to validate the models and strategies, two solutions are explored. The first one consists in providing analytical solutions to free surface Euler equations. Besides, a specific biological model is designed to permit an analytical coupling. The second one is the use of data assimilation. In order to take advantage of the kinetic description of conservation laws already used for the building of efficient schemes, an innovative data assimilation method for hyperbolic balance laws based in a Luenberger observer on the kinetic equation is developed. It provides a nice theoretical framework for scalar conservation laws, for which we study the cases of complete observations, partial observations in space, in time, and noisy observations. As far as systems are concerned, we focus on the Saint-Venant system, which is hyperbolic, nonlinear and has a topographic source term. We build an observer based only on water depths measurements. Numerical simulations are provided in the case of scalar laws and systems, in one and two dimensions, which validate the efficiency of the method.
