Development of a baroclinic discontinuous Galerkin finite element model for estuarine and coastal flows

Numerical marine models have become indispensable in ocean sciences. Despite many developments over the past decades, modelling of the coastal ocean is still an area of active research. In recent years, unstructured mesh models have gained attention, as they can better represent the complex topography of coastal domains compared to standard models. The inherent flexibility of unstructured meshes is particularly useful in multi-scale applications, where a wide spectrum of spatial scales must be captured. This thesis deals with the development of discontinuous Galerkin finite element shallow water models, with focus on shelf sea-estuary-river network systems. Two key issues in coastal marine modelling are addressed: wetting-drying and three-dimensional modelling of buoyancy driven flows. Representing the periodic exposure and submerging of tidal flats is a complicated task for Eulerian models. Most wetting-drying techniques are model specific, and require explicit time integration, which can significantly increase the computational cost. A generic wetting-drying method for depth-averaged shallow water equations is presented, which is compatible with implicit time marching, thus improving the computational efficiency. The latter part of the thesis is devoted for the development of a three-dimensional baroclinic model. A discontinuous Galerkin finite element discretisation is presented, combined with an explicit time integration method. Slope limiters are used to ensure stability in strongly baroclinic flows. To account for vertical mixing, the model is coupled to an established turbulence closure model library. The model is validated with standard benchmarks and a Rhine river plume simulation in an idealised geometry.(FSA 3) -- UCL, 201