Modelling and numerical simulation of submarine sediment shallow flows: transport and avalanches.

*(English)*Zbl 1242.86008Summary: This work presents two different types of models to study submarine sediment movements and their numerical discretization by finite volume methods. First, bedload sediment transport models are introduced. They are characterized by the slow movement of the sediment layer. The movement depends on the type of interaction between the fluid and the sediment layer, which generally is very weak. Secondly, a submarine avalanche model is presented. This model takes into account the coupling between the sediment and the fluid layer. The tsunamis generated by a submarine avalanche can be studied with this model. A family of two-dimensional finite volume methods is introduced. It is based on the fact that the models are invariant under rotations. Finally, two numerical tests are considered. In the first numerical test the spread angle for a sediment bump is studied. In the second one a submarine avalanche is simulated over a bottom with a rectangular bump.