Conservative characteristic-based schemes for shallow flows
|Advisor:||Le Roux, Daniel; Robert, Jean-Loup|
|Abstract:||Shallow water equations arise in many important cases such as in rivers, lakes, estuaries and oceans. Conservation is an important property which is usually desired to ensure the accuracy of the long term simulations and also for the case of complex flows with shockwaves. This thesis begins with semi-Lagrangian schemes, which are well known to remain stable for very high CFL numbers. However, they lose their high stability property when the fully conservative property, which is crucial for a correct simulation of shock waves, is imposed. An inherently fully conservative semi-Lagrangian scheme is developed here which remains stable for high CFL numbers. The proposed approach is then extended to the method of characteristics (MOC) and a conservative extension of MOC is developed. Contrary to the original MOC, which is unable to simulate shockwaves due to the lack of conservation, the proposed scheme easily simulates them. Further, the new scheme presents favorable features in terms of numerical diffusion and dispersion. The 2D case is then considered, and the finite volume method is employed due to its inherent conservation properties. Most available numerical methods face the problem of imbalance between the source and flux terms, particularly when unstructured grids are used. On the other hand, most available numerical schemes (such as the HLL and the ENO schemes) induce a high level of numerical diffusion in simulating recirculating flows. Three different approaches using unstructured grids are successfully developed here. The new schemes can simulate complex flow conditions including recirculating, trans-critical and discontinuous flows over variable topographies. Finally, the performance of the upwind finite volume schemes, for Rossby waves, is studied using a Fourier analysis approach. Contrary to the usual good results obtained for those schemes in the case of convection dominated flows, it is observed here that they lead to an excessive damping of the Rossby modes.|
|Document Type:||Thèse de doctorat|
|Open Access Date:||12 April 2018|
|Collection:||Thèses et mémoires|
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