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Simulation of Shallow Flows over Variable Topography using Unstructured Grid
Étudiant au doctorat au Département de Mathématiques et de Statistique
An upwind numerical method for simulating shallow /recirculating/ flows over a variable topography on unstructured grids is presented. It is able to simulate sub, super and trans-critical flows with low numerical diffusion. Most available numerical methods face problems due to the incompatibility between the discretization of /source/ and /flux/ terms , in variable topographies. Treatments for this problem generally work well for structured grids, but they are not straightforward on unstructured grids, and an upwind discretization of the source term is too expensive for general applications. On the other hand most available shock capturing schemes (Such as HLL flux and ENO schemes) have a high numerical diffusion in simulation of recirculating flows. It is well known that non-conservative schemes work better in the mild flows (such as recirculating flows), and fully conservative schemes are suitable for discontinuous flows. We propose an efficient /mass/ conservative approach, which takes advantage of the accuracy of nonconservative approaches for recirculating flows and tidal flows, and gives reasonable results for discontinuous flows on variable topographies without upwinding the source terms.
Date: 2004-01-23 à 05:30
Endroit: Local 2546, pavillon Adrien-Pouliot