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A two-dimensional finite volume morphodynamic model on unstructured triangular grids

Benkhaldoun, F. Sahmim; S. Seaid, M.

Authors

F. Sahmim Benkhaldoun

M. S. Seaid



Abstract

We discuss the application of a finite volume method to morphodynamic models on unstructured triangular meshes. The model is based on coupling the shallow water equations for the hydrodynamics with a sediment transport equation for the morphodynamics. The finite volume method is formulated for the quasi-steady approach and the coupled approach. In the first approach, the steady hydrodynamic state is calculated first and the corresponding water velocity is used in the sediment transport equation to be solved subsequently. The second approach solves the coupled hydrodynamics and sediment transport system within the same time step. The gradient fluxes are discretized using a modified Roe's scheme incorporating the sign of the Jacobian matrix in the morphodynamic system. A well-balanced discretization is used for the treatment of source terms. We also describe an adaptive procedure in the finite volume method by monitoring the bed-load in the computational domain during its transport process. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bed gradients that may form in the approximate solution. Numerical results are shown for a test problem in the evolution of an initially hump-shaped bed in a squared channel. For the considered morphodynamical regimes, the obtained results point out that the coupled approach performs better than the quasi-steady approach only when the bed-load rapidly interacts with the hydrodynamics.

Citation

Benkhaldoun, F. S., & S. Seaid, M. (2010). A two-dimensional finite volume morphodynamic model on unstructured triangular grids. International Journal for Numerical Methods in Fluids, 63(11), 1296-1327. https://doi.org/10.1002/fld.2129

Journal Article Type Article
Publication Date Aug 1, 2010
Deposit Date Oct 20, 2009
Journal International Journal for Numerical Methods in Fluids
Print ISSN 0271-2091
Electronic ISSN 1097-0363
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 63
Issue 11
Pages 1296-1327
DOI https://doi.org/10.1002/fld.2129
Keywords Morphodynamic model, Shallow water flows, Finite volume scheme, Well-balanced discretization, Unstructured mesh, Adaptive method.

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