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Modeling, analysis and simulation of two geophysical flows: Sediment transport and variable density flows

Léa Boittin 1, 2
2 ANGE - Numerical Analysis, Geophysics and Ecology
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : The present thesis deals with the modeling and numerical simulation of complex geophysical flows. Two processes are studied: sediment transport, and variable density flows. For both flows, the approach is the same. In each case, a reduced vertically-averaged model is derived from the 3D Navier-Stokes equations by making a specific asymptotic analysis. The models verify stability properties. Attention is paid to preserving these properties at the discrete level, in particular the entropy stability. The behavior of both models is illustrated numerically. Concerning the sediment transport model, the sediment layer is first studied alone. Then, a coupled sediment-water model is presented and simulated. The influence of a viscosity term in the model for the sediment layer is investigated. Due to this viscosity term, the sediment flux is non-local. A transport threshold is added to the model. The water layer is modeled by the Shallow Water equations. Adding some non-locality to the model allows to simulate dune growth and propagation. In the variable density flow model, the density is a function of one or several tracers such as temperature and salinity. The model derivation consists in removing the dependence of the density on the pressure. A layer-averaged formulation of the model is proposed, which is subsequently used to propose a numerical discretization. The numerical simulations emphasize the differences between this model and a model relying on the classical Boussinesq approximation.
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Léa Boittin. Modeling, analysis and simulation of two geophysical flows: Sediment transport and variable density flows. Numerical Analysis [math.NA]. Sorbonne Université, 2019. English. ⟨tel-02126695⟩

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