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Simulation numérique d'écoulements compressibles complexes par des méthodes de type Lagrange-projection : applications aux équations de Saint-Venant

Abstract : In this thesis we study a family of numerical schemes solving the shallow water equations system. These schemes use a Lagrange-projection like splitting operator technique in order to separate the gravity waves and the transport waves. An implicit-explicit treatment of the acoustic system (linked to the gravity waves) allows the schemes to stay stable with large time step. The correction of the pressure fluxes enables the obtain of a precise approximation solution whatever the regime flow is with respect to the Froude number. A particular attention has been paid over the source term treatment which permits to take the topography into account. We especially obtain the so-called well-balanced property giving the exact conservation of some steady states, namely the "lake at rest" state. 1D and 2D versions of this methods have been studied and implemented in the finite volumes framework. Finally, a high order discontinuous Galerkin extension has been proposed in 1D with classical limiters along with a combined MOOD loop a posteriori limiting strategy.
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Maxime Stauffert. Simulation numérique d'écoulements compressibles complexes par des méthodes de type Lagrange-projection : applications aux équations de Saint-Venant. Analyse numérique [math.NA]. Université Paris-Saclay, 2018. Français. ⟨NNT : 2018SACLV045⟩. ⟨tel-02055820⟩

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