Modélisation et simulation numérique des écoulements diphasiques

Abstract : The main topic of this work is the simulation of two-phase flows. Several hyperbolic models are considered here. In the first part, recent Finite Volume schemes are compared for the approximation of the Homogeneous Equilibrium Model, in particular when the simulation involves low densities. The existence and uniqueness of the weak entropy solution of a conservation law is proved afterwards. This scalar equation is a simplified model of a oil-liquid mixture flowing in a porous media. Two Finite Volume schemes are proposed and tested in agreement with the resonant behavior of this model. The third part deals with the numerical approximation of stiff source terms occuring in the shallow-water equations when the topography gradient is included. An original approximate Godunov scheme, which enables to simulate steady states and dry zones, is presented and compared with the methods used in the industrial context. The last part corresponds to the analysis of a class of non-conservative hyperbolic models of two-phase flows, based on the two velocity and two pressure two-fluid approach. Some closure laws for the interfacial velocity and for the interfacial pressure are proposed, allowing to define discontinuous solutions. The convective part is approximated by Finite Volume schemes and the relaxation terms are taken into account with the help of a splitting method. Several numerical experiments are investigated: shock tubes, wall boundary conditions, water faucet and sedimentation.
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https://tel.archives-ouvertes.fr/tel-00003139
Contributor : Nicolas Seguin <>
Submitted on : Friday, July 18, 2003 - 11:47:35 AM
Last modification on : Thursday, November 15, 2018 - 11:08:06 AM
Long-term archiving on : Tuesday, September 11, 2012 - 9:10:30 PM

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Nicolas Seguin. Modélisation et simulation numérique des écoulements diphasiques. Mathematics [math]. Université de Provence - Aix-Marseille I, 2002. English. ⟨tel-00003139⟩

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