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Theses

Quelques résultats mathématiques et simulations numériques d'écoulements régis par des modèles bifluides.

Abstract : We study here some aspects of the hyperbolicity, in
particular the relationship between hyperbolicity and
well-posedness for Cauchy problem obtained from system of
partial differential equations from the fluid dynamics or
the numerical simulation of such a problem.

We first recall how linearization appears in the study of a
system of partial differential equations and how, the study
of this linearized equations, particularly its
well-posedness, leads to the introduction of hyperbolicity.

We then are interested in particular by the case of a four
equations model describing a two fluid flow with viscous
terms. We prove that the Cauchy problems obtained with the
linearized equations are well-posed even if they are
non-hyperbolic.

Finally, we consider a two fluid flow model with five
equations. This model comprises instead of algebraic
closure equation (e.g. perfect gaz law). The advection
operator is still non hyperbolic but all eigenvalues are
real. The numerical simulation of Ransom faucet flow with
this model does not show instability considering that the
linearized system is non hyperbolic and as the isentropic
four equations model does.
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Theses
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https://tel.archives-ouvertes.fr/tel-00001347
Contributor : David Ramos <>
Submitted on : Friday, May 17, 2002 - 12:01:28 AM
Last modification on : Thursday, July 2, 2020 - 5:17:17 PM
Long-term archiving on: : Tuesday, September 7, 2010 - 4:31:19 PM

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  • HAL Id : tel-00001347, version 1

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David Ramos. Quelques résultats mathématiques et simulations numériques d'écoulements régis par des modèles bifluides.. Mathématiques [math]. École normale supérieure de Cachan - ENS Cachan, 2000. Français. ⟨tel-00001347⟩

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