Etude théorique et numérique de quelques problèmes d'écoulements et de chaleur hyperbolique
type: Dataset
description: The main objective of this thesis is to study nonstationary flows of incompressible Newtonian and non isothermal fluids. The problem is described by the laws of conservation of mass, momentum and energy. We consider the coupling between the Navier-Stokes system and the hyperbolic heat equation (the result of combination between the law of conservation of energy and the Cattaneo's law). This one is a modification of the commonly used Fourier's law, it overcomes "the heat paradox" and gives a more accurate description of heat propagation. The coupled system is an hyperbolic-parabolic problem where the viscosity depends on the temperature but the thermal capacity and the dissipative term depend on the velocity. To obtain an existence result for the coupled system, we first prove the existence and uniqueness of the solution of the hyperbolic problem then we introduce a time discretization and we study the convergence of the approximate solutions to those of the original problem. In the second chapter, we study the existence and uniqueness of the solution of Navier-Stokes system with Tresca or Coulomb boundary conditions in dimension 2 and 3. In the third chapter, we propose a time discretization of the flow problem in the case of Tresca boundary conditions and we establish the convergence of the approximate solutions. The last chapter is devoted to the study of the coupled problem in the case of Tresca free boundary conditions. The existence of a solution is obtained by a theoretical argument (fixed-point theorem) in dimension 2 and also by a method of time discretization leading, on each time subinterval, to a decoupled problem for the velocity and pressure of a hand and the temperature of the other hand.
landing page: https://theses.hal.science/tel-00805369
keyword: cattaneos-law
keyword: coulombs-law
keyword: dicretisation-en-temps
keyword: ecoulement-non-isotherme
keyword: equation-de-la-chaleur-hyperbolique
keyword: equation-de-navier-stokes
keyword: hyperbolic-heat-equation
keyword: infoeu-reposemanticsdoctoralthesis
keyword: loi-de-cattaneo
keyword: loi-de-coulomb
keyword: loi-de-tresca
keyword: mathmath-apmathematics-mathanalysis-of-pdes-mathap
keyword: navier-stokes-equation
keyword: non-isothermal-flow
keyword: theses
keyword: time-discretization
keyword: trescas-law
issued: 2026-05-12T00:57:57.056897
modified: 2026-05-12T00:57:57.056903
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Etude théorique et numérique de quelques problèmes d'écoulements et de chaleur hyperbolique
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00805369
issued: 2026-05-12T00:57:57.151052
modified: 2026-05-12T00:57:57.029384