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Etude asymptotique et numérique d'écoulements de fluides non-newtoniens dans des structures tubulaires minces

Abstract : In order to model the blood flow through vessels, the Stokes equation with the nonconstant viscosity is considered in a thin tube structure, i.e., in a connected union of thin rectangles with heights of order ε and bases of order 1 with smoothened boundary. An asymptotic expansion of the solution is constructed. In the case of random perturbations of the constant viscosity, we prove that the leading term for the velocity is deterministic, while for the pressure it is random, but the expectations of the pressure satisfies the deterministic Darcy equation. Estimates for the difference between the exact solution and its asymptotic approximation are proved. Finally, we give some numerical results. We extend the results for a thin tube structure composed by two thin rectangles with lateral elastic boundaries which are connected by a domain with rigid boundaries. After a variational approach of the problem which gives us existence, uniqueness, regularity results and some a priori estimates, we construct an asymptotic solution. We present and solve the problems for all the terms of the asymptotic expansion. For two different cases, we describe the order of steps of the algorithm of solving the problem and we construct the main term of the asymptotic expansion. And finally, we present a variational and an asymptotic analysis for a more general case where the viscosity depends on the infinitesimal strain tensor in a thin channel. By means of the a priori estimates, we justify our asymptotic constructions, by obtaining a small error between the exact and the asymptotic solutions
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Submitted on : Monday, June 4, 2012 - 12:32:34 PM
Last modification on : Wednesday, November 20, 2019 - 3:01:35 AM
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  • HAL Id : tel-00703763, version 1



Roula Fares. Etude asymptotique et numérique d'écoulements de fluides non-newtoniens dans des structures tubulaires minces. Mathématiques générales [math.GM]. Université Jean Monnet - Saint-Etienne, 2011. Français. ⟨NNT : 2011STET4022⟩. ⟨tel-00703763⟩



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