Delphine Dupuy’s research while affiliated with Jean Monnet University and other places

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Publications (8)


Asymptotic methods for micropolar fluids in a tube structure
  • Article

November 2011

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27 Reads

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39 Citations

Mathematical Models and Methods in Applied Sciences

D. Dupuy

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The steady motion of a micropolar fluid through a wavy tube with the dimensions depending on a small parameter is studied. An asymptotic expansion is proposed and error estimates are proved by using a boundary layer method. We apply the method of partial asymptotic decomposition of domain and we prove that the solution of the partially decomposed problem represents a good approximation for the solution of the considered problem.


Bloch waves homogenization of a Dirichlet problem in a periodically perforated domain
  • Article
  • Full-text available

January 2009

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123 Reads

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7 Citations

Asymptotic Analysis

In this paper we use the spectral method of Bloch waves to study the homogenization process of the Poisson equation in a periodically perforated domain, under homogeneous Dirichlet conditions on both exterior and interior boundaries, as the hole size goes to zero more rapidly than the micro-structure size. Using this method, we find the exact value of the critical hole size, which separates the different behaviors, where the classical strange term may or may not appear in the homogenized equation. This strange term is related to the asymptotic behavior of the first eigenvalue with respect to the hole radius.

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Asymptotic Solution for a Micropolar Flow in a Curvilinear Channel

October 2008

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36 Reads

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35 Citations

ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik

This paper is concerned with an asymptotic approach for a micropolar flow through a thin curvilinear channel. A priori estimates (which we obtain together with the existence and the uniqueness of the solution) are used to establish the error between the exact solution and the asymptotic one and to justify the asymptotic analysis. We obtain the expression of an expansion of order K and we study the general problems for the boundary layer functions. Under some additional assumptions on the data we obtain satisfactory error estimates.


Asymptotic analysis of flow in wavy tubes and simulation of the extrusion process

May 2007

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10 Reads

Mathematical Methods in the Applied Sciences

The paper is devoted to the mathematical modelling of an extrusion process. Usually, an extruder has a very complicated geometry. This generates a lot of difficulties for computations of three-dimensional flows. In the present paper, we develop and justify the asymptotic domain decomposition strategy in order to parallelize the computational process and reduce the memory. The error estimates are proved for the Stokes steady-state equation in the two-dimensional and three-dimensional cases. Then, the asymptotic domain decomposition procedure is applied for numerical testing and computations of the non-Newtonian fluid simulating a real process of the polymer extrusion. Copyright © 2007 John Wiley & Sons, Ltd.


Asymptotic analysis for micropolar fluids

January 2004

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18 Reads

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7 Citations

Comptes Rendus Mécanique

The flow of a micropolar fluid through a wavy constricted channel which depends on a small parameter ε⪡1 is considered. The asymptotic solution is built and justified thanks to a study of the boundary layers terms. The Stokes and Navier–Stokes problems set in a tube structure were previously considered. The method of partial asymptotic decomposition of domain (MAPPD) is also applied and justified for the micropolar flow problem. This method reduces the initial problem to the problem set in the boundary layers domain. To cite this article: D. Dupuy et al., C. R. Mecanique 332 (2004).


Analyse asymptotique des fluides micropolaires

January 2004

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24 Reads

Comptes Rendus Mécanique

The flow of a micropolar fluid through a wavy constricted channel which depends on a small parameter ɛ≪1 is considered. The asymptotic solution is built and justified thanks to a study of the boundary layers terms. The Stokes and Navier-Stokes problems set in a tube structure were previously considered. The method of partial asymptotic decomposition of domain (MAPPD) is also applied and justified for the micropolar flow problem. This method reduces the initial problem to the problem set in the boundary layers domain. To cite this article: D. Dupuy et al., C. R. Mecanique 332 (2004).


Multiscale Modeling for Micropolar Flow in a Structure with One Bundle of Tubes

January 2004

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11 Reads

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4 Citations

International Journal for Multiscale Computational Engineering

The asymptotic analysis of a micropolar flow through a wavy tube structure is studied. We suppose that the domain depends on a small parameter that represents the width and the order of the periodicty of the domain. The Stokes and Navier-Stokes problems in the union of tubes (with a constant section) were earlier studied. The generalization of the Method of Asymptotic Partial Decomposition of Domain in a structure with some periodic tubes is described and justified in order to propose a simplified modeling for the bloodstream.


Flow in wavy tube structure: Asymptotic analysis and numerical simulation

September 2003

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14 Reads

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3 Citations

Comptes Rendus Mécanique

This paper deals with the study of the stationary, incompressible, 2D flow of a fluid in a thin wavy tube. In this work, we consider a domain which is the union of two wavy tubes depending on a small parameter. The asymptotic expansion is constructed. The method of partial asymptotic decomposition is applied. The numerical implementation of this method for the extrusion process is developed. The new physical effects are discussed. To cite this article: A. Ainser et al., C. R. Mecanique 331 (2003).

Citations (6)


... In this section, we will prove that the neighbourhood is, in fact, independent of ρ. This requirement is essential for problems where simultaneous limits with respect to two parameters are studied, such as [28,16]; as well as for quantitative estimates, such as [10]. ...

Reference:

Combined effects of homogenization and singular perturbations: A bloch wave approach
Bloch waves homogenization of a Dirichlet problem in a periodically perforated domain

Asymptotic Analysis

... Here we mention only the references related to this work. The pioneering results on the subject can be found in earlier studies [13,14] where the authors analyze the 2D steady flow through a constricted tube and a curvilinear channel. The generalization of these results to a 3D case has been brought in previous research [15,16], while a steady-state flow in a network of thin straight pipes has been studied in Beneš and Pažanin [17]. ...

Asymptotic methods for micropolar fluids in a tube structure
  • Citing Article
  • November 2011

Mathematical Models and Methods in Applied Sciences

... In particular it significantly advanced the numerical simulation of viscolelastic fluid flow in three-dimensional space, which became more widespread in the past decade (cf. [2]). As for the numerical analysis of finite element methods for the complete set of equations governing viscoelastic flows, the contribution of Baranger and Sandri (see e.g. ...

Flow in wavy tube structure: Asymptotic analysis and numerical simulation
  • Citing Article
  • September 2003

Comptes Rendus Mécanique

... Here we mention only the references related to this work. The pioneering results on the subject can be found in earlier studies [13,14] where the authors analyze the 2D steady flow through a constricted tube and a curvilinear channel. The generalization of these results to a 3D case has been brought in previous research [15,16], while a steady-state flow in a network of thin straight pipes has been studied in Beneš and Pažanin [17]. ...

Asymptotic Solution for a Micropolar Flow in a Curvilinear Channel
  • Citing Article
  • October 2008

ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik