Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
The full numerical simulation of turbulent flows in the context of industrial applications remains a very challenging problem. One of the difficulties is the presence of a large number of interacting scales of different orders of magnitude, ranging from the macroscopic scale to the Kolmogorov dissipation scale. In order to better understand and simulate these interactions, new algorithms of incremental type have recently been introduced, stemming from the theory of infinite-dimensional dynamical systems (see, e.g., the algorithms of Foias, Jolly et al. (1988), Foias, Manley and Temam (1988), Laminie et al. (1993, 1994), Marion and Temam (1989, 1990), and Temam (1990)). These algorithms are based on decompositions of the unknown functions into a large- and a small-scale component, one of the underlying ideas being to approximate the corresponding attractor. In the context of finite element methods, the decomposition of a solution into small- and large-scale components appears when we consider hierarchical bases (Yserentant, 1986; Zienkiewicz et al., 1982). In the present article we derive several estimates of the size of the structures for the linear and nonlinear terms which correspond to interactions of different hierarchical components of the velocity field, and also their time variation. The one-step time variation of these terms can be smaller than the expected accuracy of the computation. Using this remark, we implement an adaptive spatial and temporal multilevel algorithm which treats differently the small- and large-scale components of the flow. We derive several a priori estimates in order to study the perturbation introduced into the approximated equations. All the interaction terms between small- and large-scale structures are frozen during several time steps. Finally, we implement the multilevel method in order to simulate a bidimensional flow described by the Burgers equations. We perform a parametric study of the procedure and its efficiency. The gain in CPU time is significant and the trajectories computed by our multi-scale method remain close to the trajectories obtained with the classical Galerkin method.
ISSN: 0168-9274

hal-00730710
https://hal.archives-ouvertes.fr/hal-00730710

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Porous thin films considered for applications like separation, sensing and microelectronic have to sustain mechanical stresses during their integration process or in working conditions. Thanks to recent progress in processing methods, it is now possible to precisely control the porosity and combine ordered mesopores with randomly-distributed macropores to achieve hierarchically porous materials. The mechanical properties of thin films containing different types of porosity (ordered meso, random macro and hierarchical) have been investigated by means of nanoindentation. In particular a method recently proposed by Li and Vlassak (H. Li, J.J. Vlassak, Journal of Materials Research 24 (2009) 1114-1126) is applied to account for the substrate effect. Residual indent impressions were imaged by Atomic Force Microscopy (AFM) to provide some insights in the mechanical behavior of the films. In addition, experimental indentation moduli are compared to theoretical predictions obtained via Finite Element (FE) analysis. The different porous structures have been modeled by FE to obtain the effective elastic properties from which the indentation modulus can be inferred. Finally, the experimental-model differences are discussed. © 2010 Elsevier Inc. All rights reserved.
ISSN: 1387-1811

hal-01683194
https://hal.univ-antilles.fr/hal-01683194
DOI : 10.1016/j.micromeso.2010.09.004

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
Algorithms issued from the NonLinear Galerkin method have been used in many situations and with different discretizations for the resolution of evolutionary nonlinear equations. The main idea of these methods is to use a splitting of the solution in order to model the equation. According to the splitting of the solution, a splitting of the equation is obtained. The modeling principle is to freeze terms which have a small time variation. In this work we use wavelet discretizations of the 2-D Burgers equations and compare the results with the hierarchical finite elements method. The numerical tests indicate that wavelets give better results than finite elements
ISSN: 0885-7474

hal-00383423
https://hal.archives-ouvertes.fr/hal-00383423
DOI : 10.1007/s10915-004-4806-4