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 Springer Verlag
Résumé : International audience
This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier-Stokes equations. As is well known, the use of staggered grids (e.g., MAC grids [M. Perić, R. Kessler and G. Scheuerer, Comput. & Fluids 16 (1988), no. 4, 389-403; Zbl 0672.76018]) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization [S. Faure, J Laminie and R. Temam, "Colocated finite volume schemes for fluid flows'', submitted; M. Perić, R. Kessler and G. Scheuerer, op. cit.], for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equation; the two- and three-dimensional Navier-Stokes equations, which introduce new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere [see S. Faure, J Laminie and R. Temam, op. cit.; "Finite volume discretization and multilevel methods for the Navier-Stokes equations'', in preparation].
ISSN: 0885-7474

hal-00730193
https://hal.archives-ouvertes.fr/hal-00730193

Éditeur(s) : HAL CCSD
Résumé : In an earlier paper, we developed an efficient incremental unknowns (IU) preconditioner for solving the two-dimensional (2D) Helmholtz problem in both high and low frequency (wavenumber) regimes. The multilevel preconditioning scheme involves separation of each grid into a coarser grid of the following level and a complementary grid on which the IUs are defined by interpolation. This approach is efficient as long as the mesh size of the coarsest grid is sufficiently small compared to the wavelength. In order to overcome this restriction, the authors introduced recently a modified IU method combining the conventional interpolation with the Helmholtz equation based interpolation (EBI). The EBI coefficients are derived numerically using a sufficiently large set of analytic solutions of the Helmholtz equation on a special hierarchy of stencils. The modified IUs using Helmholtz EBI are shown to provide improved preconditioning on the coarse scales where the conventional interpolation can not be employed. This study deals with the extension of this idea for solving the three-dimensional (3D) Helmholtz equation.
https://hal.univ-antilles.fr/hal-00763930

Droits : info:eu-repo/semantics/OpenAccess
hal-00763930
https://hal.univ-antilles.fr/hal-00763930
https://hal.univ-antilles.fr/hal-00763930/document
https://hal.univ-antilles.fr/hal-00763930/file/eci3D_3d.pdf

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
In a previous work, one of the authors has studied a numerical treatment (by fully implicit discretizations) of a two-dimensional Navier-Stokes-like problem and has proved existence and convergence results for the resulting discretized systems with homogeneous Dirichlet boundary conditions. In this work, we propose some new preconditioned multilevel versions of inexact-Newton algorithms to solve these equations. We also develop another multilevel preconditioner for a nonlinear GMRES algorithm. All of the preconditioners are based on incremental unknowns formulations.
ISSN: 0096-3003

hal-00770269
https://hal.univ-antilles.fr/hal-00770269
DOI : 10.1016/S0096-3003(96)00304-9

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Background: While it is known that cancer risk is related to area-level socioeconomic status, the extent to which these inequalities are explained by contextual effects is poorly documented especially for head and neck cancer. Methods: A case-control study, ICARE, included 2415 head and neck cancer cases and 3555 controls recruited between 2001 and 2007 from 10 French regions retrieved from a general cancer registry. Individual socioeconomic status was assessed using marital status, highest educational level and occupational social class. Area-level socioeconomic status was assessed using the French version of the European Deprivation Index (EDI). The relationship between both individual and area-based socioeconomic level and the risk of head and neck cancer was assessed by multilevel analyses. Results: A higher risk for head and neck cancer was found in divorced compared with married individuals (OR = 2.14, 95% CI = 1.78-2.57), for individuals with a basic school-leaving qualification compared with those with higher education (OR = 4.55 95% CI = 3.72-5.57), for manual workers compared with managers (OR = 4.91, 95% CI = 3.92-6.15) and for individuals living in the most deprived areas compared with those living in the most affluent ones (OR = 1.98, 95% CI = 1.64-2.41). The influence of area-level socioeconomic status measured by EDI remained after controlling for individual socioeconomic characteristics (OR = 1.51; 95% confidence interval: 1.23-1.85, p-value = 0.0003). Conclusions: The role of individual socioeconomic status in the risk of head and neck cancer is undeniable, although contextual effects of deprived areas also increase the susceptibility of individuals developing the disease. (C) 2017 Elsevier Ltd. All rights reserved.
ISSN: 1368-8375

hal-01578588
https://hal-univ-rennes1.archives-ouvertes.fr/hal-01578588
DOI : 10.1016/j.oraloncology.2017.06.014
PUBMED : 28688682

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
This article is devoted to the presentation of a multilevel method using finite differences that is well adapted for solving Stokes and Navier-Stokes problems in primitive variables. We use Uzawa type algorithms to solve the saddle point problems arising from spatial discretization by staggered grids and a semi-explicit temporal scheme. By means of a new change of basis operator, the two-dimensional velocity and pressure fields of an M.A.C mesh are gathered in a hierarchical order, into several grids preserving the M.A.C property on each of them. These new hierarchical unknowns, called Staggered Incremental Unknowns (SIU), allow us to develop techniques which reduce the cost of the resolution of either Stokes or generalized Stokes problems. An experimental estimation of the condition number of the inner matrix is given, and justifies the preconditioning effect of the staggered incremental unknowns.
ISSN: 0168-9274

hal-00770268
https://hal.univ-antilles.fr/hal-00770268
DOI : 10.1016/S0168-9274(99)00044-6

Éditeur(s) : HAL CCSD Taylor & Francis (Routledge)
Résumé : International audience
The influences of task difficulty (index difficulty: 2-4), input device of different length, range of motion and mode of resistance (joystick or rotorcraft stick), and directions of movement (leftward rightward) on motor patterns in a realistic control situation were examined with a multilevel analysis (joint kinematics and muscular variables, and global task performance). Eight subjects controlled the displacements of a virtual object during a slalom task characterized by a realistic inertial model. Pilots adapted the endpoint kinematic organization to increasing accuracy constraints to preserve task success whatever the device and the direction. However, the rotorcraft stick manipulation remains highly complex in comparison to the joystick due to poorer proprioceptive information, higher inertial constraints, and an asymmetrical muscle control.
ISSN: 0022-2895

hal-01442056
https://hal.archives-ouvertes.fr/hal-01442056
https://hal.archives-ouvertes.fr/hal-01442056/document
https://hal.archives-ouvertes.fr/hal-01442056/file/Fuente%20-%20J%20Motor%20Behav%20-%202013.pdf
DOI : 10.1080/00222895.2013.837424

Éditeur(s) : HAL CCSD Wiley
Résumé : International audience
We study if the multilevel algorithm introduced by Debussche, T. Dubois and R. Temam [Theoret. Comput. Fluid Dynam. 7 (1995), no. 4, 279-315; Zbl 838.76060] and Dubois, F. Jauberteau and Temam [J. Sci. Comput. 8 (1993), no. 2, 167-194; MR1242960 (94f:65098)] for the 2D Navier-Stokes equations with periodic boundary conditions and spectral discretization can be generalized to more general boundary conditions and to finite elements. We first show that a direct generalization, as in [C. Calgaro, J. Laminie and R. Temam, Appl. Numer. Math. 23 (1997), no. 4, 403-442; MR1453424 (98d:76124)], for the Burgers equation, would not be very efficient. We then propose a new approach where the domain of integration is decomposed into subdomains. This enables us to define localized small-scale components and we show that, in this context, there is a good separation of scales. We conclude that all the ingredients necessary for the implementation of the multilevel algorithm are present.
ISSN: 0271-2091

hal-00730709
https://hal.archives-ouvertes.fr/hal-00730709

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
ISSN: 0168-9274

hal-00530819
https://hal.archives-ouvertes.fr/hal-00530819
DOI : 10.1016/j.apnum.2009.12.006

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
To evaluate the performance of downhole and surface geophysical monitoring methods, a series of shallow gas injection-monitoring experiments has been performed in a coastal saline aquifer at Maguelone, France. The recorded data include pressure measurements with a Westbay multilevel completion and CO2 saturation at an observation well derived from electrical resistivity with a modified Waxman-Smits (MWS) model. In this work, the aim is to develop a simulation model capturing the gas transport behavior and consistent with field data. For this purpose, the simulation of the CO2 injection experiment is carried out with two conceptual models, a homogeneous model and a heterogeneous model treated with multiple realization Monte Carlo simulations. Numerical simulator TOUGH2 with the equation of state module EOS7C is used for the simulations. Comparison of the model results with field data suggests that the pressure responses are captured with relatively good accuracy. Similarly, the model also provides an overall reasonable agreement and correct order of magnitude for predicted gas saturation values. However, as the heterogeneity pattern in the field data remains largely unknown, the model predictions can only be used to capture the mean behavior as well as to provide insights into how heterogeneity can influence the system behavior, by means of sensitivity analyses of the influence of heterogeneities on individual realizations.
ISSN: 1750-5836

hal-01467240
https://hal.archives-ouvertes.fr/hal-01467240
DOI : 10.1016/j.ijggc.2016.09.006