Publications

2010

• Models and numerical schemes for free surface flows. Beyond the Saint-Venant system
  
  • Sainte-Marie Jacques
  , 2010. This document is an overview of the research activities carried out by the author in geophysical flows modeling and in biomechanics. Because of the scales~-- in space and time~-- of the considered problems in geophysics, there exists a demand for models of reduced complexity such as Shallow Water type models but able to represent complex flows (dam breaks, floodings, avalanches,...). We propose several models approximating the free surface Navier-Stokes equations and extending the classical Saint-Venant system. For each of them, the derivation and a numerical scheme are given. The discrete model is then confronted with with analytical solutions and/or exprimental data associated with complex flows. The numerical schemes we propose rely on a kinetic interpretation of each of the models, the microscopic description allowing to prove necessary stability conditions of the schemes. Several of the proposed models have been implemented in industrial codes. Other contributions dealing with modeling in biomechanics and especially the electro-mechanical activity of the heart are also presented.
• Consolidation effects on morphodynamics modelling: application to the Gironde estuary
  
  • Villaret Catherine
  • Anh Van Lan
  • Huybrechts Nicolas
  • Pham van Bang Damien
  • Boucher Olivier
  La Houille Blanche - Revue internationale de l'eau, EDP Sciences, 2010 (6), pp.15-24.
• Numerical modelling of the catastrophic flooding of Santa Fe City, Argentina
  
  • Tassi Pablo
  • Vionnet C.A.
  • Rodriguez L.B.
  • Ferreira C.G.
  International Journal of River Basin Management, Taylor & Francis, 2010, 4 (4), pp.301 - 314. (10.1080/15715124.2006.9635299)
  DOI : 10.1080/15715124.2006.9635299
• Simulation du clapage de sédiment avec un modèle à deux phases
  
  • Guillou Sylvain
  • Chauchat Julien
  • Pham van Bang Damien
  • Nguyen Duc Hau
  • Nguyen Kim Dan
  , 2010, pp.309-318. La maintenance des chenaux de navigation et des zones portuaires implique la réalisation d’opérations de dragage pour garantir une profondeur d’eau suffisante. Les produits de dragages sont déposés en mer (opération de clapage) si les conditions d’immersion fixées par la convention d’Oslo sont satisfaites. Toutefois, le clapage de sédiments peut induire des nuisances sur l’environnement. Nous utilisons un modèle de transport sédimentaire à deux phases que nous avons développé (BARBRY et al., 2000 ; NGUYEN et al., 2009 ; CHAUCHAT et al., 2008) pour simuler le phénomène de clapage de sédiment fin. La comparaison des simulations aux résultats expérimentaux réalisés en canal par BOUTIN (2000), VILLARET et al. (1997) et VILLARET et al. (1998) montre le bon comportement du modèle pour décrire les différentes phases dynamiques de ce phénomène. (10.5150/jngcgc.2010.037-g)
  DOI : 10.5150/jngcgc.2010.037-g
• Stable splitting scheme for general form of associated plasticity including different scales of space and time
  
  • Kassiotis Christophe
  • Ibrahimbegovic Adnan
  • Matthies Hermann G.
  • Brank Bostjan
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2010, 199 (21-22), pp.1254-1264. An efficient implementation of the operator split procedure for boundary value solution with plastic flow computation is presented for a general form of associated plasticity model. We start with the general form of phenomenological model of plasticity where the yield criterion is not restricted to a simple (quadratic) form, and the elasticity tensor does not have constant entries. We then turn to the multi-scale model of plasticity which employs the fine scale representation of the plastic deformation along with the homogenization procedure for stress computation. We also visit the plasticity model with rate sensitive plastic response where plastic flow computation is carried out at fine scale in time. We proved herein the sufficient and necessary conditions for the proposed operator split procedure to converge, for any such general form of associated plasticity. Moreover, we presented a systematic manner for constructing the main ingredients for the plastic flow computation and the global Newton's iteration, such as the consistent elastoplastic tangent.
• Elements of a Computational Framework for Coupled Simulations
  
  • Matthies Hermann G.
  • Niekamp Rainer
  • Hautefeuille Martin
  • Jürgens Dominik
  • Kassiotis Christophe
  • Srisupattarawanit Tarin
  • Colliat Jean-Baptiste
  • Ibrahimbegovic Adnan
  GAMM-Mitteilungen, WILEY-VCH Verlag GmbH, 2010, 33 (1), pp.73-78. Coupled problems arise because certain aspects of some systems have previously been modelled separately, assuming (implicitly) an uncoupled behaviour. More often then not, computational approaches and mature software have been developed for each of these aspects in isolation. If one has to consider now the coupled problem, it would be advantageous if this previous work could be put to good use. This, in particular, concerns the developed software. In this presentation we will analyse the requirements for this to be achieved, and outline some of the possible solutions. Several tasks have to be accomplished: Non-matching spatial grids and geometric representations have to be joined, fulfilling certain consistency requirements. Similarly non-matching time-stepping schemes have tobe combined. After outlining a possible mathematical formulation for the coupling, the joining of the software will be considered. We view the original software which is modelling some aspect as a software-engineering component, and we describe a component-based approach to achieve a consistently coupled and (if so desired) distributed computational simulation. (10.1002/gamm.201010006)
  DOI : 10.1002/gamm.201010006
• Reduced basis techniques for stochastic problems
  
  • Boyaval Sébastien
  • Le Bris Claude
  • Lelièvre Tony
  • Maday Yvon
  • Nguyen Ngoc Cuong
  • Patera Anthony T.
  Archives of Computational Methods in Engineering, Springer Verlag, 2010, 17 (4), pp.435-454. We report here on the recent application of a now classical general reduction technique, the Reduced-Basis approach initiated in [C. Prud'homme, D. Rovas, K. Veroy, Y. Maday, A. T. Patera, and G. Turinici. Reliable real-time solution of parametrized partial differential equations: Reduced-basis output bounds methods. Journal of Fluids Engineering, 124(1):7080, 2002.], to the specific context of differential equations with random coefficients. After an elementary presentation of the approach, we review two contributions of the authors: [S. Boyaval, C. Le Bris, Y. Maday, N.C. Nguyen, and A.T. Patera. A reduced basis approach for variational problems with stochastic parameters: Application to heat conduction with variable Robin co-efficient. Computer Methods in Applied Mechanics and Engineering, 198(4144):3187-3206, 2009.], which presents the application of the RB approach for the discretization of a simple second order elliptic equation supplied with a random boundary condition, and [S. Boyaval and T. Lelièvre, A variance reduction method for parametrized stochastic differential equations using the reduced basis paradigm with T. Lelièvre, Commun. Math. Sci. 8, special Issue "Mathematical Issue on Complex Fluids" P. Zhang ed., to appear, 2010, ARXIV preprint arXiv:0906.3600], which uses a RB type approach to reduce the variance in the Monte-Carlo simulation of a stochastic differential equation. We conclude the review with some general comments and also discuss possible tracks for further research in the direction. (10.1007/s11831-010-9056-z)
  DOI : 10.1007/s11831-010-9056-z
• Partitioned solution to fluid-structure interaction problems in application to free-surface flows
  
  • Kassiotis Christophe
  • Ibrahimbegovic Adnan
  • Matthies Hermann G.
  European Journal of Mechanics - B/Fluids, Elsevier, 2010, 29, pp.510-521. In this work we discuss a way to compute the impact of free-surface flow on nonlinear structures. The approach chosen rely on a partitioned strategy that allows to solve strongly coupled fluid-structure interaction problem. It is then possible to re-use existing and validated strategy for each sub-problem. The structure is formulated in a Lagrangian way and solved by the finite element method. The free-surface flow approach considers a Volume-Of-Fluid (VOF) strategy formulated in an Arbitrary Lagrangian-Eulerian (ALE) framework, and the finite volume are used to discrete and solve this problem. The software coupling is ensured in an efficient way using the Communication Template Library (CTL). Numerical examples presented herein concern 2D validations case but also 3D problems with a large number of equations to be solved. (10.1016/j.euromechflu.2010.07.003)
  DOI : 10.1016/j.euromechflu.2010.07.003