Le laboratoire, créé en 1969, porte le nom de son fondateur Jacques-Louis Lions. il s'agit maintenant d'une unité de recherche conjointe à l’Université Pierre et Marie Curie, à l’université Paris Diderot et au Centre National de la Recherche Scientifique.
Le Laboratoire Jacques-Louis Lions constitue le plus grand laboratoire de France et l'un des principaux au monde pour la formation et la recherche en mathématiques appliquées.
Il accueille l'activités de deux masters deuxième année ce qui représente un centaine d'étudiants. Ses activités recouvrent l’analyse, la modélisation et le calcul scientifique haute performance de phénomènes représentés par des équations aux dérivées partielles.
Fort d’environ 100 enseignants-chercheurs, chercheurs, ingénieurs, personnels administratifs permanents ou émérites, et d’autant de doctorants ou post-doctorants, il collabore avec le monde économique et avec d'autres domaines scientifiques à travers un large spectre d'applications : dynamique des fluides; physique, mécanique et chimie théoriques; contrôle, optimisation et finance; médecine et biologie; traitement du signal et des données.
Date: 20 Dec 2010 - 22:30
Desc: This paper reports investigations on the computation of material fronts in multi-fluid models using a Lagrange-Projection approach. Various forms of the Projection step are considered. Particular attention is paid to minimization of conservation errors.
Date: 14 Apr 2008 - 14:47
Desc: [...]
Date: 30 Aug 2012 - 12:59
Desc: Phase transition problems in compressible media can be modelled by mixed hyperbolicelliptic systems of conservation laws. Within this approach phase boundaries are understood as shock waves that satisfy additional constraints, sometimes called kinetic relations. In recent years several tracking-type algorithms have been suggested for numerical approximation. Typically a core piece of these algorithms is the usage of exact Riemann solvers incorporating the kinetic relation at the location of phase boundaries. However, exact Riemann solvers are computationally expensive or even not available. In this paper we present a class of approximate Riemann solvers for hyperbolic-elliptic models that relies on a generalized relaxation procedure. It preserves in particular the kinetic relation for phase boundaries exactly and gives for isolated phase transitions the correct solutions. In combination with a novel sub-iteration procedure the approximate Riemann solvers are used in the tracking algorithms. The efficiency of the approach is validated on a barotropic system with linear kinetic relation where exact Riemann solvers are available. For a nonlinear kinetic relation and a thermoelastic system we use the new method to gain information on the Riemann problem. Up to our knowledge an exact solution for arbitrary Riemann data is currently not available in these cases.
Date: 9 Jul 2013 - 15:33
Desc: We analyze the sampling of solutions to the Helmholtz equation (e.g. sound fields in the harmonic regime) using a least-squares method based on approximations of the solutions by sums of Fourier-Bessel functions or plane waves. This method compares favorably to others such as Orthogonal Matching Pursuit with a Fourier dictionary. We show that using a significant proportion of samples on the border of the domain of interest improves the stability of the reconstruction, and that using cross-validation to estimate the model order yields good reconstruction results.
Date: 16 Apr 2016 - 10:50
Desc: This paper presents a numerical study in which several partitioned solution procedures for incompressible fluid-structure interaction are compared and validated against the results of an experimental FSI benchmark. The numerical methods discussed cover the three main families of coupling schemes: strongly coupled, semi-implicit and loosely coupled. Very good agreement is observed between the numerical and experimental results. The comparisons confirm that strong coupling can be efficiently avoided, via semi-implicit and loosely coupled schemes, without compromising stability and accuracy.