Consequences of Symmetries on the Analysis and Construction of Turbulence Models

Since they represent fundamental physical properties in turbulence (conservation laws, wall laws, Kolmogorov energy spectrum, ...), symmetries are used to analyse common turbulence models. A class of symmetry preserving turbulence models is proposed. This class is refined such that the models respect the second law of thermodynamics. Finally, an example of model belonging to the class is numerically tested.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Time integration algorithm based on divergent series resummation, for ordinary and partial differential equations

International audienceBorel's technique of divergent series resummation is transformed into a numerical code and used as a time integration scheme. It is applied to the resolution of regular and singular problems arising in fluid mechanics. Its efficiency is compared to those of classical discretization schemes

Comparison between Borel-Padé summation and factorial series, as time integration methods

International audienceWe compare the performance of two algorithms of computing the Borel sum of a time power series. The first one uses Padé approximants in Borel space, followed by a Laplace transform. The second is based on factorial series. These algorithms are incorporated in a numerical scheme for time integration of differential equations

POD-based reduced order model for flows induced by rigid solids in forced rotation

This paper deals with the construction of reduced order models (ROMs) for the simulation of the interaction between a fluid and a rigid solid with imposed rotation velocity. The approach is a follows. First, we derive a monolithic description of the fluid/structure interaction by extending the Navier-Stokes equations from the fluid domain to the solid (rotor) domain similarly to the fictitious-domain approach. Second, we build a ROM by a proper orthogonal decomposition (POD) of the resulting multi-phases flow. This method consists in (i) constructing an optimal albeit empirical spatial basis for a very small sub-space of the solution space, and (ii) projecting the governing equations on this reduced basis. Third, we cope with the reconstruction of the high-dimensional velocity field needed to evaluate the imposed velocity constraint by a POD of the solid membership function. Fourth, we use state of the art method to interpolate between available POD bases to build the proposed POD-ROM for a range of parameters values. The proposed method is applied to an academic configuration and proves efficient in the reconstruction of the velocity in both the fluid and solid domains while substantially reducing the computational cost

Some robust integrators for large time dynamics

This article reviews some integrators particularly suitable for the numerical resolution of differential equations on a large time interval. Symplectic integrators are presented. Their stability on exponentially large time is shown through numerical examples. Next, Dirac integrators for constrained systems are exposed. An application on chaotic dynamics is presented. Lastly, for systems having no exploitable geometric structure, the Borel-Laplace integrator is presented. Numerical experiments on Hamiltonian and non-Hamiltonian systems are carried out, as well as on a partial differential equation. Keywords: Symplectic integrators, Dirac integrators, long-time stability, Borel summation, divergent series.Comment: 33 pages, 18 figure

Théorie des groupes de symétrie pour la modélisation en mécanique des fluides

International audienc

Modèle réduit par couplage POD-fonction caractéristique en interaction fluide structure

Une amélioration de la méthode de réduction de modèle en interaction fluide structure par POD, présentée au CFM 2007, utilisant la décomposition sur base POD de la fonction caractéristique et permettant ainsi d'obtenir un système algébrique sera presentée, ainsi qu'une méthode POD-décomposition de domaines