Section: New Results
SVV-LES of turbulent flows
Participant : Richard Pasquetti.
The SVV-LES approach for the Large-Eddy Simulation of turbulent flows is based on the so-called Spectral Vanishing Viscosity technique  , which was initially developed for conservation laws and extended to LES in the 2000's. Our SVV-LES spectral code, specially developed to compute turbulent wakes using a multi-domain Fourier-Chebyshev approximation, has been used recently to address a challenging benchmark : The Ahmed body wake flow. The Ahmed body is a simplified model of vehicle which is of special interest to outline the influence of the inclination of the slant at the rear of the vehicle. The problem is particularly difficult for low values of the slant angle, for which RANS approaches completely fail. Using the parallelized / vectorized SVV-LES code on the NEC SX8 super-computer of IDRIS, with about 25 millions of grid-points we were able to compute this wake with satisfactory results : The topology of the flows is well recovered and the statistics of the turbulence are close to the experiments  , .
The SVV-LES code was also used to compute the far wake of a sphere in a thermally stratified fluid. The idea was here to compute the spatial development of the wake first and then to use this result to start a temporal development study. Results in close agreement with the experiments of G.R. Spedding, obtained in the late 90's, have been recovered  .
Hybrid RANS-LES models
Participants : Anca Belme [ Tropics ] , Alain Dervieux, Charbel Farhat [ Stanford University ] , Bruno Koobus [ University of Montpellier 2 ] , Hilde Ouvrard [ University of Montpellier 2 ] , Maria-Vittoria Salvetti [ University of Pisa ] , Stephen Wornom [ Lemma ] .
The purpose of our works in hybrid RANS/LES is to develop new approaches for industrial applications of LES-based analyses. In the foreseen applications (aeronautics, hydraulics), the Reynolds number can be as high as 107 , far too large a number for pure LES models. However, certain regions in the flow can be much better predicted with LES than with usual statistical RANS (Reynolds averaged Navier-Stokes) models. These are mainly vortical separated regions as assumed in one of the most popular hybrid model, the hybrid Detached Eddy Simulation model. Here, “hybrid” means that a blending is applied between LES and RANS. The french-italian team has designed a novel type of hybrid model. The Continuous Correction Hybrid Model (CCHM) combines a Variational Multiscale LES component and a low-Reynolds K-epsilon model. In contrast to many existing hybrid models, the CCHM hybrid model involves a hybridisation method able to combine a very large class of LES and RANS submodel since each component is directly weighted independently of a common structure of turbulent viscosity  .
A sophisticated version relying on the computation of two flow fields has been developed by Anca Belme and will be described in an INRIA report (in preparation).
The LES component is important. In her thesis, Hilde Ouvrard compared the Smagorinsky model with new models, namely the WALE model and Vreman's model. These three models yield LES turbulent viscosities which have been encapsulated into the Variational Multiscale (VMS) formulation of Koobus and Farhat, see  and  .
A particular attention has been paid to the extension of the method to lower Reynolds ,  ,  . In that case the boundary layer flow remains laminar, to be captured by Direct Numerical Simulation, which constrains to use a mesh than can be strongly stretched due to small spatial step normal to wall. The finite-volume approximation has been improved for this purpose by Stephen Wornom and Anca Belme (INRIA report in preparation), and by Anca Belme and Hilde Ouvrard, see  .
Reduced order modeling
Participants : Alain Dervieux, Marianna Braza [ Institut de Mécanique des Fluides de Toulouse ] , Rémi Bourguet [ MIT ] .
In relation with unsteady turbulence models, a cooperation with IMFT (Marianna Braza and Rémi Bourguet) has continued on reduced order models. A novel parametrisation of a wing shape relying on the Hadamard formula has been introduced successfully in the Proper Orthogonal Decomposition compressible model developed during the two last years. Is is described in a paper submitted for publication in a journal.
Participants : Ilya Abalakin [ IMM-Moscou ] , Alain Dervieux, Tatyana Kozubskaya [ IMM-Moscow ] , Bruno Koobus [ University of Montpellier 2 ] , Hilde Ouvrard [ University of Montpellier 2 ] .
Previous works in this cooperation addressed the development of a new version of the Non-Linear Disturbance Equation of Aeroacoustics. A method for the simulation of aeroacoustics on the basis of these models has been designed and developed by a cooperation between the Computational Aeroacoustics Laboratory (CAL) of Intitute for Mathematical Modeling at Moscow and INRIA. This year the cooperation was concentrated on the study of a new third order accurate reconstruction scheme, which has been first developed in a linear scalar version by Hilde ouvrard and then extended to nonlinear acoustics by the IMM team. See  .