-DIRECTEUR du laboratoire M2P2
- Membre Senior de l'Institut Universitaire de France
- Rédacteur en chef du Journal "Computers and fluids"
- Membre du Comité de rédaction: Journal of Computational Physics, Journal of Turbulence, Journal of Scientific Computing
- Président du Conseil Scientifique et Technique de l'AFM
- Vice-Président du Conseil Scientifique de ERCOFTAC
Activités
Simulation et modélisation des écoulements turbulents
Aérodynamique, aéroacoustique, aérothermique
Méthodes numériques pour les équations de Navier-Stokes et de Boltzmann
Méthodes avancées: quantification des incertitudes et assimilation de données
Publications scientifiques au M2P2
2018
Jérôme Jacob, Pierre Sagaut. Wind comfort assessment by means of large eddy simulation with lattice Boltzmann method in full scale city area. Building and Environment, Elsevier, 2018, 139, pp.110 - 124. 〈10.1016/j.buildenv.2018.05.015〉. 〈hal-01819248〉 Plus de détails...
Jérôme Jacob, Pierre Sagaut. Wind comfort assessment by means of large eddy simulation with lattice Boltzmann method in full scale city area. Building and Environment, Elsevier, 2018, 139, pp.110 - 124. 〈10.1016/j.buildenv.2018.05.015〉. 〈hal-01819248〉
Myriam Slama, Cédric Leblond, Pierre Sagaut. A Kriging-based elliptic extended anisotropic model for the turbulent boundary layer wall pressure spectrum. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 840, pp.25 - 55. 〈10.1017/jfm.2017.810〉. 〈hal-01706751〉 Plus de détails...
The present study addresses the computation of the wall pressure spectrum for a turbulent boundary layer flow without pressure gradient, at high Reynolds numbers, using a new model, the Kriging-based elliptic extended anisotropic model (KEEAM). A space–time solution to the Poisson equation for the wall pressure fluctuations is used. Both the turbulence–turbulence and turbulence–mean shear interactions are taken into account. It involves the mean velocity field and space–time velocity correlations which are modelled using Reynolds stresses and velocity correlation coefficients. We propose a new model, referred to as the extended anisotropic model, to evaluate the latter in all regions of the boundary layer. This model is an extension of the simplified anisotropic model of Gavin (PhD thesis, 2002, The Pennsylvania State University, University Park, PA) which was developed for the outer part of the boundary layer. It relies on a new expression for the spatial velocity correlation function and new parameters calibrated using the direct numerical simulation results of Sillero et al. (Phys. Fluids, vol. 26, 2014, 105109). Spatial correlation coefficients are related to space–time coefficients with the elliptic model of He & Zhang (Phys. Rev. E, vol. 73, 2006, 055303). The turbulent quantities necessary for the pressure computation are obtained by Reynolds-averaged Navier–Stokes solutions with a Reynolds stress turbulence model. Then, the pressure correlations are evaluated with a self-adaptive sampling strategy based on Kriging in order to reduce the computation time. The frequency and wavenumber–frequency wall pressure spectra obtained with the KEEAM agree well with empirical models developed for turbulent boundary layer flows without pressure gradient.
Myriam Slama, Cédric Leblond, Pierre Sagaut. A Kriging-based elliptic extended anisotropic model for the turbulent boundary layer wall pressure spectrum. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 840, pp.25 - 55. 〈10.1017/jfm.2017.810〉. 〈hal-01706751〉
Marcello Meldi, Pierre Sagaut. Investigation of anomalous very fast decay regimes in homogeneous isotropic turbulence. Journal of Turbulence, Taylor & Francis, 2018, 19 (5), pp.390 - 413. 〈10.1080/14685248.2018.1450506〉. 〈hal-01816010〉 Plus de détails...
The emergence of anomalous fast decay regimes in homogeneous isotropic turbulence (HIT) decay is investigated via both theoretical analysis and eddy-damped quasi-normal Markovian simulations. The work provides new insight about a fundamental issue playing a role in HIT decay, namely the influence of non-standard shapes of the energy spectrum, in particular in the large energetic scale region. A detailed analysis of the kinetic energy spectrum E(k) and the non-linear energy transfer T(k) shows that anomalous decay regimes are associated with the relaxation of initial energy spectra which exhibit a bump at energetic scales. This feature induces an increase in the energy cascade rate, toward solutions with a smooth shape at the spectrum peak. Present results match observations reported in wind-tunnel experiments dealing with turbulence decay in the wake of grids and bluff bodies, including scaling laws for the dissipation parameter C-E. They also indicate that the ratio between the initial eddy turnover time and the advection time determines of how fast anomalous regimes relax toward classical turbulence free-decay. This parameter should be used for consistent data comparison and it opens perspectives for the control of multiscale effects in industrial applications.
Marcello Meldi, Pierre Sagaut. Investigation of anomalous very fast decay regimes in homogeneous isotropic turbulence. Journal of Turbulence, Taylor & Francis, 2018, 19 (5), pp.390 - 413. 〈10.1080/14685248.2018.1450506〉. 〈hal-01816010〉
Xun Wang, Shahram Khazaie, Dimitri Komatitsch, Pierre Sagaut. Sound-Source Localization in Range-Dependent Shallow-Water Environments Using a Four-Layer Model. IEEE Journal of Oceanic Engineering, Institute of Electrical and Electronics Engineers, 2017, pp.1 - 9. 〈10.1109/JOE.2017.2775978〉. 〈hal-01702364〉 Plus de détails...
Sound-source localization in shallow water is a difficult task due to the complicated environment, e.g., complex sound-speed profile and irregular water bottom reflections. Full-wave numerical techniques are currently able to accurately simulate the propagation of sound waves in such complex environments. However, the source localization problem, which generally involves a large number of sound propagation calculations, still requires a fast computation of the wave equation, and thus a simplified model is well advised. In this paper, a four-layer model is considered, which is able to approximate a wide range of shallow-water environments, particularly those in summer conditions. More specifically, the medium is assumed to be horizontally stratified and vertically divided into four layers, and the sound speed in each layer is assumed to be constant or varying linearly. Under this assumption, the wave propagation can be rapidly computed via a classical wave number integration method. The main contribution of this paper is to show the suitability of the four-layer model in terms of source localization in a complex (range-dependent) environment. The sound-speed profile is assumed to be vertically irregular and horizontally slowly varying and the bottom is nonflat. In the forward problem, sound propagation in complex underwater environments is simulated via a time-domain full-wave simulation approach called the spectral-element method. The source localization error due to model imprecision is analyzed.
Xun Wang, Shahram Khazaie, Dimitri Komatitsch, Pierre Sagaut. Sound-Source Localization in Range-Dependent Shallow-Water Environments Using a Four-Layer Model. IEEE Journal of Oceanic Engineering, Institute of Electrical and Electronics Engineers, 2017, pp.1 - 9. 〈10.1109/JOE.2017.2775978〉. 〈hal-01702364〉
Here, we explain the phenomenon of focusing using the numerical properties of space–time discretization methods involving second-order Adams–Bashforth (AB2) method for the solution of one–dimensional (1D) convection equation. It has been established that solving 1D convection equation by three–time level method invokes a numerical or spurious mode, apart from the physical mode (as explained in Sengupta et al., [27]). Here, the long elusive problem of focusing (considered as a problem of non-linear numerical aspect), is shown due to a linear mechanism. The focusing is shown for a wave–packet propagating in a non-periodic domain by a three–time level method. Long time integration shows the physical mode to cause focusing, which shows up as spectacular growth of error–packet(s) at discrete location(s), where the dominant wavenumber (k) depends only on the CFL number (Nc), for the space–time discretization method. The length scale of growing error is independent of wavenumber of the input signal. It is also established that focusing is related to numerical absolute instability, for which the numerical group velocity (VgN1) of the physical mode is zero. However, interestingly, when a compact filter is used, the focusing phenomenon is converted from absolute to convective numerical instability. This brings new insight and satisfactory explanation of focusing and its dependence on the choice of numerical methods and use of filter. As a demonstration of the focusing phenomenon for AB2 method, we use it with a well known combined compact differencing scheme to solve Navier–Stokes equation in a square lid driven cavity for a super-critical post–Hopf bifurcation Reynolds number of 10,000 (based on the side of the cavity and the constant lid velocity). Contrary to the well-established solution with polygonal vortices in the literature, here the solution breaks down after a finite time due to focusing.
Tapan Sengupta, Pierre Sagaut, Aditi Sengupta, Kumar Saurabh. Global spectral analysis of three-time level integration schemes: Focusing phenomenon. Computers & Fluids, Elsevier, 2017, 157, pp.182 - 195. 〈10.1016/j.compfluid.2017.08.033〉. 〈hal-01702350〉
V. Mons, Luca Margheri, J.-C. Chassaing, Pierre Sagaut. Data assimilation-based reconstruction of urban pollutant release characteristics. Journal of Wind Engineering and Industrial Aerodynamics, Elsevier, 2017, 169, pp.232 - 250. 〈10.1016/j.jweia.2017.07.007〉. 〈hal-01631036〉 Plus de détails...
Christophe Coreixas, Gauthier Wissocq, Guillaume Puigt, Jean-François Boussuge, Pierre Sagaut. Recursive regularization step for high-order lattice Boltzmann methods. Physical Review E , American Physical Society (APS), 2017, 96 (3), pp.033306. 〈10.1103/PhysRevE.96.033306〉. 〈hal-01596322〉 Plus de détails...
A lattice Boltzmann method (LBM) with enhanced stability and accuracy is presented for various Hermite tensor-based lattice structures. The collision operator relies on a regularization step, which is here improved through a recursive computation of nonequilibrium Hermite polynomial coefficients. In addition to the reduced computational cost of this procedure with respect to the standard one, the recursive step allows to considerably enhance the stability and accuracy of the numerical scheme by properly filtering out second-(and higher-) order nonhydrodynamic contributions in under-resolved conditions. This is first shown in the isothermal case where the simulation of the doubly periodic shear layer is performed with a Reynolds number ranging from 104 to 10(6), and where a thorough analysis of the case at Re = 3 x 10(4) is conducted. In the latter, results obtained using both regularization steps are compared against the Bhatnagar-Gross-Krook LBM for standard (D2Q9) and high-order (D2V17 and D2V37) lattice structures, confirming the tremendous increase of stability range of the proposed approach. Further comparisons on thermal and fully compressible flows, using the general extension of this procedure, are then conducted through the numerical simulation of Sod shock tubes with the D2V37 lattice. They confirm the stability increase induced by the recursive approach as compared with the standard one.
Christophe Coreixas, Gauthier Wissocq, Guillaume Puigt, Jean-François Boussuge, Pierre Sagaut. Recursive regularization step for high-order lattice Boltzmann methods. Physical Review E , American Physical Society (APS), 2017, 96 (3), pp.033306. 〈10.1103/PhysRevE.96.033306〉. 〈hal-01596322〉
Félix Gendre, Denis Ricot, Guillaume Fritz, Pierre Sagaut. Grid refinement for aeroacoustics in the lattice Boltzmann method: A directional splitting approach. Physical Review E , American Physical Society (APS), 2017, 96 (2), pp.023311. 〈10.1103/PhysRevE.96.023311〉. 〈hal-01596329〉 Plus de détails...
This study focuses on grid refinement techniques for the direct simulation of aeroacoustics, when using weakly compressible lattice Boltzmann models, such as the D3Q19 athermal velocity set. When it comes to direct noise computation, very small errors on the density or pressure field may have great negative consequences. Even strong acoustic density fluctuations have indeed a clearly lower amplitude than the hydrodynamic ones. This work deals with such very weak spurious fluctuations that emerge when a vortical structure crosses a refinement interface, which may contaminate the resulting aeroacoustic field. We show through an extensive literature review that, within the framework described above, this issue has never been addressed before. To tackle this problem, we develop an alternative algorithm and compare its behavior to a classical one, which fits our in-house vertex-centered data structure. Our main idea relies on a directional splitting of the continuous discrete velocity Boltzmann equation, followed by an integration over specific characteristics. This method can be seen as a specific coupling between finite difference and lattice Boltzmann, locally on the interface between the two grids. The method is assessed considering two cases: an acoustic pulse and a convected vortex. We show how very small errors on the density field arise and propagate throughout the domain when a vortical flow crosses the refinement interface. We also show that an increased free stream Mach number (but still within the weakly compressible regime) strongly deteriorates the situation, although the magnitude of the errors may remain negligible for purely aerodynamic studies. A drastically reduced level of error for the near-field spurious noise is obtained with our approach, especially for under-resolved simulations, a situation that is crucial for industrial applications. Thus, the vortex case is proved useful for aeroacoustic validations of any grid refinement algorithm.
Félix Gendre, Denis Ricot, Guillaume Fritz, Pierre Sagaut. Grid refinement for aeroacoustics in the lattice Boltzmann method: A directional splitting approach. Physical Review E , American Physical Society (APS), 2017, 96 (2), pp.023311. 〈10.1103/PhysRevE.96.023311〉. 〈hal-01596329〉
Vincent Mons, Jean-Camille Chassaing, Pierre Sagaut. Optimal sensor placement for variational data assimilation of unsteady flows past a rotationally oscillating cylinder. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 823, pp.230 - 277. 〈10.1017/jfm.2017.313〉. 〈hal-01548417〉 Plus de détails...
Vincent Mons, Jean-Camille Chassaing, Pierre Sagaut. Optimal sensor placement for variational data assimilation of unsteady flows past a rotationally oscillating cylinder. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 823, pp.230 - 277. 〈10.1017/jfm.2017.313〉. 〈hal-01548417〉
Congshan Zhuo, Pierre Sagaut. Acoustic multipole sources for the regularized lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit. Physical Review E , American Physical Society (APS), 2017, 95 (6), pp.063301. 〈10.1103/PhysRevE.95.063301〉. 〈hal-01548424〉 Plus de détails...
Congshan Zhuo, Pierre Sagaut. Acoustic multipole sources for the regularized lattice Boltzmann method: Comparison with multiple-relaxation-time models in the inviscid limit. Physical Review E , American Physical Society (APS), 2017, 95 (6), pp.063301. 〈10.1103/PhysRevE.95.063301〉. 〈hal-01548424〉
Marcello Meldi, Pierre Sagaut. Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 818, pp.697 - 715. 〈10.1017/jfm.2017.158〉. 〈hal-01527613〉 Plus de détails...
The effects of the finiteness of the physical domain over the free decay of homogeneous isotropic turbulence are explored in the present article. Saturation at the large scales is investigated by the use of theoretical analysis and eddy-damped quasi-normal Markovian calculations. Both analyses indicate a strong sensitivity of the large-scale features of the flow to saturation and finite Reynolds number effects. This aspect plays an important role in the general lack of agreement between grid turbulence experiments and numerical simulations. On the other hand, the statistical quantities associated with the behaviour of the spectrum in the inertial region are only marginally affected by saturation. These results suggest new guidelines for the interpretation of experimental and direct numerical simulation studies.
Marcello Meldi, Pierre Sagaut. Turbulence in a box: quantification of large-scale resolution effects in isotropic turbulence free decay. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2017, 818, pp.697 - 715. 〈10.1017/jfm.2017.158〉. 〈hal-01527613〉
The spectral analysis is a basic tool to characterise the behaviour of any convection scheme. By nature, the solution projected onto the Fourier basis enables to estimate the dissipation and the dispersion associated with the spatial discretisation of the hyperbolic linear problem. In this paper, we wish to revisit such analysis, focusing attention on two key points. The first point concerns the effects of time integration on the spectral analysis. It is shown with standard high-order Finite Difference schemes dedicated to aeroacoustics that the time integration has an effect on the required number of points per wavelength. The situation depends on the choice of the coupled schemes (one for time integration, one for space derivative and one for the filter) and here, the compact scheme with its eighth-order filter seems to have a better spectral accuracy than the considered dispersion relation preserving scheme with its associated filter, especially in terms of dissipation. Secondly, such a coupled space time approach is applied to the new class of high-order spectral discontinuous approaches, focusing especially on the Spectral Difference method. A new way to address the specific spectral behaviour of the scheme is introduced first for wavenumbers in [0,pi], following the Matrix Power method. For wavenumbers above pi, an aliasing phenomenon always occurs but it is possible to understand and to control the aliasing of the signal. It is shown that aliasing depends on the polynomial degree and on the number of time steps. A new way to define dissipation and dispersion is introduced and applied to wavenumbers larger than it. Since the new criteria recover the previous results for wavenumbers below it, the new proposed approach is an extension of all the previous ones dealing with dissipation and dispersion errors. At last, since the standard Finite Difference schemes can serve as reference solution for their capability in aeroacoustics, it is shown that the Spectral Difference method is as accurate as (or even more accurate) than the considered Finite Difference schemes.
Julien Vanharen, Guillaume Puigt, Xavier Vasseur, Jean-François Boussuge, Pierre Sagaut. Revisiting the spectral analysis for high-order spectral discontinuous methods. Journal of Computational Physics, Elsevier, 2017, 337, pp.379 - 402. 〈10.1016/j.jcp.2017.02.043〉. 〈hal-01527618〉
Xun Wang, Shahram Khazaie, Luca Margheri, Pierre Sagaut. Shallow water sound source localization using the iterative beamforming method in an image framework. Journal of Sound and Vibration, Elsevier, 2017, 395, pp.354 - 370. 〈10.1016/j.jsv.2017.02.032〉. 〈hal-01527615〉 Plus de détails...
Shallow water is a complicated sound propagation medium due to multiple reflections by water surface and bottom, imprecisely measured sound speed, noisy environment, etc. Therefore, in order to localize a shallow water sound source, classical signal processing techniques must be improved by taking these complexities into account. In this work, the multiple reflections and uncertain reflectivity of water bottom are explicitly modeled. In the proposed model, a measured signal is a mixture of the direct propagation from the source and the multiple reflections. Instead of solving the Helmholtz equation with boundary conditions of reflections, each signal is interpreted as a superposition of signals emitting from the physical source and its image sources in a free space, which results in a fast computation of sound propagation. Then, the source location, along with its amplitude, reflection paths and power loss of bottom reflection, is estimated via the iterative beamforming (IB) method, which alternatively estimates the source contributions and performs beamforming on these estimates until convergence. This approach does not need to compute the sound propagation for all the possible source locations in a large space, which thus leads to a low computational cost. Finally, numerical simulations are introduced to illustrate the advantage of the proposed model and the source estimation method. The sensitivity of the proposed method with respect to model parameter uncertainties is also investigated via a full uncertainty quantification analysis. The localization error of IB is proved to be acceptable in the given error range of sound speed and water depth. Besides, the IB source estimate is more sensitive to the sound speed while the matched-field processing methods have a stronger sensitivity to the water depth: this result can guide the choice of source localization method in different cases of model parameter uncertainties.
Xun Wang, Shahram Khazaie, Luca Margheri, Pierre Sagaut. Shallow water sound source localization using the iterative beamforming method in an image framework. Journal of Sound and Vibration, Elsevier, 2017, 395, pp.354 - 370. 〈10.1016/j.jsv.2017.02.032〉. 〈hal-01527615〉
Luca Margheri, Pierre Sagaut. A hybrid anchored-ANOVA - POD/Kriging method for uncertainty quantification in unsteady high-fidelity CFD simulations. Journal of Computational Physics, Elsevier, 2016, 324, pp.137-173. 〈10.1016/j.jcp.2016.07.036〉. 〈hal-01461789〉 Plus de détails...
To significantly increase the contribution of numerical computational fluid dynamics (CFD) simulation for risk assessment and decision making, it is important to quantitatively measure the impact of uncertainties to assess the reliability and robustness of the results. As unsteady high-fidelity CFD simulations are becoming the standard for industrial applications, reducing the number of required samples to perform sensitivity (SA) and uncertainty quantification (UQ) analysis is an actual engineering challenge. The novel approach presented in this paper is based on an efficient hybridization between the anchored-ANOVA and the POD/Kriging methods, which have already been used in CFD-UQ realistic applications, and the definition of best practices to achieve global accuracy. The anchored-ANOVA method is used to efficiently reduce the UQ dimension space, while the POD/Kriging is used to smooth and interpolate each anchored-ANOVA term. The main advantages of the proposed method are illustrated through four applications with increasing complexity, most of them based on Large-Eddy Simulation as a high-fidelity CFD tool: the turbulent channel flow, the flow around an isolated bluff-body, a pedestrian wind comfort study in a full scale urban area and an application to toxic gas dispersion in a full scale city area. The proposed c-APK method (anchored-ANOVA-POD/Kriging) inherits the advantages of each key element: interpolation through POD/Kriging precludes the use of quadrature schemes therefore allowing for a more flexible sampling strategy while the ANOVA decomposition allows for a better domain exploration. A comparison of the three methods is given for each application. In addition, the importance of adding flexibility to the control parameters and the choice of the quantity of interest (QoI) are discussed. As a result, global accuracy can be achieved with a reasonable number of samples allowing computationally expensive CFD-UQ analysis. (C) 2016 Elsevier Inc. All rights reserved.
Luca Margheri, Pierre Sagaut. A hybrid anchored-ANOVA - POD/Kriging method for uncertainty quantification in unsteady high-fidelity CFD simulations. Journal of Computational Physics, Elsevier, 2016, 324, pp.137-173. 〈10.1016/j.jcp.2016.07.036〉. 〈hal-01461789〉
Vincent Mons, Jean-Camille Chassaing, Thomas Gomez, Pierre Sagaut. Reconstruction of unsteady viscous flows using data assimilation schemes. Journal of Computational Physics, Elsevier, 2016, 316, pp.255-280. 〈10.1016/j.jcp.2016.04.022〉. 〈hal-01333881〉 Plus de détails...
This paper investigates the use of various data assimilation (DA) approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts. Variational, ensemble Kalman filter-based and ensemble-based variational DA techniques are deployed along with a 2D compressible Navier–Stokes flow solver, which is also used to generate synthetic observations of a reference flow. The performance of these DA schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2D flow field. Moreover, different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale DA problems with up to 105 control variables. In particular, we show how an iterative procedure can be used within the framework of ensemble-based methods to deal with both non-uniform unsteady boundary conditions and initial field reconstruction. The different methodologies developed and assessed in this work give a review of what can be done with DA schemes in computational fluid dynamics (CFD) paradigm. In the same time, this work also provides useful information which can also turn out to be rational arguments in the DA scheme choice dedicated to a specific CFD application.
Vincent Mons, Jean-Camille Chassaing, Thomas Gomez, Pierre Sagaut. Reconstruction of unsteady viscous flows using data assimilation schemes. Journal of Computational Physics, Elsevier, 2016, 316, pp.255-280. 〈10.1016/j.jcp.2016.04.022〉. 〈hal-01333881〉
Antoine Briard, Thomas Gomez, Vincent Mons, Pierre Sagaut. Decay and growth laws in homogeneous shear turbulence. Journal of Turbulence, Taylor & Francis, 2016, 17 (7), pp.699 - 726. 〈10.1080/14685248.2016.1191641〉. 〈hal-01429646〉 Plus de détails...
Homogeneous anisotropic turbulence has been widely studied in the past decades, both numerically and experimentally. Shear flows have received a particular attention because of the numerous physical phenomena they exhibit. In the present paper, both the decay and growth of anisotropy in homogeneous shear flows at high Reynolds numbers are revisited thanks to a recent eddy-damped quasi-normal Markovian (EDQNM) closure adapted to homogeneous anisotropic turbulence. The emphasis is put on several aspects: an asymptotic model for the slow-part of the pressure-strain tensor is derived for the return to isotropy process when mean-velocity gradients are released. Then, a general decay law for purely anisotropic quantities in Batchelor turbulence is proposed. At last, a discussion is proposed to explain the scattering of global quantities obtained in DNS and experiments in sustained shear flows: the emphasis is put on the exponential growth rate of the kinetic energy and on the shear parameter.
Antoine Briard, Thomas Gomez, Vincent Mons, Pierre Sagaut. Decay and growth laws in homogeneous shear turbulence. Journal of Turbulence, Taylor & Francis, 2016, 17 (7), pp.699 - 726. 〈10.1080/14685248.2016.1191641〉. 〈hal-01429646〉
Yongliang Feng, Pierre Sagaut, Wen-Quan Tao. A compressible lattice Boltzmann finite volume model for high subsonic and transonic flows on regular lattices. Computers and Fluids, Elsevier, 2016, 131, pp.45-55. 〈10.1016/j.compfluid.2016.03.009〉. 〈hal-01461781〉 Plus de détails...
A multi-dimensional double distribution function thermal lattice Boltzmann model has been developed to simulate fully compressible flows at moderate Mach number. The lattice Boltzmann equation is temporally and spatially discretizated by an asymptotic preserving finite volume scheme. The micro-velocities discretization is adopted on regular low-symmetry lattices (D1Q3, D2Q9, D3Q15, D3Q19, D3Q27). The third-order Hermite polynomial density distribution function on low-symmetry lattices is used to solve the flow field, while a second-order energy distribution is employed to compute the temperature field. The fully compressible Navier-Stokes equations are recovered by standard order Gauss-Hermite polynomial expansions of Maxwell distribution with cubic correction terms, which are added by an external force expressed in orthogonal polynomials form. The proposed model is validated considering several benchmark cases, namely the Sod shock tube, thermal Couette flow and two-dimensional Riemann problem. The numerical results are in very good agreement with both analytical solution and reference results. (C) 2016 Elsevier Ltd. All rights reserved.
Yongliang Feng, Pierre Sagaut, Wen-Quan Tao. A compressible lattice Boltzmann finite volume model for high subsonic and transonic flows on regular lattices. Computers and Fluids, Elsevier, 2016, 131, pp.45-55. 〈10.1016/j.compfluid.2016.03.009〉. 〈hal-01461781〉
Amaury Bannier, Eric Garnier, Pierre Sagaut. Friction drag reduction achievable by near-wall turbulence manipulation in spatially developing boundary-layer. Physics of Fluids, American Institute of Physics, 2016, 28 (035108), 16 p. 〈10.1063/1.4943625〉. 〈hal-01428632〉 Plus de détails...
Various control strategies, such as active feedback control or riblets, end up restraining near-wall turbulence. An analytical study is conducted to estimate the drag-reduction achievable by such control in zero-pressure-gradient turbulent boundary-layers. Based on an idealized control which damps all fluctuations within a near-wall layer, a composite flow profile is established. It leads to explicit models for both the drag-reduction and the boundary-layer development rate. A skin-friction decomposition is applied and gives physical insights on the underlying phenomena. The control is found to alter the spatial development of the boundary-layer, resulting in detrimental impact on the skin-friction. However, the drag-reducing mechanism, attributed to the turbulence weakening, is found predominant and massive drag reductions remain achievable at high Reynolds number, although a minute part of the boundary-layer is manipulated. The model is finally assessed against Large Eddy Simulations of riblet-controlled flow.
Amaury Bannier, Eric Garnier, Pierre Sagaut. Friction drag reduction achievable by near-wall turbulence manipulation in spatially developing boundary-layer. Physics of Fluids, American Institute of Physics, 2016, 28 (035108), 16 p. 〈10.1063/1.4943625〉. 〈hal-01428632〉
Claire David, Pierre Sagaut. Structural stability of Lattice Boltzmann schemes. Physica A, Elsevier, 2016, 444, pp.1-8. 〈10.1016/j.physa.2015.09.089〉. 〈hal-01298987〉 Plus de détails...
The goal of this work is to determine classes of traveling solitary wave solutions for Lattice Boltzmann schemes by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to Lattice Boltzmann schemes ([1], [2], [3],[4]).
Claire David, Pierre Sagaut. Structural stability of Lattice Boltzmann schemes. Physica A, Elsevier, 2016, 444, pp.1-8. 〈10.1016/j.physa.2015.09.089〉. 〈hal-01298987〉
Vincent Mons, Claude Cambon, Pierre Sagaut. A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 788, pp.147-182. 〈10.1017/jfm.2015.705 〉. 〈hal-01276637〉 Plus de détails...
A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{R}_{ij}(\mathbf k,t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\mathbf k$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.
Vincent Mons, Claude Cambon, Pierre Sagaut. A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 788, pp.147-182. 〈10.1017/jfm.2015.705 〉. 〈hal-01276637〉
Vincent Mons, Claude Cambon, Pierre Sagaut. A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 788, pp.147- 182. Plus de détails...
A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor R^ij(k,t), the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector k our final model equations in terms of the wavenumber modulus k only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.
Vincent Mons, Claude Cambon, Pierre Sagaut. A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2016, 788, pp.147- 182. <10.1017/jfm.2015.705>. <hal-01298951>
Shahram Khazaie, Xun Wang, Pierre Sagaut. Localization of random acoustic sources in an inhomogeneous medium. Journal of Sound and Vibration, Elsevier, 2016, 384, pp.75 - 93. 〈10.1016/j.jsv.2016.08.004〉. 〈hal-01375680〉 Plus de détails...
In this paper, the localization of a random sound source via different source localization methods is considered, the emphasis being put on the robustness and the accuracy of classical methods in the presence of uncertainties. The sound source position is described by a random variable and the sound propagation medium is assumed to have spatially varying parameters with known values. Two approaches are used for the source identification: time reversal and beamforming. The probability density functions of the random source position are estimated using both methods. The focal spot resolutions of the time reversal estimates are also evaluated. In the numerical simulations, two media with different correlation lengths are investigated to account for two different scattering regimes: one has a correlation length relatively larger than the wavelength and the other has a correlation length comparable to the wavelength. The results show that the required sound propagation time and source estimation robustness highly depend on the ratio between the correlation length and the wavelength. It is observed that source identification methods have different robustness in the presence of uncertainties. Advantages and weaknesses of each method are discussed.
Shahram Khazaie, Xun Wang, Pierre Sagaut. Localization of random acoustic sources in an inhomogeneous medium. Journal of Sound and Vibration, Elsevier, 2016, 384, pp.75 - 93. 〈10.1016/j.jsv.2016.08.004〉. 〈hal-01375680〉
I. Thiagalingam, Pierre Sagaut. Pseudo-homogeneous 1D RANS radial model for heat transfer in tubular packed beds. International Journal of Heat and Fluid Flow, Elsevier, 2016, 62 (Part B), pp.258-272. 〈10.1016/j.ijheatfluidflow.2016.10.005〉. 〈hal-01400641〉 Plus de détails...
A RANS zonal pseudo-homogeneous 1D radial heat transfer model is derived using an homogenization technique along with high-fidelity microscopic simulation to calibrate the model free parameters. Thus, it is brought to light the importance of the mechanical dispersion in the mixing process, the similarity between turbulent and dispersive dynamics, the existence of a near wall zone characterized by a channeling effect which is responsible for the thermal resistance over the zone. A linear law for the effective thermal conductivity is proposed to assess the heat transfer within the disrupted thermal boundary layer. The model showed its ability to estimate the effective conductivity and the temperature field in the radial direction with satisfaction. Very good agreements are also found in the near wall zone where the temperature gradients are the highest. The model well estimated also the value of the wall temperature and the wall heat transfer coefficient for an imposed heat flux at the wall.
I. Thiagalingam, Pierre Sagaut. Pseudo-homogeneous 1D RANS radial model for heat transfer in tubular packed beds. International Journal of Heat and Fluid Flow, Elsevier, 2016, 62 (Part B), pp.258-272. 〈10.1016/j.ijheatfluidflow.2016.10.005〉. 〈hal-01400641〉
Journal: International Journal of Heat and Fluid Flow
Xun Wang, Shahram Khazaie, Pierre Sagaut. Sound source localization in a randomly inhomogeneous medium using matched statistical moment method. Journal of the Acoustical Society of America, Acoustical Society of America, 2015, 138 (6), pp.3896. 〈10.1121/1.4938238〉. 〈hal-01276517〉 Plus de détails...
This paper investigates the problem of sound source localization from acoustical measurements obtained by an array of microphones. The sound propagation medium is assumed to be randomly inhomogeneous, being modelled by a random function of space. In this case, classical source localization methods (e.g., beamforming, near-field acoustical holography, and time reversal) cannot be used anymore. Therefore, an approach based on the statistical moments of acoustical measurement is proposed to solve the aforementioned problem. In this work, a Karhunen–Loève expansion is used so that the random medium can be represented by a small number of uncorrelated and identically distributed random variables. The statistical characteristics of the measurements in terms of probability density function and statistical moments are also studied. Then, the sound source is localized by minimizing the error of statistical moments between the real measurements obtained from the microphone array and the measurements simulated from an assumed source. Finally, a numerical example is introduced to justify the proposed method. This experiment shows that the random field can be replicated by a very small number of random variables, the statistical moments of measurements guarantee the convergence, and the source location can be accurately estimated using the proposed source localization method.
Xun Wang, Shahram Khazaie, Pierre Sagaut. Sound source localization in a randomly inhomogeneous medium using matched statistical moment method. Journal of the Acoustical Society of America, Acoustical Society of America, 2015, 138 (6), pp.3896. 〈10.1121/1.4938238〉. 〈hal-01276517〉
Journal: Journal of the Acoustical Society of America
Yongliang Feng, Pierre Sagaut, Wenquan Tao. A three dimensional lattice model for thermal compressible flow on standard lattices. Journal of Computational Physics, Elsevier, 2015, 303, pp.514-529. 〈10.1016/j.jcp.2015.09.011〉. 〈hal-01276507〉 Plus de détails...
A three-dimensional double distribution function thermal lattice Boltzmann model has been developed for simulation of thermal compressible flows in the low Mach number limit. Both the flow field and energy conservation equation are solved by LB approach. A higher order density distribution function on standard lattices is used to solve the flow field, while an energy distribution function is employed to compute the temperature field. The equation of state of thermal perfect gas is recovered by higher order Hermite polynomial expansions in Navier–Stokes–Fourier equations. The equilibrium distribution functions of D3Q15, D3Q19 and D3Q27 lattices are obtained from the Hermite expansion. They exhibit slight differences originating in differences in the discrete lattice symmetries. The correction terms in LB models for third order derivation are added using an external force in orthogonal polynomials form. Present models are successfully assessed considering several test cases, namely the thermal Couette flow, Rayleigh–Bénard convection, natural convection in square cavity and a spherical explosion in a 3D enclosed box. The numerical results are in good agreement with both analytical solution and results given by previous authors.
Yongliang Feng, Pierre Sagaut, Wenquan Tao. A three dimensional lattice model for thermal compressible flow on standard lattices. Journal of Computational Physics, Elsevier, 2015, 303, pp.514-529. 〈10.1016/j.jcp.2015.09.011〉. 〈hal-01276507〉
Antoine Briard, Thomas Gomez, Pierre Sagaut, Souzan Memari. Passive scalar decay laws in isotropic turbulence: Prandtl number effects. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2015, 784, pp.274 - 303. 〈10.1017/jfm.2015.575〉. 〈hal-01429641〉 Plus de détails...
The passive scalar dynamics in a freely decaying turbulent flow is studied. The classical framework of homogeneous isotropic turbulence without forcing is considered. Both low and high Reynolds number regimes are investigated for very small and very large Prandtl numbers. The long time behaviours of integrated quantities such as the scalar variance or the scalar dissipation rate are analyzed by considering that the decay follows power laws. This study addresses three major topics. Firstly, the Comte-Bellot and Corrsin (CBC) dimensional analysis for the temporal decay exponents is extended to the case of a passive scalar when the permanence of large eddies is broken. Secondly, using numerical simulations based on eddy-damped quasi-normal markovian (EDQNM) model, the time evolution of integrated quantities is accurately determined for a wide range of Reynolds and Prandtl numbers. These simulations show that, whatever the Reynolds and the Prandtl numbers are, the decay follows an algebraic law with an exponent very close to the value predicted by the CBC theory. Finally, the initial position of the scalar integral scale L T has no influence on the asymptotic values of the decay exponents, and an analytical law predicting the relative positions of the kinetic and scalar spectra peaks is derived.
Antoine Briard, Thomas Gomez, Pierre Sagaut, Souzan Memari. Passive scalar decay laws in isotropic turbulence: Prandtl number effects. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2015, 784, pp.274 - 303. 〈10.1017/jfm.2015.575〉. 〈hal-01429641〉
Amaury Bannier, Éric Garnier, Pierre Sagaut. Riblet Flow Model Based on an Extended FIK Identity. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2015, 95 (2-3), pp.351-376. 〈10.1007/s10494-015-9624-2〉. 〈hal-01276488〉 Plus de détails...
Large Eddy Simulations of zero-pressure-gradient turbulent boundary layers over riblets have been conducted. All along the controlled domain, riblets maintain a significant 11 % drag reduction with respect to the flat plate at the same R e τ (from 250 to 450). To compare the flows above riblets and a reference smooth wall, an appropriate vertical shift between the two surfaces is required. In the present study, the “vertical origin” is set using the identity of Fukagata, Iwamoto and Kasagi (FIK) in Phys. Fluids, vol. 14, 2002, L73. This identity, which provides a physically meaningful decomposition of the skin friction, has been extended to complex wall surfaces and constitutes the basis for the derivation of a new virtual origin. Using this FIK-based origin, it is shown that the complex interactions between the riblets and the near-wall turbulent structures can be taken into account by a simple shift of the two axes of the mean and turbulent velocity profiles. The appropriate upward shift Δu +, typical for drag reduction, is directly dependent on the skin friction on the riblets and on the reference smooth plate at the same R e τ .
Amaury Bannier, Éric Garnier, Pierre Sagaut. Riblet Flow Model Based on an Extended FIK Identity. Flow, Turbulence and Combustion, Springer Verlag (Germany), 2015, 95 (2-3), pp.351-376. 〈10.1007/s10494-015-9624-2〉. 〈hal-01276488〉
I. Thiagalingam, M. Dallet, I. Bennaceur, S. Cadalen, Pierre Sagaut. Exact non local expression for the wall heat transfer coefficient in tubular catalytic reactors. International Journal of Heat and Fluid Flow, Elsevier, 2015, 54, pp.97-106. 〈10.1016/j.ijheatfluidflow.2015.03.007〉. 〈hal-01276484〉 Plus de détails...
A new exact and non local expression for the wall Nusselt number is derived to have a deep insight into the physical mechanisms that govern the wall heat transfer. 3D high-fidelity numerical simulations (RANS) are then carried out in tubular packed beds and a new set of criteria is defined to extend the Representative Elementary Volume concept to packed bed configurations which enables to unequivocally up-scale 3D simulation data to the observation scale. The mean flow deviation and the mechanical dispersion are shown to play a key role in the wall heat transfer. Finally, the usual correlations of the form View the MathML source Nu=αRepβ found in the literature for the Nusselt number are validated through fine 3D simulations and on the basis of physical investigations for 4000 ⩽ Rep ⩽ 30,000.
I. Thiagalingam, M. Dallet, I. Bennaceur, S. Cadalen, Pierre Sagaut. Exact non local expression for the wall heat transfer coefficient in tubular catalytic reactors. International Journal of Heat and Fluid Flow, Elsevier, 2015, 54, pp.97-106. 〈10.1016/j.ijheatfluidflow.2015.03.007〉. 〈hal-01276484〉
Journal: International Journal of Heat and Fluid Flow
Marcello Meldi, Hugo Lejemble, Pierre Sagaut. On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014, 756, pp.816-843. 〈10.1017/jfm.2014.476〉. 〈hal-01064518〉 Plus de détails...
The present paper addresses the issue of finding key parameters that may lead to the occurrence of non-classical decay regimes for fractal/multiscale generated grid turbulence. To this aim, a database of numerical simulations has been generated by the use of the eddy-damped quasi-normal Markovian (EDQNM) model. The turbulence production in the wake of the fractal/multiscale grid is modelled via a turbulence production term based on the forcing term developed for direct numerical simulations (DNS) purposes and the dynamics of self-similar wakes. The sensitivity of the numerical results to the simulation parameters has been investigated successively. The analysis is based on the observation of both the time evolution of the turbulent energy spectrum $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E(k,t)$ and the decay of the flow statistical quantities, such as the turbulent kinetic energy $\mathcal{K}(t)$ and the energy dissipation rate $\varepsilon (t)$. A satisfactory agreement with existing experimental data published by different research teams is observed. In particular, it is observed that the key parameter that governs the nature of turbulence decay is $\alpha ={d/U_{\infty }}\, {(\varepsilon (0)/\mathcal{K}(0))}={d/L(0)} \, {(\sqrt{\mathcal{K}(0)}/U_{\infty })}$ (with $d$ the bar diameter and $U_{\infty }$ the upstream uniform velocity), which measures the ratio of the time scale largest grid bar $d/U_{\infty }$ to the turbulent time scale $\mathcal{K}(0)/\varepsilon (0)$. Two asymptotic behaviours for $\alpha \rightarrow + \infty $ and $\alpha \rightarrow 0$ are identified: (i) a fast algebraic decay law regime for rapidly decaying production terms, due to strongly modified initial kinetic energy spectrum and (ii) a real exponential decay regime associated with strong, very slowly decaying production terms. The present observations are in full agreement with conclusions drawn from recent fractal grid experiments, and it provides a physical scenario for occurrence of anomalous decay regime which encompasses previous hypotheses.
Marcello Meldi, Hugo Lejemble, Pierre Sagaut. On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014, 756, pp.816-843. 〈10.1017/jfm.2014.476〉. 〈hal-01064518〉
Roux B., Bohbot J., Tran Q. H., Sagaut P.. Prediction of cyclic combustion variability in internal combustion engines via coupled 1D-3D LES methods. E. Oate, J. Oliver and A. Huerta. Proceedings of the 6th European Conference on Computational Fluid Dynamics, pp.5474--5485, 2014. 〈hal-01307241〉 Plus de détails...
Roux B., Bohbot J., Tran Q. H., Sagaut P.. Prediction of cyclic combustion variability in internal combustion engines via coupled 1D-3D LES methods. E. Oate, J. Oliver and A. Huerta. Proceedings of the 6th European Conference on Computational Fluid Dynamics, pp.5474--5485, 2014. 〈hal-01307241〉
Imran Afgan, Sofiane Benhamadouche, Xingsi Han, Pierre Sagaut, Dominique Laurence. Flow over a flat plate with uniform inlet and incident coherent gusts. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2013, 720, pp.457-485. 〈10.1017/jfm.2013.25〉. 〈hal-01715550〉 Plus de détails...
The flow over a flat plate at a Reynolds number of 750 is numerically investigated via fine Large Eddy Simulation (LES) first, at normal (90 0) and then at oblique (45 0) incidence flow direction with a uniform steady inlet. The results are in complete agreement to the Direct Numerical Simulation (DNS) and experimental data, thereby serving as a validation for the present simulations. For the normal (90 0) uniform inflow case, coherent vortices are alternatively shed from both leading edges of the plate, whereas for the oblique (45 0) uniform inflow case the shedding from the two sides of the plate interact strongly resulting in a quasi-periodic force response. The normal flat plate is then analyzed with an incident gust signal with varying amplitude and time period. For these incident coherent gust cases, a reference test case with variable coherent inlet is first studied and the results are compared to a steady inlet simulation, with a detailed analysis of the flow behavior and the wake response under the incident gust. Finally, the flat plate response to 16 different gust profiles is studied. Transient drag reconstruction for these incident coherent gust cases is then presented based on frequency dependent transfer function and phase spectrum analysis.
Imran Afgan, Sofiane Benhamadouche, Xingsi Han, Pierre Sagaut, Dominique Laurence. Flow over a flat plate with uniform inlet and incident coherent gusts. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2013, 720, pp.457-485. 〈10.1017/jfm.2013.25〉. 〈hal-01715550〉
P. Sagaut, S. Deck, M. Terracol. Multiscale and multiresolution approaches in turbulence (second edition). Imperial College Press, 2, 2013. 〈hal-01313533〉 Plus de détails...
P. Sagaut, S. Deck, M. Terracol. Multiscale and multiresolution approaches in turbulence (second edition). Imperial College Press, 2, 2013. 〈hal-01313533〉
Meldi M., Lucor L., Sagaut P.. Quantification of the effects of uncertainties in turbulent flows through generalized polynomial chaos. 13th European Turbulence Conference (ETC 13), 2011. 〈hal-01307214〉 Plus de détails...
Meldi M., Lucor L., Sagaut P.. Quantification of the effects of uncertainties in turbulent flows through generalized polynomial chaos. 13th European Turbulence Conference (ETC 13), 2011. 〈hal-01307214〉
