Evaluation du potentiel de LBM pour applications aérothermiques tournantes hors veine turbomachines incluant des zones de haut MACH (thèse 2016 - 2019) hors labo
Publications scientifiques au M2P2
2023
Gauthier Wissocq, Said Taileb, Song Zhao, Pierre Boivin. A hybrid lattice Boltzmann method for gaseous detonations. Journal of Computational Physics, 2023, 494, pp.112525. ⟨10.1016/j.jcp.2023.112525⟩. ⟨hal-04244340⟩ Plus de détails...
This article is dedicated to the construction of a robust and accurate numerical scheme based on the lattice Boltzmann method (LBM) for simulations of gaseous detonations. This objective is achieved through careful construction of a fully conservative hybrid lattice Boltzmann scheme tailored for multi-species reactive flows. The core concept is to retain LBM low dissipation properties for acoustic and vortical modes by using the collide and stream algorithm for the particle distribution function, while transporting entropic and species modes via a specifically designed finite-volume scheme. The proposed method is first evaluated on common academic cases, demonstrating its ability to accurately simulate multi-species compressible and reactive flows with discontinuities: the convection of inert species, a Sod shock tube with two ideal gases and a steady one-dimensional inviscid detonation wave. Subsequently, the potential of this novel approach is demonstrated in one- and two-dimensional inviscid unsteady gaseous detonations, highlighting its ability to accurately recover detonation structures and associated instabilities for high activation energies. To the authors' knowledge, this study is the first successful simulation of detonation cellular structures capitalizing on the LBM collide and stream algorithm.
Gauthier Wissocq, Said Taileb, Song Zhao, Pierre Boivin. A hybrid lattice Boltzmann method for gaseous detonations. Journal of Computational Physics, 2023, 494, pp.112525. ⟨10.1016/j.jcp.2023.112525⟩. ⟨hal-04244340⟩
Gauthier Wissocq, Pierre Sagaut. Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes. Journal of Computational Physics, 2022, 450, pp.110858. ⟨10.1016/j.jcp.2021.110858⟩. ⟨hal-04064045⟩ Plus de détails...
With the aim of better understanding the numerical properties of the lattice Boltzmann method (LBM), a general methodology is proposed to derive its hydrodynamic limits in the discrete setting. It relies on a Taylor expansion in the limit of low Knudsen numbers. With a single asymptotic analysis, two kinds of deviations with the Navier-Stokes (NS) equations are explicitly evidenced: consistency errors, inherited from the kinetic description of the LBM, and numerical errors attributed to its space and time discretization. The methodology is applied to the Bhatnagar-Gross-Krook (BGK), the regularized and the multiple relaxation time (MRT) collision models in the isothermal framework. Deviation terms are systematically confronted to linear analyses in order to validate their expressions, interpret them and provide explanations for their numerical properties. The low dissipation of the BGK model is then related to a particular pattern of its error terms in the Taylor expansion. Similarly, dissipation properties of the regularized and MRT models are explained by a phenomenon referred to as hyperviscous degeneracy. The latter consists in an unexpected resurgence of high-order Knudsen effects induced by a large numerical prefactor. It is at the origin of over-dissipation and severe instabilities in the low-viscosity regime.
Gauthier Wissocq, Pierre Sagaut. Hydrodynamic limits and numerical errors of isothermal lattice Boltzmann schemes. Journal of Computational Physics, 2022, 450, pp.110858. ⟨10.1016/j.jcp.2021.110858⟩. ⟨hal-04064045⟩
Gauthier Wissocq, Thomas Coratger, Gabriel Farag, Song Zhao, Pierre Boivin, et al.. Restoring the conservativity of characteristic-based segregated models: application to the hybrid lattice Boltzmann method. Physics of Fluids, 2022, 34 (4), pp.046102. ⟨10.1063/5.0083377⟩. ⟨hal-03627520⟩ Plus de détails...
A general methodology is introduced to build conservative numerical models for fluid simulations based on segregated schemes, where mass, momentum and energy equations are solved by different methods. It is here especially designed for developing new numerical discretizations of the total energy equation, adapted to a thermal coupling with the lattice Boltzmann method (LBM). The proposed methodology is based on a linear equivalence with standard discretizations of the entropy equation, which, as a characteristic variable of the Euler system, allows efficiently decoupling the energy equation with the LBM. To this extent, any LBM scheme is equivalently written under a finite-volume formulation involving fluxes, which are further included in the total energy equation as numerical corrections. The viscous heat production is implicitly considered thanks to the knowledge of the LBM momentum flux. Three models are subsequently derived: a first-order upwind, a Lax-Wendroff and a third-order Godunov-type schemes. They are assessed on standard academic test cases: a Couette flow, entropy spot and vortex convections, a Sod shock tube, several two-dimensional Riemann problems and a shock-vortex interaction. Three key features are then exhibited: 1) the models are conservative by construction, recovering correct jump relations across shock waves, 2) the stability and accuracy of entropy modes can be explicitly controlled, 3) the low dissipation of the LBM for isentropic phenomena is preserved.
Gauthier Wissocq, Thomas Coratger, Gabriel Farag, Song Zhao, Pierre Boivin, et al.. Restoring the conservativity of characteristic-based segregated models: application to the hybrid lattice Boltzmann method. Physics of Fluids, 2022, 34 (4), pp.046102. ⟨10.1063/5.0083377⟩. ⟨hal-03627520⟩
Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, Pierre Sagaut. Lattice Boltzmann method for computational aeroacoustics on non-uniform meshes: A direct grid coupling approach. Journal of Computational Physics, 2021, 447, pp.110667. ⟨10.1016/j.jcp.2021.110667⟩. ⟨hal-03514616⟩ Plus de détails...
The present study proposes an accurate lattice Boltzmann direct coupling algorithm, well suited for industrial purposes, making it highly valuable for aeroacoustic applications. It is indeed known that the convection of vortical structures across a grid refinement interface, where cell size is abruptly doubled, is likely to generate spurious noise that may corrupt the solution over the whole computational domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. Consequently, any interfering noise that may pollute the acoustic predictions must be reduced. The proposed grid refinement algorithm differs from conventionally used ones, in which an overlapping mesh layer is considered. Instead, it provides a direct connection allowing a tighter link between fine and coarse grids, especially with the use of a coherent equilibrium function shared by both grids. Moreover, the direct coupling makes the algorithm more local and prevents the duplication of points, which might be detrimental for massive parallelization. This work follows our first study (Astoul et al. 2020 [1]) on the deleterious effect of non-hydrodynamic modes crossing mesh transitions, which can be addressed using an appropriate collision model: the hybrid recursive regularization. The grid coupling algorithm is assessed in the context of computational aeroacoustics and compared to a widely-used cell-vertex algorithm. The validation benchmark includes the simulation of (1) an acoustic pulse, (2) a vortex transport by a mean flow, and finally, (3) a turbulent circular cylinder wake flow at high Reynolds number. In the end, the proposed approach is proven to drastically reduced the spurious noise generated at grid interfaces, hence, paving the way for accurate and efficient aeroacoustic simulations based on lattice Boltzmann methods. (C) 2021 Elsevier Inc. All rights reserved.
Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, Pierre Sagaut. Lattice Boltzmann method for computational aeroacoustics on non-uniform meshes: A direct grid coupling approach. Journal of Computational Physics, 2021, 447, pp.110667. ⟨10.1016/j.jcp.2021.110667⟩. ⟨hal-03514616⟩
G. Farag, T. Coratger, G. Wissocq, S. Zhao, Pierre Boivin, et al.. A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods. Physics of Fluids, 2021, 33 (8), pp.086101. ⟨10.1063/5.0057407⟩. ⟨hal-03324229⟩ Plus de détails...
A unified expression for high-speed compressible segregated consistent lattice Boltzmann methods, namely, pressure-based and improved density-based methods, is given. It is theoretically proved that in the absence of forcing terms, these approaches are strictly identical and can be recast in a unique form. An important result is that the difference with classical density-based methods lies in the addition of fourth-order term in the equilibrium function. It is also shown that forcing terms used to balance numerical errors in both original pressure-based and improved density-based methods can be written in a generalized way. A hybrid segregated efficient lattice-Boltzmann for compressible flow based on this unified model, equipped with a recursive regularization kernel, is proposed and successfully assessed on a wide set of test cases with and without shock waves.
G. Farag, T. Coratger, G. Wissocq, S. Zhao, Pierre Boivin, et al.. A unified hybrid lattice-Boltzmann method for compressible flows: Bridging between pressure-based and density-based methods. Physics of Fluids, 2021, 33 (8), pp.086101. ⟨10.1063/5.0057407⟩. ⟨hal-03324229⟩
Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, Pierre Sagaut. Analysis and reduction of spurious noise generated at grid refinement interfaces with the lattice Boltzmann method. Journal of Computational Physics, 2020, 418, pp.109645. ⟨10.1016/j.jcp.2020.109645⟩. ⟨hal-02960150⟩ Plus de détails...
The present study focuses on the unphysical effects induced by the use of non-uniform grids in the lattice Boltzmann method. In particular, the convection of vortical structures across a grid refinement interface is likely to generate spurious noise that may impact the whole computation domain. This issue becomes critical in the case of aeroacoustic simulations, where accurate pressure estimations are of paramount importance. The purpose of this article is to identify the issues occurring at the interface and to propose possible solutions yielding significant improvements for aeroacoustic simulations. More specifically, this study highlights the critical involvement of non-physical modes in the generation of spurious vorticity and acoustics. The identification of these modes is made possible thanks to linear stability analyses performed in the fluid core, and non-hydrodynamic sensors specifically developed to systematically emphasize them during a simulation. Investigations seeking pure acoustic waves and sheared flows allow for isolating the contribution of each mode. An important result is that spurious wave generation is intrinsically due to the change in the grid resolution (i.e. aliasing) independently of the details of the grid transition algorithm. Finally, the solution proposed to minimize spurious wave amplitude consists of choosing an appropriate collision model in the fluid core so as to cancel the non-hydrodynamic mode contribution regardless the grid coupling algorithm. Results are validated on a convected vortex and on a turbulent flow around a cylinder where a huge reduction of both spurious noise and vorticity are obtained.
Thomas Astoul, Gauthier Wissocq, Jean-François Boussuge, Alois Sengissen, Pierre Sagaut. Analysis and reduction of spurious noise generated at grid refinement interfaces with the lattice Boltzmann method. Journal of Computational Physics, 2020, 418, pp.109645. ⟨10.1016/j.jcp.2020.109645⟩. ⟨hal-02960150⟩
Gauthier Wissocq, Jean-François Boussuge, Pierre Sagaut. Consistent vortex initialization for the athermal lattice Boltzmann method. Physical Review E , 2020, 101 (4), ⟨10.1103/PhysRevE.101.043306⟩. ⟨hal-02892501⟩ Plus de détails...
A barotropic counterpart of the well-known convected vortex test case is rigorously derived from the Euler equations along with an athermal equation of state. Starting from a given velocity distribution corresponding to an intended flow recirculation, the athermal counterpart of the Euler equations are solved to obtain a consistent density field. The present initialization is assessed on a standard lattice Boltzmann solver based on the D2Q9 lattice. Compared to the usual isentropic initialization, a much lower spurious relaxation toward the targeted solution is observed, which is due to the spatial resolution rather than approximated macroscopic quantities. The amplitude of the spurious waves can be further reduced by including an off-equilibrium part in the initial distribution functions.
Gauthier Wissocq, Jean-François Boussuge, Pierre Sagaut. Consistent vortex initialization for the athermal lattice Boltzmann method. Physical Review E , 2020, 101 (4), ⟨10.1103/PhysRevE.101.043306⟩. ⟨hal-02892501⟩
Gauthier Wissocq, Pierre Sagaut, Jean-François Boussuge. An extended spectral analysis of the lattice Boltzmann method: modal interactions and stability issues. Journal of Computational Physics, 2019, 380, pp.311-333. ⟨10.1016/j.jcp.2018.12.015⟩. ⟨hal-02176969⟩ Plus de détails...
An extension of the von Neumann linear analysis is proposed for the study of the discrete-velocity Boltzmann equation (DVBE) and the lattice Boltzmann (LB) scheme. While the standard technique is restricted to the investigation of the spectral radius and the dissipation and dispersion properties, a new focus is put here on the information carried by the modes. The technique consists in the computation of the moments of the eigenvectors and their projection onto the physical waves expected by the continuous linearized Navier-Stokes (NS) equations. The method is illustrated thanks to some simulations with the BGK (Bhatnagar-Gross-Krook) collision operator on the D2Q9 and D2V17 lattices. The present analysis reveals the existence of two kinds of modes: non-observable modes that do not carry any macroscopic information and observable modes. The latter may carry either a physical wave expected by the NS equations, or an unphysical information. Further investigation of modal interactions highlights a phenomenon called curve veering occurring between two observable modes: a swap of eigenvectors and dissipation rate is observed between the eigencurves. Increasing the Mach number of the mean flow yields an eigenvalue collision at the origin of numerical instabilities of the BGK model, arising from the error in the time and space discretization of the DVBE. (C) 2019 Elsevier Inc. All rights reserved.
Gauthier Wissocq, Pierre Sagaut, Jean-François Boussuge. An extended spectral analysis of the lattice Boltzmann method: modal interactions and stability issues. Journal of Computational Physics, 2019, 380, pp.311-333. ⟨10.1016/j.jcp.2018.12.015⟩. ⟨hal-02176969⟩
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 , 2017, 96 (3), pp.033306. ⟨10.1103/PhysRevE.96.033306⟩. ⟨hal-01596322⟩
Eric Serre, Sandrine Hugues, Emilia Crespo del Arco, Anthony Randriamampianina, Patrick Bontoux. Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow. International Journal of Heat and Fluid Flow, 2001, 22 (1), pp.82-93. ⟨hal-01023080⟩ Plus de détails...
Eric Serre, Sandrine Hugues, Emilia Crespo del Arco, Anthony Randriamampianina, Patrick Bontoux. Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow. International Journal of Heat and Fluid Flow, 2001, 22 (1), pp.82-93. ⟨hal-01023080⟩
Journal: International Journal of Heat and Fluid Flow
