Projet de recherche : Evaluation des méthodes Lattice-Boltzmann pour la propulsion spatiale
Publications scientifiques au M2P2
2024
Mostafa Taha, Song Zhao, Aymeric Lamorlette, Jean-Louis Consalvi, Pierre Boivin. Large eddy simulation of fire-induced flows using Lattice-Boltzmann methods. International Journal of Thermal Sciences, 2024, 197, pp.108801. ⟨10.1016/j.ijthermalsci.2023.108801⟩. ⟨hal-04338538⟩ Plus de détails...
Large-eddy simulations (LES) of the near-field region of large-scale fire plumes are performed for the first time with a pressure-based Lattice Boltzmann method (LBM) with low-Mach number approximation. Two scenarios are considered: the large-scale non-reactive helium plume and the 1 m methane pool fire, both investigated experimentally at Sandia. In the second scenario, a simplified modeling of the combustion and radiation processes is introduced involving a one-step irreversible reaction eddydissipation concept-based combustion model and a radiant fraction model, respectively. In both scenarios, a quantitative agreement is observed with the experimental data and model predictions are consistent with previouslypublished numerical studies. Our simulations demonstrate the computational efficiency of the proposed LBM solver to tackle fire-induced flows, suggesting that LBMs are a good alternative candidate for the modeling of fire-related problems.
Mostafa Taha, Song Zhao, Aymeric Lamorlette, Jean-Louis Consalvi, Pierre Boivin. Large eddy simulation of fire-induced flows using Lattice-Boltzmann methods. International Journal of Thermal Sciences, 2024, 197, pp.108801. ⟨10.1016/j.ijthermalsci.2023.108801⟩. ⟨hal-04338538⟩
Journal: International Journal of Thermal Sciences
Song Zhao, Karthik Bhairapurada, Muhammad Tayyab, Renaud Mercier, Pierre Boivin. Lattice-Boltzmann modelling of the quiet and unstable PRECCINSTA burner modes. Computers and Fluids, 2023, pp.105898. ⟨10.1016/j.compfluid.2023.105898⟩. ⟨hal-04085625⟩ Plus de détails...
Song Zhao, Karthik Bhairapurada, Muhammad Tayyab, Renaud Mercier, Pierre Boivin. Lattice-Boltzmann modelling of the quiet and unstable PRECCINSTA burner modes. Computers and Fluids, 2023, pp.105898. ⟨10.1016/j.compfluid.2023.105898⟩. ⟨hal-04085625⟩
Marc Le Boursicaud, Song Zhao, Jean-Louis Consalvi, Pierre Boivin. An improved passive scalar model for hydrogen hazardous ignition prediction. Combustion and Flame, 2023, 256, pp.112938. ⟨10.1016/j.combustflame.2023.112938⟩. ⟨hal-04169558⟩ Plus de détails...
With an increasing interest in hydrogen as an alternative fuel for transportation, there is a need to develop tools for the prediction of ignition events. A cost-effective passive scalar formulation has been recently developed to predict hydrogen auto-ignition. A single scalar advection-diffusion-reaction equation is used to reproduce the chain-branched ignition process, where the scalar represents the radical pool responsible of ignition (H, O, OH, HO2 , H2O2). The scalar reaction rate is analytically deduced from the Jacobian matrix associated to hydrogen ignition chemistry. This method was found to reproduce with good accuracy the ignition delays obtained by detailed chemistry for temperature where the branching is the leading process. For temperature close or below the crossover temperature, where other phenomenon such as the thermal runaway are important, the scalar approach fails to predict correctly ignition events. Thus, an extension of the scalar source term formulation is proposed to extend its validity over the entire temperature range. In addition, a simple way to approximate the diffusion properties of the scalar is introduced: the radical pool composition may vary drastically, with molecules having very different diffusion properties (e.g. H and HO2). The complete modified framework is presented and its capability is assessed in canonical scenarios and more complex simulations relevant to hydrogen safety.
Marc Le Boursicaud, Song Zhao, Jean-Louis Consalvi, Pierre Boivin. An improved passive scalar model for hydrogen hazardous ignition prediction. Combustion and Flame, 2023, 256, pp.112938. ⟨10.1016/j.combustflame.2023.112938⟩. ⟨hal-04169558⟩
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⟩
Said Taileb, Alejandro Millán-Merino, Song Zhao, Pierre Boivin. Lattice-Boltzmann modeling of lifted hydrogen jet flames: A new model for hazardous ignition prediction. Combustion and Flame, 2022, 245, pp.112317. ⟨10.1016/j.combustflame.2022.112317⟩. ⟨hal-03796395⟩ Plus de détails...
This numerical study deals with the hazardous ignition of a jet flame in a vitiated co-flow. A novel formulation, based on a passive scalar variable, will be presented to predict hydrogen auto-ignition events. The model, derived from the theoretical analysis of the Jacobian, correctly describes the appearance and absence of auto-ignition in complex configurations based on initial thermodynamic and mixture conditions. No chemical reaction and species equations are required to perform the simulations. Results of Lattice Boltzmann Methods (LBM) simulations of a 3D H 2 /N 2 Cabra flame will be presented using a detailed H 2-Air mechanism. Validation against experimental and numerical results will be provided for the lift-off (distance to auto-ignition). The passive scalar predictions are successfully compared with the reactive simulations. The results show a potential extension of this model to an extensive spectrum of hydrogen safety and large-scale turbulent combustion applications.
Said Taileb, Alejandro Millán-Merino, Song Zhao, Pierre Boivin. Lattice-Boltzmann modeling of lifted hydrogen jet flames: A new model for hazardous ignition prediction. Combustion and Flame, 2022, 245, pp.112317. ⟨10.1016/j.combustflame.2022.112317⟩. ⟨hal-03796395⟩
Mostafa Taha, Song Zhao, Aymeric Lamorlette, Jean-Louis Consalvi, Pierre Boivin. Lattice-Boltzmann modeling of buoyancy-driven turbulent flows. Physics of Fluids, 2022, ⟨10.1063/5.0088409⟩. ⟨hal-03661928⟩ Plus de détails...
The pressure-based hybrid lattice-Boltzmann method presented by Farag & al (Phys. Fluids 2020) is assessed for the simulation of buoyancy driven flows. The model is first validated on Rayleigh-Benard and Rayleigh-Taylor two-dimensional cases. A large-eddy simulation of a turbulent forced plume is then carried out, and results are validated against experiments. A good overall agreement is obtained, both for mean and fluctuations quantities, as well as global entertainment. The self-similarity character of the plume in the far-field is also recovered.
Mostafa Taha, Song Zhao, Aymeric Lamorlette, Jean-Louis Consalvi, Pierre Boivin. Lattice-Boltzmann modeling of buoyancy-driven turbulent flows. Physics of Fluids, 2022, ⟨10.1063/5.0088409⟩. ⟨hal-03661928⟩
Guanxiong Wang, Song Zhao, Pierre Boivin, Eric Serre, Pierre Sagaut. A new hybrid lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation. Physics of Fluids, 2022, 34 (4), pp.046114. ⟨10.1063/5.0091517⟩. ⟨hal-03796386⟩ Plus de détails...
A new low-Mach algorithm for the thermal lattice Boltzmann method (LBM) is proposed aiming at reducing the computational cost of thermal flow simulations in the low Mach number limit. The well-known low Mach number approximation is adopted to accelerate the simulations by enlarging the time step through re-scaling the psuedoacoustic speed to the same order of the fluid motion velocity. This specific process is inspired by the similarity between the artificial compressibility method and the isothermal LBM and is further extended to its thermal counterpart. It must be emphasized that such low-Mach acceleration strategy is in a general form, thus can be easily applied to other compressible LB methods. The present method overcomes the drawback of the classical pressure gradient scaling method due to the pressure gradient changing. The new algorithm is validated by various well-documented academic test cases in laminar [one dimensional gravity column, 2D (two dimensional) rising thermal bubble, and 2D differentially heated square cavity] and turbulent [3D (three dimensional) Taylor–Green vortex and 3D heated cylinder] regimes. All the results show excellent agreement with the reference data and high computational efficiency.
Guanxiong Wang, Song Zhao, Pierre Boivin, Eric Serre, Pierre Sagaut. A new hybrid lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation. Physics of Fluids, 2022, 34 (4), pp.046114. ⟨10.1063/5.0091517⟩. ⟨hal-03796386⟩
Guanxiong Wang, Song Zhao, Pierre Boivin, Eric Serre, Pierre Sagaut. A new hybrid Lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation. Physics of Fluids, 2022, Physics of fluids, 34 (046114). ⟨hal-03636905⟩ Plus de détails...
Guanxiong Wang, Song Zhao, Pierre Boivin, Eric Serre, Pierre Sagaut. A new hybrid Lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation. Physics of Fluids, 2022, Physics of fluids, 34 (046114). ⟨hal-03636905⟩
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⟩
T. Coratger, G. Farag, S. Zhao, Pierre Boivin, P. Sagaut. Large-eddy lattice-Boltzmann modeling of transonic flows. Physics of Fluids, 2021, 33 (11), pp.115112. ⟨10.1063/5.0064944⟩. ⟨hal-03424286⟩ Plus de détails...
T. Coratger, G. Farag, S. Zhao, Pierre Boivin, P. Sagaut. Large-eddy lattice-Boltzmann modeling of transonic flows. Physics of Fluids, 2021, 33 (11), pp.115112. ⟨10.1063/5.0064944⟩. ⟨hal-03424286⟩
Pierre Boivin, M. Tayyab, S. Zhao. Benchmarking a lattice-Boltzmann solver for reactive flows: Is the method worth the effort for combustion?. Physics of Fluids, 2021, 33 (7), pp.071703. ⟨10.1063/5.0057352⟩. ⟨hal-03276189⟩ Plus de détails...
Pierre Boivin, M. Tayyab, S. Zhao. Benchmarking a lattice-Boltzmann solver for reactive flows: Is the method worth the effort for combustion?. Physics of Fluids, 2021, 33 (7), pp.071703. ⟨10.1063/5.0057352⟩. ⟨hal-03276189⟩
Arnaud Mura, Song Zhao. Turbulence topology evolution in weakly turbulent premixed flames. Physics of Fluids, 2021, 33 (3), pp.035110. ⟨10.1063/5.0039330⟩. ⟨hal-03442314v2⟩ Plus de détails...
In turbulent premixed flames, not only the isotropy of velocity fluctuations is altered by the thermal expansion effect, the dissipative structure of the turbulent flowfield and the flow topology are also deeply influenced by the flame. Considering the joint probability density function (JPDF) of the second and third invariants of the velocity gradient tensor (VGT)-or its traceless counterpart-is a classical way to educe the topology of turbulent flows at these smallest scales. These quantities are analyzed by considering direct numerical simulation databases of premixed flame kernel growth in homogeneous isotropic turbulence (HIT). Two conditions of turbulence-combustion interaction (TCI) are considered, which correspond to two distinct values of the Bray number. The analysis of the VGT shows that the propagating premixed flame and its associated density variations significantly modify the turbulence structure and flow topology. To understand this behavior as the flow interacts with the flame front, Lagrangian dynamics of the VGT and its invariants are studied by considering the conditional mean rate of change vectors. Special emphasis is thus placed on the Lagrangian evolution equations (LEE) of these invariants. To the best of the authors' knowledge, this is first time that such budgets are scrutinized in premixed combustion conditions. The pressure Hessian contribution to the VGT invariants transport equations is shown to be one of the leading-order terms in this evolution, making it critically important to the flow dynamics and turbulence structure.
Arnaud Mura, Song Zhao. Turbulence topology evolution in weakly turbulent premixed flames. Physics of Fluids, 2021, 33 (3), pp.035110. ⟨10.1063/5.0039330⟩. ⟨hal-03442314v2⟩
M. Tayyab, S. Zhao, Pierre Boivin. Lattice-Boltzmann modeling of a turbulent bluff-body stabilized flame. Physics of Fluids, 2021, 33 (3), pp.031701. ⟨10.1063/5.0038089⟩. ⟨hal-03160901⟩ Plus de détails...
This letter reports the first large eddy simulation of a turbulent flame using a Lattice-Boltzmann model. To that end, simulation of a bluff-body stabilized propane-air flame is carried out, showing an agreement similar to those available in the literature. Computational costs are also reported, indicating that Lattice-Boltzmann modelling of reactive flows is competitive, with around 1000cpuh required to simulate one residence time in the 1,5m burner.
M. Tayyab, S. Zhao, Pierre Boivin. Lattice-Boltzmann modeling of a turbulent bluff-body stabilized flame. Physics of Fluids, 2021, 33 (3), pp.031701. ⟨10.1063/5.0038089⟩. ⟨hal-03160901⟩
G. Farag, S. Zhao, G. Chiavassa, Pierre Boivin. Consistency study of Lattice-Boltzmann schemes macroscopic limit. Physics of Fluids, 2021, 33 (3), pp.037101. ⟨10.1063/5.0039490⟩. ⟨hal-03160898⟩ Plus de détails...
Owing to the lack of consensus about the way Chapman-Enskog should be performed, a new Taylor-Expansion of Lattice-Boltzmann models is proposed. Contrarily to the Chapman-Enskog expansion, recalled in this manuscript, the method only assumes an su ciently small time step. Based on the Taylor expansion, the collision kernel is reinterpreted as a closure for the stress-tensor equation. Numerical coupling of Lattice-Boltzmann models with other numerical schemes, also encompassed by the method, are shown to create error terms whose scalings are more complex than those obtained via Chapman-Enskog. An athermal model and two compressible models are carefully analyzed through this new scope, casting a new light on each model's consistency with the Navier-Stokes equations.
G. Farag, S. Zhao, G. Chiavassa, Pierre Boivin. Consistency study of Lattice-Boltzmann schemes macroscopic limit. Physics of Fluids, 2021, 33 (3), pp.037101. ⟨10.1063/5.0039490⟩. ⟨hal-03160898⟩
Isabelle Cheylan, Song Zhao, Pierre Boivin, Pierre Sagaut. Compressible pressure-based Lattice-Boltzmann applied to humid air with phase change. Applied Thermal Engineering, 2021, pp.116868. ⟨10.1016/j.applthermaleng.2021.116868⟩. ⟨hal-03180596⟩ Plus de détails...
A new compressible pressure-based Lattice Boltzmann Method is proposed to simulate humid air flows with phase change. The variable density and compressible effects are fully resolved, effectively lifting the Boussinesq approximation commonly used, e.g. for meteorological flows. Previous studies indicate that the Boussinesq assumption can lead to errors up to 25%, but the model remains common, for compressible models often suffer from a lack of stability. In order to overcome this issue, a new pressure-based solver is proposed, exhibiting excellent stability properties. Mass and momentum conservation equations are solved by a hybrid recursive regularized Lattice-Boltzmann approach, whereas the enthalpy and species conservation equations are solved using a finite volume method. The solver is based on a pressure-based method coupled with a predictor-corrector algorithm, and incorporates a humid equation of state, as well as a specific boundary condition treatment for phase change. In particular, boundary conditions that handle mass leakage are also proposed and validated. Three test cases are investigated in order to validate this new approach: the Rayleigh-Bénard instability applied to humid air, the atmospheric rising of a condensing moist bubble, and finally the evaporation of a thin liquid film in a vertical channel. Results indicate that the proposed pressure-based Lattice-Boltzmann model is stable and accurate on all cases.
Isabelle Cheylan, Song Zhao, Pierre Boivin, Pierre Sagaut. Compressible pressure-based Lattice-Boltzmann applied to humid air with phase change. Applied Thermal Engineering, 2021, pp.116868. ⟨10.1016/j.applthermaleng.2021.116868⟩. ⟨hal-03180596⟩
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⟩
S. Zhao, G. Farag, Pierre Boivin, P. Sagaut. Toward fully conservative hybrid lattice Boltzmann methods for compressible flows. Physics of Fluids, 2020, 32 (12), pp.126118. ⟨10.1063/5.0033245⟩. ⟨hal-03087980⟩ Plus de détails...
S. Zhao, G. Farag, Pierre Boivin, P. Sagaut. Toward fully conservative hybrid lattice Boltzmann methods for compressible flows. Physics of Fluids, 2020, 32 (12), pp.126118. ⟨10.1063/5.0033245⟩. ⟨hal-03087980⟩
G. Farag, S. Zhao, T. Coratger, Pierre Boivin, G. Chiavassa, et al.. A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows. Physics of Fluids, 2020, 32 (6), pp.066106. ⟨10.1063/5.0011839⟩. ⟨hal-02885427⟩ Plus de détails...
A new pressure-based Lattice-Boltzmann method (HRR-p) is proposed for the simulation of flows for Mach numbers ranging from 0 to 1.5. Compatible with nearest neighbor lattices (e.g. D3Q19), the model consists of a predictor step comparable to classical athermal Lattice-Boltzmann methods, appended with a fully local and explicit correction step for the pressure. Energy conservation-for which the Hermi-tian quadrature is not accurate enough on such lattice-is solved via a classical finite volume MUSCL-Hancock scheme based on the entropy equation. The Euler part of the model is then validated for the transport of three canonical modes (vortex, en-tropy, and acoustic propagation), while its diffusive/viscous properties are assessed via thermal Couette flow simulations. All results match the analytical solutions, with very limited dissipation. Lastly, the robustness of the method is tested in a one dimensional shock tube and a two-dimensional shock-vortex interaction.
G. Farag, S. Zhao, T. Coratger, Pierre Boivin, G. Chiavassa, et al.. A pressure-based regularized lattice-Boltzmann method for the simulation of compressible flows. Physics of Fluids, 2020, 32 (6), pp.066106. ⟨10.1063/5.0011839⟩. ⟨hal-02885427⟩
M. Tayyab, S. Zhao, Y. Feng, Pierre Boivin. Hybrid regularized Lattice-Boltzmann modelling of premixed and non-premixed combustion processes. Combustion and Flame, 2020, 211, pp.173-184. ⟨10.1016/j.combustflame.2019.09.029⟩. ⟨hal-02346556⟩ Plus de détails...
A Lattice-Boltzmann model for low-Mach reactive flows is presented, built upon our recently published model (Comb & Flame, 196, 2018). The approach is hybrid and couples a Lattice-Boltzmann solver for the resolution of mass and momentum conservation and a finite difference solver for the energy and species conservation. Having lifted the constant thermodynamic and transport properties assumptions, the model presented now fully accounts for the classical reactive flow thermodynamic closure: each component is assigned NASA coefficients for calculating its thermodynamic properties. A temperature-dependent viscosity is considered, from which are deduced thermo-diffusive properties via specification of Prandtl and component-specific Schmidt numbers. Another major improvement from our previous contribution is the derivation of an advanced collision kernel compatible of multi-component reactive flows stable in high shear flows. Validation is carried out first on premixed configurations, through simulation of the planar freely propagating flame, the growth of the associated Darrieus-Landau instability and three regimes of flame-vortex interaction. A double shear layer test case including a flow-stabilized diffusion flame is then presented and results are compared with DNS simulations, showing excellent agreement.
M. Tayyab, S. Zhao, Y. Feng, Pierre Boivin. Hybrid regularized Lattice-Boltzmann modelling of premixed and non-premixed combustion processes. Combustion and Flame, 2020, 211, pp.173-184. ⟨10.1016/j.combustflame.2019.09.029⟩. ⟨hal-02346556⟩
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
