39 research outputs found

    Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

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    The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

    A linear stability analysis of compressible hybrid lattice Boltzmann methods

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    An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite difference (FD) schemes solve an energy equation. Both systems are coupled with each other thanks to an ideal gas equation of state. This work aims at answering some questions regarding the numerical stability of such models, which strongly depends on the choice of numerical parameters. To this extent, several one- and two-dimensional HLBM classes based on different energy variables, formulation (primitive or conservative), collision terms and numerical schemes are scrutinized. Once appropriate corrective terms introduced, it is shown that all continuous HLBM classes recover the Navier-Stokes Fourier behavior in the linear approximation. However, striking differences arise between HLBM classes when their discrete counterparts are analysed. Multiple instability mechanisms arising at relatively high Mach number are pointed out and two exhaustive stabilization strategies are introduced: (1) decreasing the time step by changing the reference temperature TrefT_{ref} and (2) introducing a controllable numerical dissipation σ\sigma via the collision operator. A complete parametric study reveals that only HLBM classes based on the primitive and conservative entropy equations are found usable for compressible applications. Finally, an innovative study of the macroscopic modal composition of the entropy classes is conducted. Through this study, two original phenomena, referred to as shear-to-entropy and entropy-to-shear transfers, are highlighted and confirmed on standard two-dimensional test cases.Comment: 49 pages, 23 figure

    Lattice Boltzmann method for computational aeroacoustics on non-uniform meshes: a direct grid coupling approach

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    The present study proposes a highly accurate lattice Boltzmann direct coupling cell-vertex 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~\textit{et al. 2020}) on the deleterious effect of non-hydrodynamic modes crossing mesh transitions, which can be addressed using an appropriate collision model. The Hybrid Recursive Regularized model is then used for this study. The grid coupling algorithm is assessed and compared to a widely-used cell-vertex algorithm on an acoustic pulse test case, a convected vortex and a turbulent circular cylinder wake flow at high Reynolds number.Comment: also submitted to Journal of Computational Physic

    Updated Hybrid Lattice-Boltzmann Model for Low-Mach Reactive Flows

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    High-order extension of the recursive regularized lattice Boltzmann method

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    This thesis is dedicated to the derivation and the validation of a new collision model as a stabilization technique for high-order lattice Boltzmann methods (LBM). More specifically, it intends to stabilize simulations of: (1) isothermal and weakly compressible flows at high Reynolds numbers, and (2) fully compressible flows including discontinuities such as shock waves. The new collision model relies on an enhanced regularization step. The latter includes a recursive computation of nonequilibrium Hermite polynomial coefficients. These recursive formulas directly derive from the Chapman-Enskog expansion, and allow to properly filter out second- (and higher-) order nonhydrodynamic contributions in underresolved conditions. This approach is even more interesting since it is compatible with a very large number of velocity sets. This high-order LBM is first validated in the isothermal case, and for high-Reynolds number flows. The coupling with a shock-capturing technique allows to further extend its validity domain to the simulation of fully compressible flows including shockwaves. The present work ends with the linear stability analysis(LSA) of the new approach, in the isothermal case. This leads to a proper quantification of the impact induced by each discretization (velocity and numerical) on the spectral properties of the related set of equations. The LSA of the recursive regularized LBM finally confirms the drastic stability gain obtained with this new approach

    Investigation of Lattice Boltzmann Methods applied to multiphase flows

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    The purpose of this thesis is the study of Lattice Boltzmann Methods (LBM), applied to multiphase flows. First, general principles of statistical physics and of Lattice Boltzmann Methods are introduced, followed by a historical review about Lattice Gas Automata. A state of the art of the multiphase flow simulation methods is then proposed, with a particular emphasize on diffuse interface methods. In particular, the phase field methods are introduced, and different methods allowing to numerically simulate surface tension are also presented. A second review concerning multiphase flow simulation in a Lattice Boltzmann framework is presented. More precisely, general principals are presented, and the four major methods, Color Gradient, Pseudo-Potential, Free Energy and HCZ, are successively presented. Lattice Boltzmann Methods advanced notions are then introduced, in particular, a Taylor expansion based method that allows to determine Lattice Boltzmann schemes equivalent macroscopic equation is described. A Gradient Color method theoretical study is proposed. First, an original reformulation of the algorithm allowing an improvement in computational efficiency is proposed. The Taylor expansion method is then applied to Gradient Color Method in order to determine the high order error induced by the numerical scheme. This expression allows to demonstrate how the degree of isotropy is essential to the scheme numerical stability. In particular, a numerical operator allowing to introduce an equation of states that differs from the athermal perfect gas equation is proposed. This operator efficiency is illustrated by being applied to academical testcases. The Taylor expansion method is also applied in order to show how the Color Gradient Method allows to solve an Allen-Cahn phase field equation. This theoretical result is then validated numerically. Finally, an original improved version of the Gradient Color Method is proposed. In this method, the efficient formulation and the isotropic Equation of State operator is used, and an original temporal correction term is proposed. This correction term improves the scheme numerical stability and allows to expands the method application range to higher density ratios. Finally, this method is validated through academical testcases

    Towards Wall-Modeled LES with Lattice Boltzmann Method for Aeroacoustics: Application and Understanding

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    The aim of this work is direct noise computation (DNC) of high-lift wing using Wall-modeled LES (WMLES) with Lattice Boltzmann Method (LBM). There are two aspects of this work: application, where the commercial LB solver ProLB is used as a DNC tool to compute highlift noise, and understanding, where an effort is made to gather know-how about the intricate details/nuances involved with wall-modeling in LBM by implementing it. For the present study, the Category 6 LEISA2 F16 high-lift configuration from the Benchmark for Airframe Noise Computations (BANC) workshop has been selected as the high-lift airfoil. The three-element unswept high-lift wing with deployed slat and flap is resolved on a mesh with different spanwise resolutions ranging from 5% to 20% clean chord length. Periodic boundary condition is used along the spanwise direction. The results of WMLES-LBM simulations were validated for relative accuracy against the extensive experimental BANC database. Results of both aerodynamic and aeroacoustic comparison with the experiments is discussed in detail. For the aspect of understanding, a quasi-analytical wall function for flat walls has been introduced into the academic LB research code Musubi. Results of the simulation were compared with the published DNS results
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