39 research outputs found
Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics
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
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
and (2) introducing a controllable numerical dissipation 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
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
International audienc
High-order extension of the recursive regularized lattice Boltzmann method
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
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
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