The lattice Boltzmann method for nearly incompressible flows

Lallemand, Pierre; Luo, Li‐Shi; Krafczyk, Manfred; Yong, Wen‐An

doi:10.1016/j.jcp.2020.109713

Cited by 81 publications

(35 citation statements)

References 405 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The lattice Boltzmann (LB) methods, which arise as minimally discretized numerical schemes of the Boltzmann transport equation-a cornerstone formulation in kinetic theory, have attracted much attention in recent decades [1][2][3][4][5]. As a mesoscopic approach, these methods have enriched the variety of computational fluid dynamics (CFD) techniques that are being developed and has been applied to a wide range of fluid flows successfully [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

View full text Add to dashboard Cite

Lattice Boltzmann (LB) methods are usually developed on cubic lattices that discretize the configuration space using uniform grids. For efficient computations of anisotropic and inhomogeneous flows, it would be beneficial to develop LB algorithms involving the collision-and-stream steps based on orthorhombic cuboid lattices. We present a new 3D central moment LB scheme based on a cuboid D3Q27 lattice. This scheme involves two free parameters representing the ratios of the characteristic particle speeds along the two directions with respect to those in the remaining direction, and these parameters are referred to as the grid aspect ratios. Unlike the existing LB schemes for cuboid lattices, which are based on orthogonalized raw moments, we construct the collision step based on the relaxation of central moments and avoid the orthogonalization of moment basis, which leads to a more robust formulation. Moreover, prior cuboid LB algorithms prescribe the mappings between the distribution functions and raw moments before and after collision by using a moment basis designed to separate the trace of the second order moments (related to bulk viscosity) from its other components (related to shear viscosity), which lead to cumbersome relations for the transformations. By contrast, in our approach, the bulk and shear viscosity effects associated with the viscous stress tensor are naturally segregated only within the collision step and not for such mappings, while the grid aspect ratios are introduced via simpler pre- and post-collision diagonal scaling matrices in the above mappings. These lead to a compact approach, which can be interpreted based on special matrices. It also results in a modular 3D LB scheme on the cuboid lattice, which allows the existing cubic lattice implementations to be readily extended to those based on the more general cuboid lattices. To maintain the isotropy of the viscous stress tensor of the 3D Navier–Stokes equations using the cuboid lattice, corrections for eliminating the truncation errors resulting from the grid anisotropy as well as those from the aliasing effects are derived using a Chapman–Enskog analysis. Such local corrections, which involve the diagonal components of the velocity gradient tensor and are parameterized by two grid aspect ratios, augment the second order moment equilibria in the collision step. We present a numerical study validating the accuracy of our approach for various benchmark problems at different grid aspect ratios. In addition, we show that our 3D cuboid central moment LB method is numerically more robust than its corresponding raw moment formulation. Finally, we demonstrate the effectiveness of the 3D cuboid central moment LB scheme for the simulations of anisotropic and inhomogeneous flows and show significant savings in memory storage and computational cost when used in lieu of that based on the cubic lattice.

show abstract

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Yahia

Schupbach

Premnath

2021

Fluids

View full text Add to dashboard Cite

show abstract

“…Here and in the following i,j∈falsefalse{0,1,2,…,q−1falsefalse} are reserved as discrete velocity counters. The MRT collision operator can be generically formulated as [36] Ji=−Kifalse[bold-italicf−feqfalse], where feq=false(fieqfalse)i∈double-struckRq is the typical second-order truncated Maxwellian [4,5] to obtain (2.1) in the diffusive limit, and Ki=false(Ki,jfalse)j∈double-struckRq denotes the i-th row vector of the matrix K=M−1SM∈double-struckRq×q. The relaxation matrix S=diagfalse(bold-italicsfalse)∈double-struckRq×q contains the relaxation frequencies ...…”

Section: Methodsmentioning

confidence: 99%

“…In the past three decades, the lattice Boltzmann method (LBM) has attracted increasing attention for the numerical simulation of various multiphysics problems [1–3]. Owing to its high parallelizability and ease of implementation, especially as a numerical method to approximate the weakly compressible Navier–Stokes equations (NSE) for turbulent fluid flow, the LBM has matured in applicability and extensibility [4]. On the one hand, generic passages to include large eddy simulation (LES) techniques in a consistent way have been proposed [5].…”

Section: Introductionmentioning

confidence: 99%

“…the approximate deconvolution method [7–9], have been combined with LBM. On the other hand, the capabilities of LBM as a tool for direct numerical simulation (DNS) [4,10] have been investigated. From a third perspective, some contributions [10–17] also provide evidence that specific LBM variants comprise numerical features which resemble implicit turbulence model behaviour through numerical dissipation [18].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Simonis

Haussmann

Kronberg

et al. 2021

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

show abstract

“…In the applications, the discretization of these equations in the velocity (and physical) space is usually performed. One of the most popular discretization approaches is the Lattice-Boltzmann (LB) method [2][3][4][5] which was initially developed as an alternative to the continuum fluid methods like Navier-Stokes equations [6]; furthermore, the method has been extended to the rarefied flows modeling [7][8][9][10][11][12][13][14][15][16][17][18][19]. The conventional LB model has the following form…”

Section: Introductionmentioning

confidence: 99%

Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Ilyin

2021

Mathematics

View full text Add to dashboard Cite

In this paper, we consider the development of the two-dimensional discrete velocity Boltzmann model on a nine-velocity lattice. Compared to the conventional lattice Boltzmann approach for the present model, the collision rules for the interacting particles are formulated explicitly. The collisions are tailored in such a way that mass, momentum and energy are conserved and the H-theorem is fulfilled. By applying the Chapman–Enskog expansion, we show that the model recovers quasi-incompressible hydrodynamic equations for small Mach number limit and we derive the closed expression for the viscosity, depending on the collision cross-sections. In addition, the numerical implementation of the model with the on-lattice streaming and local collision step is proposed. As test problems, the shear wave decay and Taylor–Green vortex are considered, and a comparison of the numerical simulations with the analytical solutions is presented.

show abstract

The lattice Boltzmann method for nearly incompressible flows

Cited by 81 publications

References 405 publications

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Three-Dimensional Central Moment Lattice Boltzmann Method on a Cuboid Lattice for Anisotropic and Inhomogeneous Flows

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Discrete Velocity Boltzmann Model for Quasi-Incompressible Hydrodynamics

Contact Info

Product

Resources

About