Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability

By Pierre Lallemand, Li-Shi Luo. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000

2,110 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/8442cbdbd36da4fbe2246f259d5953d1fb4a2ee1

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In Computational Mechanics

In Electrical and Electronic Engineering

Citations in the corpus

Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method (2014, methodology): “The diagonal collision matrix bS is given by [26].”
Assessment of the two relaxation time Lattice‐Boltzmann scheme to simulate Stokes flow in porous media (2012, neutral): “=3 p , [Lallemand and Luo, 2000].”
Incompressible limits of lattice Boltzmann equations using multiple relaxation times (2003, methodology): “Lallemand and Luo [25] used a non-hydrodynamic relaxation time τg slightly larger that∆t/2, while Higueraet al.”
Lattice Boltzmann method for moving boundaries (2003, background): “The constraints of isotropy may lead to some relationships between these relaxation parameters [19,27].”
Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks (2012, methodology): “In addition, the MRT algorithm has also been reported to give enhanced stability when treating very low viscosities (Lallemand and Luo 2000).”
Lattice Boltzmann Method for 3-D Flows with Curved Boundary (2000, methodology): “However, the stability of the LBE models, which is very much a ected by these spurious invariants, di ers from one model to another, and also depends on other factors such as boundary conditions and the local Reynolds number [18].”
Lattice‐Boltzmann simulation of two‐phase flow in porous media (2004, methodology): “It was shown by Lallemand and Luo [2000] and d’Humieres et al. [2002] that a multiple-relaxationtime (MRT) LB model, which separates relaxations for the kinetic modes, is more stable than the BGK LB model, which uses a single-time relaxation approximation.”
Analysis of lattice Boltzmann equation for microscale gas flows: Relaxation times, boundary conditions and the Knudsen layer (2008, positive): “Without loss of generality, here we consider the two-dimensional-nine-velocity (D2Q9) LBE model with a multiple-relaxation-time (MRT) collision operator (d'Humieres 1992 , Lallemand and Luo 2000 ):where { f i ( x , t ): i = 0,1,…,8} are the discrete distribution functions at position x and”
TeraFLOP computing on a desktop PC with GPUs for 3D CFD (2008, neutral): “The relaxation rates s n and s 0 n are related to the viscosity by The collision rates s e and s h are not relevant for the incompressible limit of the Navier–Stokes equations and can be chosen in the range ]0, 2[ to improve stability (Lallemand and Luo 2000).”
Comparison between lattice Boltzmann method and Navier-Stokes high order schemes for computational aeroacoustics (2009, neutral): “The LBM–MRT model The multiple relaxation time model [10,16], has been presented recently and is an alternative to the standard BGK model.”
Study of Simple Hydrodynamic Solutions with the Two-Relaxation-Times Lattice Boltzmann Scheme (2008, methodology): “These models are simple and efficient, explicit in time, numerical schemes for solving the hydrodynamic Navier-Stokes equations in two [21, 27] and three dimensions [22, 23].”