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

@article{Lallemand2000TheoryOT, title={Theory of the lattice boltzmann method: dispersion, dissipation, isotropy, galilean invariance, and stability}, author={Lallemand and Luo}, journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics}, year={2000}, volume={61 6 Pt A}, pages={ 6546-62 } }

The generalized hydrodynamics (the wave vector dependence of the transport coefficients) of a generalized lattice Boltzmann equation (LBE) is studied in detail. The generalized lattice Boltzmann equation is constructed in moment space rather than in discrete velocity space. The generalized hydrodynamics of the model is obtained by solving the dispersion equation of the linearized LBE either analytically by using perturbation technique or numerically. The proposed LBE model has a maximum number…

## 1,712 Citations

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- 2020

The discrete velocity Boltzmann equations (DVBE) underlie the attainable properties of all numerical lattice Boltzmann methods (LBM). To that regard, a thorough understanding of their intrinsic…

### Investigation of Stability and Hydrodynamics of Different Lattice Boltzmann Models

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- 2004

Stability and hydrodynamic behaviors of different lattice Boltzmann models including the lattice Boltzmann equation (LBE), the differential lattice Boltzmann equation (DLBE), the…

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- 2008

An alternative approach to solving the dispersion equation based on a formal perturbation analysis is described and can be readily applied to other lattices, and does not require the reciprocals of the relaxation times to be small.

### High-order lattice-Boltzmann

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- 2016

Unlike conventional CFD methods, the lattice Boltzmann method (LBM) describes the dynamic behaviour of physical systems in a mesoscopic scale, based on discrete forms of kinetic equations. In…

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- 2017

The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on…

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Results obtained in this study show that correct choices of the "second relaxation coefficient" lead to a more consistent dispersion and dissipation for large values of the first relaxation coefficient, thus improving the stability of the LKS.

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ABSTRACT Various collision and velocity models of the lattice Boltzmann model (LBM) were compared to determine their effects on the efficiency of a three-dimensional homogeneous isotropic decaying…

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