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• W2040900959 abstract "The lattice Boltzmann equation replaces continuous particle velocity space by a finite set; the velocity distribution function then varies over a finite-dimensional vector space instead of over an infinite-dimensional function space. The number of linearly independent moments of the distribution function in a lattice Boltzmann model cannot exceed the number of velocities; finite dimensionality therefore necessarily induces linear dependences among the moments that do not exist in a continuous theory. Given a finite velocity set, it is important to know which moments are free of these dependences. Elementary group theory is applied to the solution of this problem. It is found that decomposing the velocity set into subsets that transform among themselves under an appropriate symmetry group makes it straightforward to uncover linear dependences among the moments. The construction of some standard two- and three-dimensional models is reviewed from this viewpoint, and procedures for constructing higher-dimensional models are suggested." @default.
• W2040900959 created "2016-06-24" @default.
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• W2040900959 date "2008-03-25" @default.
• W2040900959 modified "2023-10-18" @default.
• W2040900959 title "Theory of the lattice Boltzmann equation: Symmetry properties of discrete velocity sets" @default.
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• W2040900959 doi "https://doi.org/10.1103/physreve.77.036709" @default.
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