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On the generalized Hermite-based lattice Boltzmann construction, lattice sets, weights, moments, distribution functions and high-order models

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Abstract

The influence of the use of the generalized Hermite polynomial on the Hermite-based lattice Boltzmann (LB) construction approach, lattice sets, the thermal weights, moments and the equilibrium distribution function (EDF) are addressed. A new moment system is proposed. The theoretical possibility to obtain a unique high-order Hermite-based singel relaxation time LB model capable to exactly match some first hydrodynamic moments thermally i) on-Cartesian lattice, ii) with thermal weights in the EDF, iii) whilst the highest possible hydrodynamic moments that are exactly matched are obtained with the shortest on-Cartesian lattice sets with some fixed real-valued temperatures, is also analyzed.

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Machado, R. On the generalized Hermite-based lattice Boltzmann construction, lattice sets, weights, moments, distribution functions and high-order models. Front. Phys. 9, 490–510 (2014). https://doi.org/10.1007/s11467-014-0417-1

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