%A Raúl Machado %T On the generalized Hermite-based lattice Boltzmann construction, lattice sets, weights, moments, distribution functions and high-order models %0 Journal Article %D 2014 %J Front. Phys. %J Frontiers of Physics %@ 2095-0462 %R 10.1007/s11467-014-0417-1 %P 490-510 %V 9 %N 4 %U {https://journal.hep.com.cn/fop/EN/10.1007/s11467-014-0417-1 %8 2014-08-26 %X

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.