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

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.