Higher Order Galilean Invariant Lattice Boltzmann Model and Entropic Gauss-Hermite Quadrature

We introduce a novel scheme obtained by distorting energy level of the velocity shells, which give rise to additional degree of freedom for the same number of discrete velocities. We claim that the proposed model is the smallest known 3-dimensional system in terms of the number of velocities for the accuracy of full sixth-order moments. Velocity profile is solved for the current model, which contains the Knudsen layers terms, and the Knudsen minima exists for the flowrate.