A novel conservative velocity discretization approach for BGK model and the Lattice Boltzmann method

A new hierarchy of isothermal Lattice Boltzmann models is constructed starting from conventional D1Q3 model. Each N-s step in the hierarchy consists of the model having 2N + 1 velocities, the model is constructed using a special summation procedure associated with the probability distribution for a sum of independent identically distributed random variables. The central limit theorem guarantees the convergence of the LB model sequence to BGK equation. Multi-dimensional models can be constructed as the product of 1D models. The procedure for the removal of ballistic streamers is introduced. Several test problems are considered: Poiseuille flow across flat walls and Knudsen paradox, Couette plane flow. It is shown that the models from the hierarchy have good precision in comparison to the conventional Lattice Boltzmann models. Finally, some analytic properties can be obtained: closed form for moment generating function, N−2 error reduction for all moments in comparison to the Gaussian moments.