Central Moment Lattice Boltzmann Method with Fokker-Planck Guided Collision for Non-Equilibrium Flows*

Central moments-based lattice Boltzmann method (LBM), a recent approach for flow simulations, is generally based on the relaxation of various central moments to their equilibria under collision. The latter is usually constructed either directly from the Maxwell distribution function or by exploiting its factorization property. We propose a central moment LBM from a different perspective, where its collision operator is constructed by matching the changes in different discrete central moments under collision to the changes in the corresponding continuous central moments as given by the Fokker-Planck (FP) collision model of the Boltzmann equation. The resulting formulation can be interpreted in terms of the relaxation of the various central moments to “equilibria” that depend only on the adjacent, lower order post-collision moments. We designate such newly constructed chain of equilibria as the Markovian central moment attractors and the relaxation rates are based on scaling the drift coefficient of the FP model by the order of the participating moment. We will demonstrate the accuracy and robustness of our new formulation for simulations of a variety of flows using the standard D2Q9 and D3Q27 lattices and also present a comparison against other collision models.