Fokker-Planck Central Moment Lattice Boltzmann Method for Computation of Turbulent Flows

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by matching the changes in different discrete central moments under collision to those given by the CBE under FP collision. This can be interpreted as a new path in terms of the relaxation of the various central moments to ``equilibria'', which we term as the Markovian central moment attractors that depend on the adjacent lower order post-collision moments and the diffusion coefficient; the relaxation rates are based on scaling the drift coefficient by the order of the moment. We demonstrate its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient in accurately representing flows at high Reynolds numbers. As illustrative examples, we show 3D simulation of turbulent flows and liquid-gas systems with interfacial effects modulated by surfactant effects.