On lattice Boltzmann modeling of phase transition in an isothermal non-ideal fluid

Abstract

A new lattice Bolztmann BGK model for isothermal non-ideal fluid is introduced and formulated for an arbitrary lattice, composed of several D -dimensional sublattices. The model is a generalization of the free-energy-based lattice Bolztmann BGK model developed by Swift et al. (1996). We decompose the equilibrium distribution function in the BGK collision operator into ideal and non-ideal parts and employ second-order Chapman–Enskog expansion for treatment of both parts. Expansion coefficients for the non-ideal part are, in general, functions of macroscopic variables, designed to reproduce desired pressure tensor (thermodynamic aspects) and to eliminate the aphysical artifacts in the lattice Bolztmann model. The new model is shown to significantly improve quality of lattice Boltzmann modeling of interfacial phenomena. In the present model, the interface spurious velocity is orders of magnitude lower than that for existing LBE models of non-ideal fluids. A new numerical scheme for treatment of advection and collision operators is proposed to significantly extend stability limits, in comparison to existing solution methods of the ‘master’ lattice Bolztmann equation. Implementation of a ‘multifractional stepping’ procedure for advection operator allows to eliminate severe restriction CFL=1 in traditionally used ‘stream-and-collide’ scheme. An implicit trapezoidal discretization of the collision operator is shown to enable excellent performance of the present model in stiff high-surface-tension regime. The proposed numerical scheme is second order accurate, both in time and space.