A volume-preserving sharpening approach for the propagation of sharp phase boundaries in multiphase lattice Boltzmann simulations

Abstract

Lattice Boltzmann models that recover a macroscopic description of multiphase flow of immiscible liquids typically represent the boundaries between phases using a scalar function, the phase field, that varies smoothly over several grid points. Attempts to tune the model parameters to minimise the thicknesses of these interfaces typically lead to the interfaces becoming fixed to the underlying grid instead of advecting with the fluid velocity. This phenomenon, known as lattice pinning, is strikingly similar to that associated with the numerical simulation of conservation laws coupled to stiff algebraic source terms. We present a lattice Boltzmann formulation of the model problem proposed by LeVeque

Characterization of immiscible fluid displacement processes with various capillary numbers and viscosity ratios in 3D natural sandstone

“…It should be noted that it is difficult to consider a significant density contrast of two-phase fluids using the present model, and such conditions require the use of other more appropriate models (e.g., Bao and Schaefer, 10 bounceback scheme. The lattice pinning problem in this multiphase model, which implies that the interface cannot move when the convection flow is weak, has been recognized by several authors (Leclaire et al, 2012;Reis and Dellar, 2011;Latva-Kokko and Rothman, 2005). Due to this limitation, we simulate the two-phase flow in a relatively high Ca (10 -5~1 0 -1 ) regime ( Figure 3).…”

Chromodynamic multirelaxation-time lattice Boltzmann scheme for fluids with density difference

“…for a red drop, with the usual convention on surface normal, n. Color field ρ N is considered continuous, changing rapidly only in the interfacial region. Its variation may be sharpened [21,22] and it may be used to control kinematic viscosity, by setting ν(ρ N ) = 1 6 ( 2 λ 3 (ρ N ) − 1) [24,34]. Kinetic-scale, postcollision color segregation is an adaptation of Ref.…”

“…(Note, Reiss and Phillips [20] developed an interfacial perturbation to replace immersed boundary forces, which is the most physically consistent encapsulation of MCLB interfacial tension as a perturbation to the stress.) The method is the most direct descendant of Gunstensen's original, in which the problems of lattice pinning and faceting have been reduced, Reiss and Dellar [21,22] having identified their origin and a means to reduce the impact of the unphysical interface width scale. Such limitations notwithstanding, chromodynamic method is robust, transparent, has low microcurrent and allows direct parametrization of interfacial tension, width [23], and the separated fluids' viscosity contrast [24], the interface propagation in the base model is reasonably understood [25,26] (but see below) and different color gradient (CG) models have been applied successfully to numerical study of steady and unsteady flow [27][28][29][30].…”