Multirelaxation-time interaction-potential-based lattice Boltzmann model for two-phase flow

Abstract

The application of the lattice Boltzmann method in two-phase flows is often restricted by the numerical instability at low viscosities. In this work, a multirelaxation-time ͑MRT͒ lattice Boltzmann model ͑LBM͒ is developed using the interaction potential approach. With the MRT collision term and a general force term, the new MRT model is able to significantly enhance the numerical stability at low viscosities, without appreciable increase in computation time or memory use. Advanced force formulation using the multirange potential can also be readily incorporated into the current MRT scheme. Numerical tests are first performed in two dimensions under equilibrium conditions. The MRT model is able to reduce the lowest stable viscosity by an order of magnitude compared to the single relaxation time LBM. In addition, the spurious velocity at the gas-liquid interface can also be significantly decreased by tuning the adjustable relaxation parameters. Then two sets of three-dimensional simulations are conducted to investigate the buoyant rise of a gas bubble in a low-viscosity liquid. In particular, millimeter air bubble in water, which is difficult for traditional two-phase LBM due to both low viscosity and high-surface tension, is successfully simulated using the MRT technique developed in this study. The simulated bubble shape and velocity are compared with the experimental results and empirical correlations in the literature, and the satisfactory agreement proves the validity of the MRT-LBM for two-phase flows.

Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model

“…With the MRT collision operator [37,38], the evolution equation of the density distribution function can be written as [28,32,39] …”

“…In addition, McCracken and Abraham [28] have also proposed an incompressible MRT multiphase LB model based on the multiphase LB model of He et al [29]. Besides these models, a MRT free-energy LB model has been devised by Pooley et al [30,31] and a MRT pseudopotential LB model has been formulated by Yu and Fan [32]. Using the MRT free-energy model, Pooley et al [30] have accurately reproduced the well-known Washburn's law and they found that the MRT model can stop the unphysical currents appearing near the interfaces for simulating wetting dynamics [31].…”

Multiphase lattice Boltzmann simulations for porous media applications

“…Recently, several methods have been developed to alleviate the limitations of the original inter-particle potential model and improve its performance. These techniques include incorporating a realistic equation of state into the model [111,112], increasing the isotropy order of the interactive force [113,114], improving the force scheme [115][116][117][118], and using the Multi-Relaxation Time (MRT) scheme [109,119] instead of the BGK approximation. These techniques have been demonstrated to be effective in reducing the magnitude of spurious velocities, eliminating the unphysical dependence of equilibrium density and interfacial tension on viscosity (relaxation time), and increasing the viscosity and density ratios in simple systems [120][121][122][123][124].…”

Lattice Boltzmann simulation of the trapping of a microdroplet in a well of surface energy

“…(23) can greatly suppress unphysical spurious currents in the vicinity of the contact line, avoiding generation of incorrect contact angle in BGK LBM simulations. Note that the use of MRT for reducing spurious currents at interfaces was also found in other multiphase LBMs [43,44,11].…”