Modified curved boundary scheme for two-phase lattice Boltzmann simulations

Abstract

The lattice Boltzmann (LB) method has gained much success in a variety of fields involving fluid flow and/or heat transfer. In this method, the bounce-back scheme is a popular technique for the treatment of nonslip boundaries. However, this scheme leads to a staircase representation of curved walls. Therefore many curved boundary schemes have been proposed, but mostly have detrimental effects such as mass leakage. Several correction schemes have been suggested for simulating single-phase flows, but very few discussions or studies have been made for two-phase LB simulations with curved boundaries. In this paper, the performances of three well-known schemes for dealing with curved boundaries in two-phase LB simulations are investigated through modeling a droplet resting on a circular cylinder. For all of the investigated schemes, the results show that the simulated droplet rapidly “evaporates” under the nonslip and isothermal condition, owing to the imbalance between the mass streamed out of the system by outgoing distribution functions and the mass streamed into the system by incoming distribution functions at each boundary node. Based on the numerical investigation, we formulate two modified mass-conservative curved boundary schemes for two-phase LB simulations. The accuracy of the modified curved boundary schemes and their capability of conserving mass in two-phase LB simulations are numerically demonstrated.