A stencil adaptive phase‐field lattice Boltzmann method for two dimensional incompressible multiphase flows

Abstract

SUMMARYThis paper presents a stencil adaptive phase‐field lattice Boltzmann method (LBM) for the simulation of two‐dimensional multiphase flows. In the phase‐field model, the interface is viewed as a layer with finite thickness where physical parameters vary steeply and continuously. In the present study, a phase‐field LBM is used. In this model, the Cahn–Hilliard equation can be correctly recovered by LBM without additional terms. The phase‐field LBM can easily resolve topology change and large deformation of an interface. The major challenge faced by the phase‐field model is to approach sharp interface limit within affordable computational loads. A natural solution is to supplement the phase‐field model with the adaptive mesh refinement technique. In fact, much effort has been devoted to alleviate this issue with regards to Navier–Stokes solvers. However, in the realm of LBM, few works can be found in the literature. The present work is the first endeavour to incorporate the stencil adaptive technique into the phase‐field LBM. The proposed method enables high resolution of interface with considerable savings in grid points. In addition, owing to the symmetric structure of two stencils used, the present adaptive phase‐field LBM is freed from complicated spatial and temporal interpolation and modification of the collision term. First, the accuracy, efficiency and convergence of this method are testified through the simulation of a stationary bubble. Furthermore, its ability to probe several types of interfacial dynamics including bubbly flows and contact line problems has also been demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.