title: Comparative study of the lattice Boltzmann models for Allen-Cahn and Cahn-Hilliard equations.
abstract: In this paper, a comparative study of the lattice Boltzmann (LB) models for the Allen-Cahn (A-C) and Cahn-Hilliard (C-H) equations is conducted. To this end, a new LB model for the A-C equation is first proposed, where the equilibrium distribution function and the source term distribution function are delicately designed to recover the A-C equation correctly. The gradient term in this model can be computed by the nonequilibrium part of the distribution function such that the collision process can be implemented locally. Then a detailed numerical study on several classical problems is performed to give a comparison between the present model for the A-C equation and the recently developed LB model [H. Liang et al., Phys. Rev. E 89, 053320 (2014)PLEEE81539-375510.1103/PhysRevE.89.053320] for the C-H equation in terms of tracking the interface of two-phase flow. The results show that the present LB model for the A-C equation is more accurate and more stable, and also has a second-order convergence rate in space, while the convergence rate of the previous LB model for the C-H equation is only about 1.5.
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.
authors.forename: H L
authors.initials: HL
authors.lastname: Wang
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.|State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
authors.forename: Z H
authors.initials: ZH
authors.lastname: Chai
authors.affiliation: School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China.|State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China.
authors.forename: B C
authors.initials: BC
authors.lastname: Shi
authors.affiliation: Department of Physics, Hangzhou Dianzi University, Hangzhou 310018, China.
authors.forename: H
authors.initials: H
authors.lastname: Liang