TY - JOUR

T1 - Nonlocal operator method for the Cahn-Hilliard phase field model

AU - Ren, Huilong

AU - Zhuang, Xiaoying

AU - Trung, Nguyen Thoi

AU - Rabczuk, Timon

N1 - Funding Information: The authors acknowledge the supports from the National Basic Research Program of China (973 Program: 2011CB013800) and NSFC (51474157), the Ministry of Science and Technology of China (Grant No.SLDRCE14-B-28, SLDRCE14-B-31).

PY - 2021/5

Y1 - 2021/5

N2 - In this paper we propose a Nonlocal Operator Method (NOM) for the solution of the Cahn-Hilliard (CH) equation exploiting the higher order continuity of the NOM. The method is derived based on the method of weighted residuals and implemented in 2D and 3D. Periodic boundary conditions and solid-wall boundary conditions are considered. For these boundary conditions, the highest order in the NOM scheme is 2 and 3, respectively. The proposed NOM makes use of variable support domains allowing for adaptive refinement. The generalized α-method is employed for time integration and the Newton-Raphson method to iterate nonlinearity. The performance of the proposed method is demonstrated for several two and three dimensional benchmark problems. We also implemented a CH equation with 6th order partial differential derivative and studied the influence of higher order coefficients on the pattern evolution of the phase field.

AB - In this paper we propose a Nonlocal Operator Method (NOM) for the solution of the Cahn-Hilliard (CH) equation exploiting the higher order continuity of the NOM. The method is derived based on the method of weighted residuals and implemented in 2D and 3D. Periodic boundary conditions and solid-wall boundary conditions are considered. For these boundary conditions, the highest order in the NOM scheme is 2 and 3, respectively. The proposed NOM makes use of variable support domains allowing for adaptive refinement. The generalized α-method is employed for time integration and the Newton-Raphson method to iterate nonlinearity. The performance of the proposed method is demonstrated for several two and three dimensional benchmark problems. We also implemented a CH equation with 6th order partial differential derivative and studied the influence of higher order coefficients on the pattern evolution of the phase field.

KW - Implicit adaptive time integration

KW - Nonlocal operator method

KW - Periodic boundary condition

KW - Solid-wall boundary condition

KW - Weighted residual method

UR - http://www.scopus.com/inward/record.url?scp=85099519156&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2020.105687

DO - 10.1016/j.cnsns.2020.105687

M3 - Article

AN - SCOPUS:85099519156

VL - 96

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

M1 - 105687

ER -