Details
| Original language | English |
|---|---|
| Article number | 105687 |
| Journal | Communications in Nonlinear Science and Numerical Simulation |
| Volume | 96 |
| Early online date | 30 Dec 2020 |
| Publication status | Published - May 2021 |
Abstract
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.
Keywords
- Implicit adaptive time integration, Nonlocal operator method, Periodic boundary condition, Solid-wall boundary condition, Weighted residual method
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Mathematics(all)
- Applied Mathematics
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In: Communications in Nonlinear Science and Numerical Simulation, Vol. 96, 105687, 05.2021.
Research output: Contribution to journal › Article › Research › peer review
}
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 -