TY - JOUR
T1 - Unconditionally energy stable second-order numerical scheme for the Allen–Cahn equation with a high-order polynomial free energy
AU - Kim, Junseok
AU - Lee, Hyun Geun
N1 - Funding Information:
The first author (J. Kim) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1A2C1003053). The corresponding author (H.G. Lee) was supported by the Research Grant of Kwangwoon University in 2021 and by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2019R1C1C1011112).
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12
Y1 - 2021/12
N2 - In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the nonlinear parts in the governing equation, we have a linear convex splitting scheme of the energy for the high-order AC equation. In addition, by combining the linear convex splitting with a strong-stability-preserving implicit–explicit Runge–Kutta (RK) method, the proposed method is linear, temporally second-order accurate, and unconditionally energy stable. Computational tests are performed to demonstrate that the proposed method is accurate, efficient, and energy stable.
AB - In this article, we consider a temporally second-order unconditionally energy stable computational method for the Allen–Cahn (AC) equation with a high-order polynomial free energy potential. By modifying the nonlinear parts in the governing equation, we have a linear convex splitting scheme of the energy for the high-order AC equation. In addition, by combining the linear convex splitting with a strong-stability-preserving implicit–explicit Runge–Kutta (RK) method, the proposed method is linear, temporally second-order accurate, and unconditionally energy stable. Computational tests are performed to demonstrate that the proposed method is accurate, efficient, and energy stable.
KW - Allen–Cahn equation
KW - High-order polynomial free energy
KW - Implicit–explicit RK scheme
KW - Linear convex splitting
UR - http://www.scopus.com/inward/record.url?scp=85114878926&partnerID=8YFLogxK
U2 - 10.1186/s13662-021-03571-x
DO - 10.1186/s13662-021-03571-x
M3 - Article
AN - SCOPUS:85114878926
SN - 1687-1839
VL - 2021
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 416
ER -