Ham Seokjun, Li Yibao, Jeong Darae, Lee Chaeyoung, Kwak Soobin, Hwang Youngjin, Kim Junseok
Department of Mathematics, Korea University, Seoul, 02841 Republic of Korea.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049 China.
J Nonlinear Sci. 2022;32(6):80. doi: 10.1007/s00332-022-09844-3. Epub 2022 Sep 5.
In this study, we propose an explicit adaptive finite difference method (FDM) for the Cahn-Hilliard (CH) equation which describes the process of phase separation. The CH equation has been successfully utilized to model and simulate diverse field applications such as complex interfacial fluid flows and materials science. To numerically solve the CH equation fast and efficiently, we use the FDM and time-adaptive narrow-band domain. For the adaptive grid, we define a narrow-band domain including the interfacial transition layer of the phase field based on an undivided finite difference and solve the numerical scheme on the narrow-band domain. The proposed numerical scheme is based on an alternating direction explicit (ADE) method. To make the scheme conservative, we apply a mass correction algorithm after each temporal iteration step. To demonstrate the superior performance of the proposed adaptive FDM for the CH equation, we present two- and three-dimensional numerical experiments and compare them with those of other previous methods.
在本研究中，我们针对描述相分离过程的Cahn-Hilliard（CH）方程提出了一种显式自适应有限差分法（FDM）。CH方程已成功用于对各种领域应用进行建模和模拟，如复杂的界面流体流动和材料科学。为了快速有效地数值求解CH方程，我们使用了FDM和时间自适应窄带域。对于自适应网格，我们基于未分割的有限差分定义一个包含相场界面过渡层的窄带域，并在该窄带域上求解数值格式。所提出的数值格式基于交替方向显式（ADE）方法。为使该格式具有守恒性，我们在每个时间迭代步骤之后应用质量校正算法。为了证明所提出的用于CH方程的自适应FDM的优越性能，我们给出了二维和三维数值实验，并将它们与其他先前方法的实验进行比较。
