1. The high-order exponential semi-implicit scalar auxiliary variable approach for the general nonlocal Cahn-Hilliard equation.
- Author
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Meng, Xiaoqing, Cheng, Aijie, and Liu, Zhengguang
- Subjects
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PHASE transitions , *FAST Fourier transforms , *CONSERVATION of mass , *EQUATIONS , *CRANK-nicolson method , *HEAT equation - Abstract
The nonlocal Cahn-Hilliard equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard equation. In this paper, based on the exponential semi-implicit scalar auxiliary variable method, the highly efficient and accurate schemes (in time) with unconditional energy stability for solving the nonlocal Cahn-Hilliard equation are proposed. On the one hand, we have demonstrated the unconditional energy stability and mass conservation for the nonlocal Cahn-Hilliard equation with its high-order numerical schemes in the continuous and discrete level carefully and rigorously. On the other hand, in order to reduce the calculation and storage cost in numerical simulation, we use the fast solver based on fast Fourier transform and conjugate gradient approach for spatial discretization. Some numerical simulations involving the Gaussian kernel are presented and show the stability, accuracy, efficiency and unconditional energy stability of the proposed schemes. • We establish and analyze the unconditionally energy stable schemes from first- to fourth-order based on ESI-SAV approach for general NCH equation. • The proposed schemes are high-order accurate, easy-to-implement, and unconditionally energy stable. • We use a fast solver based on fast Fourier transform and conjugate gradient approach for spatial discretization of nonlocal terms to reduce the calculation and storage cost. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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