First-and second-order accurate, unconditionally energy gradient stable, uniquely solvable, and mass-preserving linear numerical schemes for Cahn-Hilliard equation with source term

초록

The Cahn-Hilliard equation describes the phase separation phenomena at the microscale, such as those observed for diblock copolymers. However, its standard form is limited to capturing diverse real-world behaviors. To address this issue, we propose a structure-preserving Cahn-Hilliard equation with a generalized source term. Based on the total energy of the suggested total energy functional, the schemes were constructed using a linearly stabilized splitting method and a fast Fourier transform. A second-order extension was achieved using the implicit-explicit Runge-Kutta method. We prove the unique solvability, mass conservation, and energy gradient stability of both first-and second-order schemes. Temporal accuracy was validated through convergence tests. Numerical experiments further illustrate the phase behaviors under varying source term orders.

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