Efficient schemes with unconditionally energy stability for the anisotropic Cahn-Hilliard Equation using the stabilized-Scalar Augmented Variable (S-SAV) approach

Abstract

In this paper, we consider numerical approximations for the anisotropic Cahn-Hilliard equation. The main challenge of constructing numerical schemes with unconditional energy stabilities for this model is how to design proper temporal discretizations for the nonlinear terms with the strong anisotropy. We propose two, second order time marching schemes by combining the recently developed SAV approach with the linear stabilization approach, where three linear stabilization terms are added. These terms are shown to be crucial to remove the oscillations caused by the anisotropic coefficients, numerically. The novelty of the proposed schemes is that all nonlinear terms can be treated semi-explicitly, and one only needs to solve three decoupled linear equations with constant coefficients at each time step. We further prove the unconditional energy stabilities rigorously, and present various 2D and 3D numerical simulations to demonstrate the stability and accuracy.

References in corpus (1)

• Numerical Approximations for a three components Cahn-Hilliard phase-field Model based on the Invariant Energy Quadratization method

Cited by in corpus (3)

• Stability and Error estimates of the SAV Fourier-spectral method for the Phase Field Crystal Equation
• Linear Second Order Energy Stable Schemes of Phase Field Model with Nonlocal Constraints for Crystal Growth
• Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints