On Efficient Second Order Stabilized Semi-Implicit Schemes for the Cahn-Hilliard Phase-Field Equation

Abstract

Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit schemes for the Cahn-Hilliard phase-field equation. One uses backward differentiation formula and the other uses Crank-Nicolson method to discretize linear terms. In both schemes, the nonlinear bulk forces are treated explicitly with two second-order stabilization terms. This treatment leads to linear elliptic systems with constant coefficients, for which lots of robust and efficient solvers are available. The discrete energy dissipation properties are proved for both schemes. Rigorous error analysis is carried out to show that, when the time step-size is small enough, second order accuracy in time is obtained with a prefactor controlled by a fixed power of $1/\epsilon$, where $\epsilon$ is the characteristic interface thickness. Numerical results are presented to verify the accuracy and efficiency of proposed schemes.

References in corpus (5)

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Cited by in corpus (9)

• On energy dissipation theory and numerical stability for time-fractional phase field equations
• Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines
• Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model
• A stabilized semi-implicit Fourier spectral method for nonlinear space-fractional reaction-diffusion equations
• Second-order Decoupled Energy-stable Schemes for Cahn-Hilliard-Navier-Stokes equations
• Comparison of Energy Stable Simulation of Moving Contact Line Problems using a Thermodynamically Consistent Cahn-Hilliard Navier-Stokes Model
• An Energy Stable Linear Diffusive Crank-Nicolson Scheme for the Cahn-Hilliard Gradient Flow
• A general class of linear unconditionally energy stable schemes for the gradient flows
• Energetic Spectral-Element Time Marching Methods for Phase-Field Nonlinear Gradient Systems