Analysis of the operator splitting scheme for the Cahn‐Hilliard equation with a viscosity term

In this paper, we consider a second‐order fast explicit operator splitting method for the viscous Cahn‐Hilliard equation, which includes a viscosity term α Δ u t ( α ∈ (0, 1)) described the influences of internal micro‐forces. The choice α  = 0 corresponds to the classical Cahn‐Hilliard equation whilst the choice α  = 1 recovers the nonlocal Allen‐Cahn equation. The fundamental idea of our method is to split the original problem into linear and nonlinear parts. The linear subproblem is numerically solved using a pseudo‐spectral method, and thus an ordinary differential equation is obtained. The nonlinear one is solved via TVD‐RK method. The stability and convergence are discussed in L 2 ‐norm. Numerical experiments are performed to validate the accuracy and efficiency of the proposed method. Besides, a detailed comparison is made for the dynamics and the coarsening process of the metastable pattern for various values of α . Moreover, energy degradation and mass conservation are also verified.