An adaptive time‐stepping scheme for the numerical simulation of Cahn‐Hilliard equation with variable mobility

In spinodal decomposition phenomena, the initial perturbations evolve at a faster time scale while there is a slower growth at a later time. Therefore, using uniform small time‐steps for tracking the fast dynamics is computationally expensive. On the other hand, uniform large time‐steps may overlook the rapid changes. In this article, we propose an adaptive time‐stepping scheme for faster time scale simulations of spinodal decomposition by solving the Cahn‐Hilliard equation numerically. We consider the double well potential having a polynomial of 6 th ‐order along with 4 th ‐order polynomial for the variable mobility. A diagonally implicit fractional step θ‐scheme(DIFSTS) for temporal discretization while conforming finite element method for spatial discretization is used. Accuracy and efficiency of the method are given and simulations of 2D spinodal decomposition are illustrated graphically.