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.