Imex methods for thin film equations and Cahn Hilliard equations with variable mobility.

We consider a class of splitting schemes using implicit-explicit (IMEX) time stepping to obtain accurate and energy-stable solutions to thin-film equations and Cahn-Hilliard models with variable mobility. The splitting method gives a linear constant coefficient implicit step allowing for efficient computational implementation. The influence of the stabilizing splitting parameters over the numerical solution is studied computationally with choices of initial conditions. In addition, we compute energy-stability plots for the proposed methods for different choices of splitting parameter values and different sizes of the timestep. The methods improve the accuracy of the original bi-harmonic-modified (BHM) approach and retain the energy-decreasing property while reaching second-order accuracy. Numerical experiments are presented to demonstrate the performance of the proposed methods.

Bio
https://sites.google.com/alumni.iastate.edu/orizaga/