Comparison study of the conservative Allen-Cahn and the Cahn-Hilliard equations

In this paper, a comparison study of conservative Allen-Cahn and Cahn-Hilliard equations is presented. We consider two mass-conservative Allen-Cahn equations and two Cahn-Hilliard equations with constant and variable mobilities. The equations are discretized using finite difference schemes, and discrete systems of the equations are solved using a nonlinear multigrid method. The generation and motion of interface are investigated for the conservative equations. We then present numerical experiments which highlight different dynamics of the four equations. (C) 2015 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.