Second Order Finite Difference Scheme For Cahn-Hilliard Equation

Cahn-Hilliard (CH) equation is a forth-order, nonlinear parabolic partial diferen-tial equation.It is proposed to describe the spinodal decomposition process in whichbinary alloys quenched with temperature. Eyre proposed a convex-splitting schemefor the Allen-Cahn equation, with the property of unconditionally energy stable andunconditonally unique solvable. For CH equation, the scheme is frst-order accurate intime.In this paper we discuss a second order accurate convex-concave splitting schemefor the Cahn-Hilliard equation. The second order accuracy is in both time and s-pace, and the discrete energy is bounded by its initial value for any time step. Wesolve the nonlinear equations using an efcient nonlinear multigrid method. Numericalsimulations are presented, which confrm the stablility, efciency and accuracy of thescheme.