A practically unconditionally gradient stable scheme for the -component Cahn–Hilliard system

We present a practically unconditionally gradient stable conservative nonlinear numerical scheme for the N -component Cahn–Hilliard system modeling the phase separation of an N -component mixture. The scheme is based on a nonlinear splitting method and is solved by an efficient and accurate nonlinear multigrid method. The scheme allows us to convert the N -component Cahn–Hilliard system into a system of N − 1 binary Cahn–Hilliard equations and significantly reduces the required computer memory and CPU time. We observe that our numerical solutions are consistent with the linear stability analysis results. We also demonstrate the efficiency of the proposed scheme with various numerical experiments.