A second-order accurate non-linear difference scheme for the N -component Cahn–Hilliard system

We consider a second-order conservative nonlinear numerical scheme for the NN-component Cahn–Hilliard system modeling the phase separation of a NN-component mixture. The scheme is based on a Crank–Nicolson finite-difference method and is solved by an efficient and accurate nonlinear multigrid method. We numerically demonstrate the second-order accuracy of the numerical scheme. We observe that our numerical solutions are consistent with the exact solutions of linear stability analysis results. We also describe numerical experiments such as the evolution of triple junctions and the spinodal decomposition in a quaternary mixture. We investigate the effects of a concentration dependent mobility on phase separation.