Chebyshev collocation method for the constant mobility Cahn–Hilliard equation in a square domain

摘要

Chebyshev collocation method was developed for constant mobility Cahn-Hilliard equation. The accuracy of the method was indirectly checked with the aid of two separate calculations of temporal derivative of total free energy. We found that the derivatives of total free energy by two different ways of calculation coincided exactly when the number of grid points in the transitional layer within mixing region was 16 or more when the coefficient of gradient energy ϵ2 was chosen correspondingly in the given domain. We also investigated the application of Kosloff and Tal-Ezer mapping for the Chebyshev collocation grid points in space and showed the possibility of the use of much larger timestep size than that of the Chebyshev collocation method without mapping.