A Bound Preserving Energy Stable Scheme for a Nonlocal Cahn–Hilliard Equation

We present a finite-volume based numerical scheme for a nonlocal Cahn–Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn–Hilliard equations. The equation of interest is a special case of a previously derived and studied system of equations which describes phase separation in ternary mixtures. We prove the scheme is both energy stable and respects the analytical bounds of the solution. Furthermore, we present numerical demonstrations of the theoretical results using both the Flory–Huggins (FH) and Ginzburg–Landau (GL) free-energy potentials.