A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters

In this paper, we construct and analyze a uniquely solvable, positivity preserving unconditionally energy stable finite-difference scheme for the periodic three-component Macromolecular Microsphere Composite (MMC) hydrogels system, ternary Cahn-Hilliard system with Flory-Huggins-deGennes free potential. The proposed is based on convex-concave decomposition of given functional two variables, centered difference method adopted in space. We provide theoretical justification that numerical has pair unique solutions, such always preserved all singular terms, i.e., not only phase variables are between 0 1, but also sum at point-wise level. addition, use local Newton approximation multigrid to solve nonlinear scheme, various results presented, including convergence test, positivity-preserving property dissipation mass conservation properties.