Conservative multigrid methods for ternary Cahn-Hilliard systems. (English) Zbl 1085.65093

Kim, Junseok; Kang, Kyungkeun; Lowengrub, John

Commun. Math. Sci. 2, No. 1, 53-77 (2004).

Summary: We develop a conservative, second-order accurate fully implicit discretization of ternary (three-phase) Cahn-Hilliard (CH) systems that has an associated discrete energy functional. This is an extension of our work for two-phase systems [cf. the authors, J. Comput. Phys. 193, No. 2, 511–543 (2004; Zbl 1109.76348)]. We analyze and prove convergence of the scheme. To efficiently solve the discrete system at the implicit time-level, we use a nonlinear multigrid method. The resulting scheme is efficient, robust and there is at most a 1st order time step constraint for stability. We demonstrate convergence of our scheme numerically and we present several simulations of phase transitions in ternary systems.

MSC:

65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
76T30	Three or more component flows
65M20	Method of lines for initial value and initial-boundary value problems involving PDEs
82C26	Dynamic and nonequilibrium phase transitions (general) in statistical mechanics
35Q35	PDEs in connection with fluid mechanics
80A22	Stefan problems, phase changes, etc.
80M25	Other numerical methods (thermodynamics) (MSC2010)
76M25	Other numerical methods (fluid mechanics) (MSC2010)

Keywords:

semidiscretization; numerical examples; nonlinear multigrid method; convergence; phase transitions

Citations:

Zbl 1109.76348