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 . 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.
|Number of pages||25|
|Journal||Communications in Mathematical Sciences|
|Publication status||Published - 2004|
- Nonlinear multigrid method
- Ternary cahn-hilliard system
ASJC Scopus subject areas
- Applied Mathematics