A numerical method for the ternary Cahn--Hilliard system with a degenerate mobility

Authors:
Junseok Kim;Kyungkeun Kang
Affiliations:
Department of Mathematics, Korea University, Seoul 136-701, Republic of Korea;Department of Mathematics, Sungkyunkwan University and Institute of Basic Sciences, Suwon 440-746, Republic of Korea
Venue:
Applied Numerical Mathematics
Year:
2009

Citing 7
Cited 3

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Computationally efficient solution to the Cahn-Hilliard equation: Adaptive implicit time schemes, mesh sensitivity analysis and the 3D isoperimetric problem

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Efficient numerical solution of discrete multi-component Cahn-Hilliard systems

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Abstract

We applied a second-order conservative nonlinear multigrid method for the ternary Cahn-Hilliard system with a concentration dependent degenerate mobility for a model for phase separation in a ternary mixture. First, we used a standard finite difference approximation for spatial discretization and a Crank-Nicolson semi-implicit scheme for the temporal discretization. Then, we solved the resulting discretized equations using an efficient nonlinear multigrid method. We proved stability of the numerical solution for a sufficiently small time step. We demonstrate the second-order accuracy of the numerical scheme. We also show that our numerical solutions of the ternary Cahn-Hilliard system are consistent with the exact solutions of the linear stability analysis results in a linear regime. We demonstrate that the multigrid solver can straightforwardly deal with different boundary conditions such as Neumann, periodic, mixed, and Dirichlet. Finally, we describe numerical experiments highlighting differences of constant mobility and degenerate mobility in one, two, and three spatial dimensions.