Abstract
This paper presents a conservative finite difference scheme for solving the N-component Cahn–Hilliard (CH) system on curved surfaces in three-dimensional (3D) space. Inspired by the closest point method (Macdonald and Ruuth, SIAM J Sci Comput 31(6):4330–4350, 2019), we use the standard seven-point finite difference discretization for the Laplacian operator instead of the Laplacian–Beltrami operator. We only need to independently solve (N- 1) CH equations in a narrow band domain around the surface because the solution for the Nth component can be obtained directly. The N-component CH system is discretized using an unconditionally stable nonlinear splitting numerical scheme, and it is solved by using a Jacobi-type iteration. Several numerical tests are performed to demonstrate the capability of the proposed numerical scheme. The proposed multicomponent model can be simply modified to simulate phase separation in a complex domain on 3D surfaces.
Original language | English |
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Pages (from-to) | 149-166 |
Number of pages | 18 |
Journal | Journal of Engineering Mathematics |
Volume | 119 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2019 Dec 1 |
Keywords
- Closest point method
- Conservative scheme
- N-component Cahn–Hilliard equation
- Narrow band domain
ASJC Scopus subject areas
- Mathematics(all)
- Engineering(all)