TY - JOUR
T1 - A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space
AU - Jeong , Darae
AU - Li , Yibao
AU - Lee , Chaeyoung
AU - Yang , Junxiang
AU - Kim , Junseok
JO - Communications in Computational Physics
VL - 2
SP - 412
EP - 430
PY - 2019
DA - 2019/12
SN - 27
DO - http://doi.org/10.4208/cicp.OA-2018-0202
UR - https://global-sci.org/intro/article_detail/cicp/13452.html
KW - Cahn–Hilliard equation, mass correction scheme, narrow band domain, closest point
method.
AB - <p style="text-align: justify;">In this paper, we develop a conservative numerical method for the Cahn–
Hilliard equation with generalized mobilities on curved surfaces in three-dimensional
space. We use an unconditionally gradient stable nonlinear splitting numerical scheme
and solve the resulting system of implicit discrete equations on a discrete narrow band
domain by using a Jacobi-type iteration. For the domain boundary cells, we use the
trilinear interpolation using the closest point method. The proposing numerical algorithm is computationally efficient because we can use the standard finite difference
Laplacian scheme on three-dimensional Cartesian narrow band mesh instead of discrete Laplace–Beltrami operator on triangulated curved surfaces. In particular, we employ a mass conserving correction scheme, which enforces conservation of total mass.
We perform numerical experiments on the various curved surfaces such as sphere,
torus, bunny, cube, and cylinder to demonstrate the performance and effectiveness of
the proposed method. We also present the dynamics of the CH equation with constant
and space-dependent mobilities on the curved surfaces.</p>