A Conservative Numerical Method for the Cahn–Hilliard Equation with Generalized Mobilities on Curved Surfaces in Three-Dimensional Space (Communications in Computational Physics, 2019)
In this paper, we develop a conservative numerical method for the Cahn–Hilliard equation with generalized mobilities on curved surfaces in three-dimensionalspace. We use an unconditionally gradient stable nonlinear splitting numerical schemeand solve the resulting system of implicit discrete equations on a discrete narrow banddomain by using a Jacobi-type iteration. For the domain boundary cells, we use thetrilinear interpolation using the closest point method. The proposing numerical algorithm is computationally efficient because we can use the standard finite differenceLaplacian 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 ofthe proposed method. We also present the dynamics of the CH equation with constantand space-dependent mobilities on the curved surfaces.