An unconditionally energy-stable second-order time-accurate scheme for the Cahn-Hilliard equation on surfaces

作者：Li, Yibao; Kim, Junseok^*; Wang, Nan

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 53: 213-227.

DOI：10.1016/j.cnsns.2017.05.006

• Cahn-Hilliard equation
• Laplace-Beltrami operator
• Triangular surface mesh
• Unconditionally energy-stable
• Mass conservation

In this paper, we propose an unconditionally energy-stable second-order time-accurate scheme for the Cahn-Hilliard equation on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. The proposed scheme, which combines a Crank-Nicolson-type scheme with a linearly stabilized splitting scheme, is second-order accurate in time. The discrete system is shown to be conservative and unconditionally energy-stable. The resulting system of discrete equations is simple to implement, and can be solved using a biconjugate gradient stabilized method. We demonstrate the performance of our proposed algorithm through several numerical experiments.

• 出版日期2017-12
• 单位西安交通大学