J Sci Comput https://doi.org/10.1007/s10915-018-0742-6 Direct Discretization Method for the Cahn–Hilliard Equation on an Evolving Surface 1 1 2 Yibao Li · Xuelin Qi · Junseok Kim Received: 29 August 2017 / Revised: 22 February 2018 / Accepted: 20 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We propose a simple and efﬁcient direct discretization scheme for solving the Cahn–Hilliard (CH) equation on an evolving surface. By using a conservation law and trans- port formulae, we derive the CH equation on evolving surfaces. An evolving surface is discretized using an unstructured triangular mesh. The discrete CH equation is deﬁned on the surface mesh and its dual surface polygonal tessellation. The evolving triangular sur- faces are then realized by moving the surface nodes according to a given velocity ﬁeld. The proposed scheme is based on the Crank–Nicolson scheme and a linearly stabilized splitting scheme. The scheme is second-order accurate, with respect to both space and time. The resulting system of discrete equations is easy to implement, and is solved by using an efﬁ- cient biconjugate gradient stabilized method. Several numerical experiments are presented to demonstrate the performance and effectiveness of the proposed numerical scheme. Keywords Cahn–Hilliard
Journal of Scientific Computing – Springer Journals
Published: May 29, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
All the latest content is available, no embargo periods.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud