A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case

Qing Cheng, Chun Liu, Jie Shen

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a new Lagrangian approach — flow dynamic approach to effectively capture the interface in the Allen-Cahn type equations. The underlying principle of this approach is the Energetic Variational Approach (EnVarA), motivated by Rayleigh and Onsager [27,28]. Its main advantage, comparing with numerical methods in Eulerian coordinates, is that thin interfaces can be effectively captured with few points in the Lagrangian coordinate. We concentrate in the one-dimensional case and construct numerical schemes for the trajectory equation in Lagrangian coordinate that obey the variational structures, and as a consequence, are energy dissipative. Ample numerical results are provided to show that only fewer points are enough to resolve very thin interfaces by using our flow dynamic approach.

Original languageEnglish (US)
Article number109509
JournalJournal of Computational Physics
Volume419
DOIs
StatePublished - Oct 15 2020

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates, I. One-dimensional case'. Together they form a unique fingerprint.

Cite this