The extended finite element method for two-phase and free-surface flows: A systematic study

Henning Sauerland*, Thomas Peter Fries

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In immiscible two-phase flows, jumps or kinks are present in the velocity and pressure fields across the interfaces of the two fluids. The extended finite element method (XFEM) is able to reproduce such discontinuities within elements. Robust and accurate interface capturing schemes with no restrictions on the interface topology are thereby enabled. This paper investigates different enrichment schemes and time-integration schemes within the XFEM. Test cases with and without surface tension on moving or stationary meshes are studied and compared to interface tracking results when possible. A particularly useful setting is extracted which is recommended for two-phase flows. An extension of this formulation for the simulation of free-surface flows and of floating objects is proposed.

Original languageEnglish
Pages (from-to)3369-3390
Number of pages22
JournalJournal of Computational Physics
Issue number9
Publication statusPublished - 1 May 2011


  • Enrichment
  • Extended finite element method
  • Free-surface flows
  • Two-phase flows
  • XFEM

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

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