A finite element technique for multifluid incompressible flow using Eulerian grids

P. D. Minev*, T. Chen, K. Nandakumar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


The paper presents a finite element method for 3D incompressible fluid flows with capillary free boundaries. It uses a fixed Eulerian grid of 10 nodes (ℙ2 - ℙ1) tetrahedra and tracks the free boundary using a six nodes (ℙ2) triangular surface grid. In order to improve the mass conservation properties of the method, a local enrichment of the finite element basis in the elements intersected by the free boundaries is employed. In addition to the surface tracking, it also advects a smooth indicator function for an easy identification of the fluid properties in the different parts of the domain. The advective part of the Navier-Stokes equations is split and integrated with a characteristic method. The remaining generalized Stokes problem is resolved by means of an inexact outer-inner (Uzawa) iteration with a properly chosen preconditioner. The performance of this technique is evaluated on several problems involving droplets in viscous liquids.

Original languageEnglish
Pages (from-to)255-273
Number of pages19
JournalJournal of Computational Physics
Issue number1
StatePublished - 1 May 2003
Externally publishedYes


  • Finite element method
  • Free boundary problems
  • Incompressible flow


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