A projection scheme for incompressible multiphase flow using adaptive Eulerian grid

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


This paper presents a finite element method for incompressible multiphase flows with capillary interfaces based on a (formally) second-order projection scheme. The discretization is on a fixed Eulerian grid. The fluid phases are identified and advected using a level set function. The grid is temporarily adapted around the interfaces in order to maintain optimal interpolations accounting for the pressure jump and the discontinuity of the normal velocity derivatives. The least-squares method for computing the curvature is used, combined with piecewise linear approximation to the interface. The time integration is based on a formally second order splitting scheme. The convection substep is integrated over an Eulerian grid using an explicit scheme. The remaining generalized Stokes problem is solved by means of a formally second order pressure-stabilized projection scheme. The pressure boundary condition on the free interface is imposed in a strong form (pointwise) at the pressure-computation substep. This allows capturing significant pressure jumps across the interface without creating spurious instabilities. This method is simple and efficient, as demonstrated by the numerical experiments on a wide range of free-surface problems.

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalInternational Journal for Numerical Methods in Fluids
Issue number1
StatePublished - 10 May 2004
Externally publishedYes


  • Finite element method
  • Multiphase flows
  • Navier-Stokes equations


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