A finite element technique for multifluid incompressible flow using Eulerian grids

  • Authors:

  • P. D. Minev;T. Chen;K. Nandakumar

  • Affiliations:

  • Department of Mathematical Sciences, University of Alberta, Edmonton, Alta, Canada T6G 2G1;Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alta, Canada T6G 2G6;Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alta, Canada T6G 2G6

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2003

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Abstract

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.