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.
|Number of pages||19|
|Journal||Journal of Computational Physics|
|State||Published - 1 May 2003|
- Finite element method
- Free boundary problems
- Incompressible flow