A three-dimensional finite element method for incompressible multiphase flows with capillary interfaces is developed based on a (formally) second-order projection scheme. The discretization is on a fixed (Eulerian) reference grid with an edge-based local h-refinement in the neighbourhood of the interfaces. The fluid phases are identified and advected using the level-set function. The reference grid is then temporarily reconnected around the interface to maintain optimal interpolations accounting for the singularities of the primary variables. Using a time splitting procedure, the convection substep is integrated with an explicit scheme. The remaining generalized Stokes problem is solved by means of a pressure-stabilized projection. This method is simple and efficient, as demonstrated by a wide range of difficult free-surface validation problems, considered in the paper.
|Number of pages||12|
|Journal||International Journal for Numerical Methods in Fluids|
|State||Published - 10 Jun 2005|
- Finite element method
- Free-boundary flows
- Navier-Stokes equations