A finite element strategy for the solution of interface tracking problems

Abstract

A finite element-based numerical strategy for interface tracking is developed for the simulation of two-phase flows. The method is based on the solution of an advection equation for the so-called ‘pseudo-concentration’ of one of the phases. To obtain an accurate description of the interface, a streamline upwind Petrov–Galerkin (SUPG) scheme is combined with an automatic mesh refinement procedure and a filtering technique, making it possible to generate an oscillation-free pseudo-concentration field. The performance of the proposed approach is successfully tested on four classical two-dimensional benchmark problems: the advection skew to the mesh, the transport of a square shape in a constant velocity flow field, the transport of a cut-out cylinder in a rotating flow field and the transport of a disc in a shear flow. Copyright © 2005 John Wiley & Sons, Ltd.