An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties

Abstract

This paper presents an XFEM implementation of a projection algorithm to compute in an Eulerian framework 3D incompressible two-fluid flows with arbitrary high contrasts in material properties. It is designed to deal with both strong and weak discontinuities across the interface for pressure and velocity fields, respectively. A classical enrichment function accounts for velocity gradient discontinuities across the interface and a new quadratic enrichment function accounts for pressure discontinuities across the interface. A splitting of two-fluid elements is performed to achieve accurate numerical integrations, meanwhile a scaling coefficient accounting for both physical and geometrical considerations alleviates ill-conditioning. Various validations have been carried and very good solution accuracy is achieved even on coarse meshes, as from the minimal mesh not conforming to the interface. This implementation enables to compute accurate solutions regardless of discontinuity magnitude (arbitrary high contrast in material properties) and mesh size of two-fluid elements, which can constitute a decisive advantage for large size 3D computations.