An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties (Communications in Computational Physics, 2018)
This paper presents an XFEM implementation of a projection algorithm tocompute in an Eulerian framework 3D incompressible two-fluid flows with arbitraryhigh contrasts in material properties. It is designed to deal with both strong and weakdiscontinuities across the interface for pressure and velocity fields, respectively. A classicalenrichment function accounts for velocity gradient discontinuities across the interfaceand a new quadratic enrichment function accounts for pressure discontinuitiesacross the interface. A splitting of two-fluid elements is performed to achieve accuratenumerical integrations, meanwhile a scaling coefficient accounting for both physicaland geometrical considerations alleviates ill-conditioning. Various validations havebeen carried and very good solution accuracy is achieved even on coarse meshes, asfrom the minimal mesh not conforming to the interface. This implementation enablesto compute accurate solutions regardless of discontinuity magnitude (arbitrary highcontrast in material properties) and mesh size of two-fluid elements, which can constitutea decisive advantage for large size 3D computations.