TY - JOUR
T1 - An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties
AU - Daniela Garajeu & Marc Medale
JO - Communications in Computational Physics
VL - 3
SP - 593
EP - 622
PY - 2018
DA - 2018/05
SN - 24
DO - http://doi.org/10.4208/cicp.OA-2017-0152
UR - https://global-sci.org/intro/article_detail/cicp/12272.html
KW - Incompressible two-fluid flows, strong and weak field discontinuities, Extended Finite Element Method, projection algorithms.
AB - <p style="text-align: justify;">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.</p>