Volume 24, Issue 3
An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties

Daniela Garajeu & Marc Medale

Commun. Comput. Phys., 24 (2018), pp. 593-622.

Published online: 2018-05

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  • 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.

  • Keywords

Incompressible two-fluid flows, strong and weak field discontinuities, Extended Finite Element Method, projection algorithms.

  • AMS Subject Headings

76D05, 76D45, 76M10, 76M30, 76T99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-24-593, author = {}, title = {An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties}, journal = {Communications in Computational Physics}, year = {2018}, volume = {24}, number = {3}, pages = {593--622}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2017-0152}, url = {http://global-sci.org/intro/article_detail/cicp/12272.html} }
TY - JOUR T1 - An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties JO - Communications in Computational Physics VL - 3 SP - 593 EP - 622 PY - 2018 DA - 2018/05 SN - 24 DO - http://dor.org/10.4208/cicp.OA-2017-0152 UR - https://global-sci.org/intro/cicp/12272.html KW - Incompressible two-fluid flows, strong and weak field discontinuities, Extended Finite Element Method, projection algorithms. AB -

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.

Daniela Garajeu & Marc Medale. (2020). An XFEM Implementation of a Projection Method for 3D Incompressible Two-Fluid Flows with Arbitrary High Contrasts in Material Properties. Communications in Computational Physics. 24 (3). 593-622. doi:10.4208/cicp.OA-2017-0152
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