Reformulation of XFEM based on PUFEM for solving problem caused by blending elements

Shibanuma, Kazuki; Utsunomiya, Tomoaki

doi:10.1016/j.finel.2009.06.007

Cited by 38 publications

(33 citation statements)

References 16 publications

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“…A modified interpolation scheme must be used in these elements to maintain an optimal convergence rate, as described in Fries (2008); Shibanuma and Utsunomiya (2009). A more compact way to write (4) is by use the more standard matrix form (5).…”

Section: Enriched Interpolation Schemementioning

confidence: 99%

A XFEM Lagrange Multiplier Technique for Stefan Problems

Martin¹,

Chaouki²,

Robert³

et al. 2016

Frontiers in Heat and Mass Transfer

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The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust and precise.

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Section: Enriched Interpolation Schemementioning

confidence: 99%

A XFEM Lagrange Multiplier Technique for Stefan Problems

Martin¹,

Chaouki²,

Robert³

et al. 2016

Frontiers in Heat and Mass Transfer

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“…In general, a special treatment is required in blending elements to remove unwanted terms. Some blending methods have been already published [26,[28][29][30][31][32]. In this study, the effect of "blending elements" is ignored.…”

Section: Extended Finite Element Methods For Viscoelastic Cracked Probmentioning

confidence: 99%

Modeling crack in viscoelastic media using the extended finite element method

Yu¹,

Ren²

2011

Sci. China Technol. Sci.

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In this paper, the problem of modeling crack in 2D viscoelastic media is studied using the extended finite element method. The paper focuses on the definition of enrichment functions suitable for cracks assessment in viscoelastic media and the generalized domain integrals used in the determination of crack tip parameters. The opening mode and mixed mode solutions of crack tip fracture problems in viscoelastic media are also undertaken. The results obtained by the proposed method show good agreement with the analytical methods and provide reasonable background information to enhance the modeling of crack growth in viscoelastic media. viscoelastic media, extended finite element method, crack, crack tip parameters Citation:Yu T T, Ren Q W. Modeling crack in viscoelastic media using the extended finite element method.

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“…A modified interpolation scheme must be used in these elements to maintain an optimal convergence rate, as described in Fries (2008); Shibanuma and Utsunomiya (2009). In order to capture the jump in the heat flux at the interface, a Lagrange multiplier q will be used Gerstenberger (2010).…”

Section: Enriched Interpolation Schemementioning

confidence: 99%

A Xfem Phase Change Model With Convection

Martin¹,

Chaouki²,

Robert³

et al. 2018

Frontiers in Heat and Mass Transfer

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A model for two dimensional solidification problems including convection was developed by coupling the Stefan problem with the Stokes problem. The extended finite element method (XFEM) was used to capture the strong discontinuity in velocity and pressure as well as the jump in heat flux at the phase change interface. The melting temperature and no-slip condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration algorithm. The model was able to reproduce the benchmark simulations while maintaining a sharp phase change interface.

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Reformulation of XFEM based on PUFEM for solving problem caused by blending elements

Cited by 38 publications

References 16 publications

A XFEM Lagrange Multiplier Technique for Stefan Problems

A XFEM Lagrange Multiplier Technique for Stefan Problems

Modeling crack in viscoelastic media using the extended finite element method

A Xfem Phase Change Model With Convection

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