XFEM with hanging nodes for two-phase incompressible flow

Cheng, Kwok Wah; Fries, Thomas‐Peter

doi:10.1016/j.cma.2012.07.011

Cited by 27 publications

(22 citation statements)

References 35 publications

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“…Some of them use a smeared interface approach -where the piecewice constant properties ρ and µ in eqs. (1,2) are regularized so that their derivatives are finite -like e.g. the works of Herrmann [7].…”

Section: Treatment Of Surface Tension In Numerical Methodsmentioning

confidence: 99%

Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

Kummer

Warburton

2016

Commun. Comput. Phys.

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In two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the curvature incorporates second derivatives, it is prone to numerical instabilities. Within this work, the interface is described by a level-set method based on a discontinuous Galerkin discretization. In order to stabilize the evaluation of the curvature, a patch-recovery operation is employed. There are numerous ways in which this filtering operation can be applied in the whole process of curvature computation. Therefore, an extensive numerical study is performed to identify optimal settings for the patch-recovery operations with respect to computational cost and accuracy.

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Section: Treatment Of Surface Tension In Numerical Methodsmentioning

confidence: 99%

Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

Kummer

Warburton

2016

Commun. Comput. Phys.

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“…An alternative idea suggested by [33,34] is to enhance the coarse elements with suitable shape modes, which recover the C 0 continuity between interconnected elements. Although this idea is very appealing and leads to optimal convergence, it has the disadvantage that an extension to high-order shape functions is not straightforward.…”

Section: Classical Refinement Schemesmentioning

confidence: 99%

Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes

et al. 2015

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The implementation of hp-adaptivity is challenging as hanging nodes, edges, and faces have to be constrained to ensure compatibility of the shape functions. For this reason, most hp-code frameworks restrict themselves to 1-irregular meshes to ease the implementational effort. This work alleviates these difficulties by introducing a new formulation for high-order mesh adaptivity that provides full local hp-refinement capabilities at a comparably small implementational effort. Its main idea is the extension of the hp-d-method such that it allows for high-order overlay meshes yielding a hierarchical, multi-level hp-formulation of the Finite Element Method. This concept enables intuitive refinement and coarsening procedures, while linear independence and compatibility of the shape functions are guaranteed by construction. The proposed method is demonstrated to achieve exponential rates of convergence-both in terms of degrees of freedom and in run-time-for problems with nonsmooth solutions. Furthermore, the scheme is used alongside the Finite Cell Method to simulate the heat flow around moving objects on a non-conforming background mesh and is combined with an energy-based refinement indicator for automatic hp-adaptivity.

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“…To overcome the problems associated with FEM, the extended finite element method (XFEM) [8][9][10][11] has been developed to model the problems involving discontinuities. Recently, it has been applied to solve various problems involving discontinuities [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31] since it has the following advantages over FEM:…”

Section: Introductionmentioning

confidence: 99%

The Effect of Inhomogeneities on an Edge Crack: A Numerical Study using XFEM

Sharma

Singh

Mishra

et al. 2013

International Journal for Computational Methods in Engineering

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In this work, the effect of inhomogeneities (holes, cracks, inclusions) on an edge crack has been studied by the extended finite element method (XFEM). In XFEM, finite element approximation is enriched by additional functions using partition of unity. The level set method is used for tracking the location of holes, cracks, and inclusions. The multiple discontinuities of random size (in a given range) are arbitrarily distributed in the plate/domain. The values of stress intensity factors (SIFs) are extracted from the XFEM solution by domain-based interaction integral approach.These simulations show that the presence of inhomogeneities has a significant effect on SIFs.

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XFEM with hanging nodes for two-phase incompressible flow

Cited by 27 publications

References 35 publications

Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

Patch-Recovery Filters for Curvature in Discontinuous Galerkin-Based Level-Set Methods

Multi-level hp-adaptivity: high-order mesh adaptivity without the difficulties of constraining hanging nodes

The Effect of Inhomogeneities on an Edge Crack: A Numerical Study using XFEM

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