Untangling of 2D meshes in ALE simulations

Váchal, Pavel; Garimella, Rao V.; Shashkov, Mikhail

doi:10.1016/j.jcp.2003.11.011

Cited by 43 publications

(28 citation statements)

References 14 publications

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“…We make the assumption that the input grid (the grid produced by the Lagrangian phase) is unfolded. If the Lagrangian phase produces non valid cells then we use an untangling procedure [46]. We first recall the condition number smoothing algorithm for an internal node, then we present an original extension to the case of nodes located on a boundary.…”

Section: Condition Number Smoothingmentioning

confidence: 99%

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

Galera

Maire

Breil

2010

Journal of Computational Physics

183

218

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We present a new cell-centered multi-material Arbitrary Lagrangian Eulerian (ALE) scheme to solve the compressible gaz dynamics equations on two-dimensional unstructured grid. Our ALE method is of the explicit time-marching Lagrange plus remap type. Namely, it involves the following three phases: a Lagrangian phase wherein the flow is advanced using a cell-centered scheme; a rezone phase in which the nodes of the computational grid are moved to more optimal positions; a cellcentered remap phase which consists in interpolating conservatively the Lagrangian solution onto the rezoned grid. The multi-material modeling utilizes either concentration equations for miscible fluids or the Volume Of Fluid (VOF) capability with interface reconstruction for immiscible fluids. The main original feature of this ALE scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the Lagrangian one. In this formalism, the rezoned grid is defined as a convex combination between the Lagrangian grid and the grid resulting from condition number smoothing. This convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the Cauchy-Green tensor over the Lagrangian phase. Regarding the cell-centered remap phase, we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the Lagrangian cells. The first one is a simplified swept face-based method whereas the second one is a cell-intersection-based method. Our multi-material ALE methodology is assessed through several demanding two-dimensional tests. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme.

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Section: Condition Number Smoothingmentioning

confidence: 99%

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

Galera

Maire

Breil

2010

Journal of Computational Physics

183

218

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“…For this reason, various authors have proposed techniques for untangling inverted meshes. For example, [VGS04] used † e-mail: irving@cs.stanford.edu ‡ e-mail: jteran@stanford.edu § e-mail: fedkiw@cs.stanford.edu feasible set methods and optimization to untangle twodimensional meshes, [ERM * 03] extended various tetrahedron quality metrics intended for mesh smoothing to the case of inverted tetrahedra allowing untangling to occur simultaneously with optimization, etc. However, none of these techniques are guaranteed to work, and fail quite often in practice especially if the boundary of the mesh is also tangled.…”

Section: Introductionmentioning

confidence: 99%

Invertible finite elements for robust simulation of large deformation

Irving

Teran

Fedkiw

2004

Proceedings of the 2004 ACM SIGGRAPH/Eurographics Symposium on Computer Animation - SCA '04

317

250

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“…For both types of rezoning we make the assumption that the input grid (the grid produced by the Lagrangian phase) is unfolded. If the Lagrangian phase produces non valid cells then we have to use an untangling procedure [18].…”

Section: Rezoning Phasementioning

confidence: 99%

A cell-centered Arbitrary Lagrangian Eulerian (ALE) method for multi-material compressible flows

et al. 2008

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Abstract. We present an original and accurate unstructured cell-centered ALE algorithm devoted to the simulation of two-dimensional multi-material compressible fluid flows. Gas dynamics equations are discretized with an unstructured finite volume scheme.Résumé. Nous présentons dans cet article une méthode du type ALE appliquéeà la résolution d'écoulements multimatériaux compressibles. Leséquations de la dynamique des gaz sont discrétisées sur des maillages non structurés en utilisant un schéma du type volume fini.

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Untangling of 2D meshes in ALE simulations

Cited by 43 publications

References 14 publications

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

Invertible finite elements for robust simulation of large deformation

A cell-centered Arbitrary Lagrangian Eulerian (ALE) method for multi-material compressible flows

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