A simple package for front tracking

Du, Jian; Fix, Brian; Glimm, James; Jia, Xicheng; Li, Xin; Li, Yuanhua; Wu, Lingling

doi:10.1016/j.jcp.2005.08.034

Cited by 136 publications

(130 citation statements)

References 21 publications

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“…Advective motion 5.1.1. Rotation of slotted sphere Rotation has been widely used in the literature to test moving interface methods [7][8][9]14]. We adopt the problem of rotating the Zalesak's sphere [7], which is a unit sphere with a slot of 1/3 unit wide and 5/6 unit high aligned along the YZ plane.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The geometric errors associated with vertex redistribution may be alleviated by projecting the vertices onto a high-order approximation of the surface after moving them [25]. Such an approach may be cumbersome for moving interfaces, so a common practice in interface propagation has been to avoid vertex redistribution but only adapt the mesh by adding or removing vertices or changing the connectivity [6,9], although vertex redistribution can be potentially much more efficient.…”

Section: Redistribute Verticesmentioning

confidence: 99%

“…This problem is commonly referred to as interface propagation. Because singularities and topological changes may develop during the evolution of the surface, this problem poses daunting challenges in developing accurate, efficient, and robust techniques, and has attracted significant interests in the past two decades [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, existing Lagrangian methods often suffer from instabilities in the form of growing oscillations or self-intersections [3] and sometimes must resort to ad hoc techniques to trim off self-intersections [18,19]. Due to this mixed success of pure Lagrangian or Eulerian methods, in an attempt to seek a better compromise between the accuracy of Lagrangian methods and robustness of Eulerian methods, a number of hybrid methods have appeared in recent years [7][8][9][10]. These methods unfortunately are more complex to implement than traditional methods and still suffer from smearing of singularities (although milder than pure Eulerian methods).…”

Section: Introductionmentioning

confidence: 99%

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Face offsetting: A unified approach for explicit moving interfaces

Jiao

2007

Journal of Computational Physics

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Dynamic moving interfaces are central to many scientific, engineering, and graphics applications. In this paper, we introduce a novel method for moving surface meshes, called the face offsetting method, based on a generalized Huygens' principle. Our method operates directly on a Lagrangian surface mesh, without requiring an Eulerian volume mesh. Unlike traditional Lagrangian methods, which move each vertex directly along an approximate normal or user-specified direction, our method propagates faces and then reconstructs vertices through an eigenvalue analysis locally at each vertex to resolve normal and tangential motion of the interface simultaneously. The method also includes techniques for ensuring the integrity of the surface as it evolves. Face offsetting provides a unified framework for various dynamic interface problems and delivers accurate physical solutions even in the presence of singularities and large curvatures. We present the theoretical foundation of our method, and also demonstrate its accuracy, efficiency, and flexibility for a number of benchmark problems and a real-world application.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Redistribute Verticesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Face offsetting: A unified approach for explicit moving interfaces

Jiao

2007

Journal of Computational Physics

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“…Finally, a Rayleigh-Taylor instability is run in order to assess the feasibility of capturing physical instability in an almost Lagrangian fashion. For this problem we compare our results with results obtained by the front tracking code (FronTier - [38], [55], [56]) and a an implicit large eddy simulation (ILES) incompressible Eulerian code (RTI3D - [3]). …”

Section: Numerical Testsmentioning

confidence: 99%

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Loubère

Maire

Shashkov

et al. 2010

Journal of Computational Physics

182

130

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We present a new reconnection-based Arbitrary Lagrangian Eulerian (ALE) method. The main elements in a standard ALE simulation are an explicit Lagrangian phase in which the solution and grid are updated, a rezoning phase in which a new grid is defined, and a remapping phase in which the Lagrangian solution is transferred (conservatively interpolated) onto the new grid. In standard ALE methods the new mesh from the rezone phase is obtained by moving grid nodes without changing connectivity of the mesh. Such rezone strategy has its limitation due to the fixed topology of the mesh. In our new method we allow connectivity of the mesh to change in rezone phase, which leads to general polygonal mesh and allows to follow Lagrangian features of the mesh much better than for standard ALE methods. Rezone strategy with reconnection is based on using Voronoi tessellation. We demonstrate performance of our new method on series of numerical examples and show it superiority in comparison with standard ALE methods without reconnection.

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Combined Extended Finite Element and Level Set Method ( XFE ‐ LSM ) for Free Boundary Problems

Duddu

2023

Partition of Unity Methods

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A simple package for front tracking

Cited by 136 publications

References 21 publications

Face offsetting: A unified approach for explicit moving interfaces

Face offsetting: A unified approach for explicit moving interfaces

ReALE: A reconnection-based arbitrary-Lagrangian–Eulerian method

Combined Extended Finite Element and Level Set Method ( XFE ‐ LSM ) for Free Boundary Problems

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