A Review of Geometrical Interface Properties for 3D Front-Tracking Methods

Bi, Désir-André Koffi; Tavares, Mathilde; Chénier, Eric; Vincent, Stéphane

doi:10.1007/978-3-030-65820-5_15

Cited by 2 publications

(2 citation statements)

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“…with σ the surface tension coefficient, κ the curvature and n the normal vector of the interface. The surface tension force on a triangulated front element E can be computed by using the Frenet-Element method given as [4,13,15]…”

Section: Rising Bubblementioning

confidence: 99%

“…The major advantage arising from the explicit representation of the interface is the straightforward computation of the normal vector at each point on the interface and, particularly, of the curvature of the interface for the calculation of the surface tension force. In the works of Tryggvason et al [13] as well as Shin et al [14], the surface tension force is evaluated as a triangle or vertex centered value by a Frenet-Element or Frenet-Vertex method [15]. Further possible computational methods for the curvature are given, for instance, by Todd and McLeod [16], Meyer et al [17] as well as de Sousa et al [18].…”

Section: Introductionmentioning

confidence: 99%

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Reducing volume and shape errors in front tracking by divergence-preserving velocity interpolation and parabolic fit vertex positioning

Gorges,

Evrard,

van Wachem

et al. 2022

Preprint

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Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, this paper proposes a divergence-preserving velocity interpolation method and a parabolic fit vertex positioning method for remeshing operations for three-dimensional front tracking. Errors in preserving the divergence of the velocity field when interpolating the velocity from the fluid mesh to the vertices of the triangles of the front are a primary reason for volume conservation errors when advecting the front. The proposed interpolation method preserves the discrete divergence of the fluid velocity by construction and is compared in this work with other known interpolation methods in divergence-free and non-divergence-free test cases, with respect to volume conservation and shape preservation of the front. The presented interpolation method conserves the volume and shape up to an order of magnitude better than the conventionally used interpolation methods and is within the range of higher order interpolation methods at lower computational cost. Additionally, the parabolic fit vertex positioning method for remeshing operations locally approximates the front with a smooth polynomial surface, improving volume conservation and shape preservation by an order of magnitude compared to conventional remeshing algorithms.

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Section: Rising Bubblementioning

confidence: 99%