Deforming Fluid Domains Within the Finite Element Method: Five Mesh-Based Tracking Methods in Comparison

Elgeti, Stefanie; Sauerland, Henning

doi:10.1007/s11831-015-9143-2

Cited by 47 publications

(42 citation statements)

References 194 publications

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“…Commonly, a first distinction is made between interface capturing and interface tracking methods [1]. In the former approach, one employs an implicit description of the dynamic boundary or interface on some reference mesh.…”

Section: Introductionmentioning

confidence: 99%

The Virtual Ring Shear-Slip Mesh Update Method

2018

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A novel method -the Virtual Ring Shear-Slip Mesh Update Method (VR-SSMUM)for the efficient and accurate modeling of moving boundary or interface problems in the context of the numerical analysis of fluid flow is presented. We focus on cases with periodic straight-line translation including object entry and exit. The periodic character of the motion is reflected in the method via a mapping of the physical domain onto a closed virtual ring. Therefore, we use an extended mesh, where unneeded portions are deactivated to control the computational overhead. We provide a validation case as well as examples for the applicability of the method to 2D and 3D models of packaging machines.

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Section: Introductionmentioning

confidence: 99%

The Virtual Ring Shear-Slip Mesh Update Method

2018

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“…In order to discretize equations (1), (2), (5) and (10), P 1P 1 finite elements are used. The Galerkin/least-squares (GLS) stabilization method is applied for this purpose.…”

Section: Solution Techniquementioning

confidence: 99%

“…The Navier-Stokes equations (1) and (2), the heat equation (5) and the level-set transport equation (10) have the following space-time discretized forms, respectively, after stabilization:…”

Section: Solution Techniquementioning

confidence: 99%

Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

et al. 2019

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The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.

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“…Considering the description of the free surface, an implicit or explicit technique can be used [1]. The implicit approach uses a fixed computational mesh and introduces an additional scalar field to capture the interface.…”

Section: Introductionmentioning

confidence: 99%

Space‐time NURBS‐enhanced finite elements for free‐surface flows in 2D

Stavrev

Knechtges

Elgeti

et al. 2015

Numerical Methods in Fluids

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This is the accepted version of the following article: Stavrev, A., Knechtges, P., Elgeti, S., and Huerta, A. (2016) Space-time NURBS-enhanced finite elements\ud for free-surface flows in 2D., Int. J. Numer. Meth. Fluids, doi: 10.1002/fld.4189, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/fld.4189/abstractThe accuracy of numerical simulations of free-surface flows depends strongly on the computation of geometric quantities like normal vectors and curvatures. This geometrical information is additional to the actual degrees of freedom and usually requires a much finer discretization of the computational domain than the flow solution itself. Therefore, the utilization of a numerical method, which uses standard functions to discretize the unknown function in combination with an enhanced geometry representation is a natural step to improve the simulation efficiency. An example of such method is the NURBS-enhanced finite element method (NEFEM), recently proposed by Sevilla et al. The current paper discusses the extension of the spatial NEFEM to space-time methods and investigates the application of space-time NURBS-enhanced elements to free-surface flows. Derived is also a kinematic rule for the NURBS motion in time, which is able to preserve mass conservation over time. Numerical examples show the ability of the space-time NEFEM to account for both pressure discontinuities and surface tension effects and compute smooth free-surface forms. For these examples, the advantages of the NEFEM compared with the classical FEM are shown.Peer ReviewedPostprint (author's final draft

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Deforming Fluid Domains Within the Finite Element Method: Five Mesh-Based Tracking Methods in Comparison

Cited by 47 publications

References 194 publications

The Virtual Ring Shear-Slip Mesh Update Method

The Virtual Ring Shear-Slip Mesh Update Method

Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

Space‐time NURBS‐enhanced finite elements for free‐surface flows in 2D

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