The Point-Set Method: Front-Tracking without Connectivity

Torres, David J.; Brackbill, J. U.

doi:10.1006/jcph.2000.6635

Cited by 141 publications

(147 citation statements)

References 32 publications

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“…This test case is similar to that used by Torres and Brackbill [25] and Hermann [12] and we compare the results obtained using Gerris with the results presented in both of these papers. A comparison between the theoretical and numerical values of the frequency is given in Figure 2 for n = 2 and = 0.05.…”

Section: Methodsmentioning

confidence: 89%

Numerical simulation of droplets, bubbles and waves: state of the art

et al. 2009

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Abstract. This work present current advances in the numerical simulation of twophase flows using a VOF method, balanced-force surface tension and quad/octree adaptive mesh refinement. The simulations of the atomization of a liquid sheet, the capillary retraction of a liquid sheet and two-and three-dimensional wave breaking all for air/water systems, are used to show the potential of the numerical techniques. New simulations of atomization processes for air/water conditions are allowing to investigate the processes leading to the appearance of instabilities in the primary atomization zone in real conditions. For the retracting liquid sheet, the new simulations show that two different regimes can be encountered as a function of the Ohnesorge number. For large values, a laminar flow is encountered inside the rim and a steady state is reached after a quick transient state. For small values, a turbulent flow is generated inside the rim which is responsible of large oscillations in the rim size and neck thickness. The breaking wave case study demonstrates the orders-of-magnitude efficiency gains of the adaptive mesh refinement method.

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Section: Methodsmentioning

confidence: 89%

Numerical simulation of droplets, bubbles and waves: state of the art

et al. 2009

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“…First observed in Boltzmann interfacial methods, parasitic currents are also presented by Lafaurie et al in [24] where they suggested the alternative Continuum Surface Stress (CSS) method. Then follow several approaches to tackle this problem [35,32,53,34,41,52,26]. Their key ideas in suppressing parasitic currents, usually mentioned in this literature, are (i) improvement of curvature computation, (ii) achievement of discrete balance between surface tension and pressure gradient (iii) adaptive time integration scheme to tackle the stiffness induced by surface tension [25].…”

Section: Introductionmentioning

confidence: 99%

On stability condition for bifluid flows with surface tension: Application to microfluidics

Galusinski

Vigneaux

2008

Journal of Computational Physics

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Models for incompressible immiscible bifluid flows with surface tension are here considered. Since Brackbill, Kothe and Zemach (J. Comput. Phys. 100, pp 335-354, 1992) introduced the Continuum Surface Force (CSF) method, many methods involved in interface tracking or capturing are based on this reference work. Particularly, the surface tension term is discretized explicitly and therefore, a stability condition is induced on the computational time step. This constraint on the time step allows the containment of the amplification of capillary waves along the interface and puts more emphasis on the terms linked with the density in the Navier-Stokes equation (i. e. unsteady and inertia terms) rather than on the viscous terms. Indeed, the viscosity does not appear, as a parameter, in this stability condition.We propose a new stability condition which takes into account all fluid characteristics (density and viscosity) and for which we present a theoretical estimation. We detail the analysis which is based on a perturbation study -with capillary wave -for which we use energy estimate on the induced perturbed velocity. We validate our analysis and algorithms with numerical simulations of microfluidic flows using a Level Set method, namely the exploration of different mixing dynamics inside microdroplets.

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“…Among the recent works on surface-tracking we could mention Shyy et al (1996), Popinet & Zaleski (1999) and Tornberg (2000). The modified surface-tracking methods not using a connectivity of the set of interface points have been proposed in Torres & Brackbill (2000) and in Shin & Juric (2002). The comparison of front-tracking with lattice-Boltzmann method has been recently carried out in Sankaranarayanan et al (2003).…”

Section: Introductionmentioning

confidence: 99%

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

Smolianski

2005

Int. J. Numer. Meth. Fluids

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The present work is devoted to the study on unsteady flows of two immiscible viscous fluids separated by free moving interface. Our goal is to elaborate a unified strategy for numerical modeling of twofluid interfacial flows, having in mind possible interface topology changes (like merger or break-up) and realistically wide ranges for physical parameters of the problem. The proposed computational approach essentially relies on three basic components: the finite element method for spatial approximation, the operator-splitting for temporal discretization and the level-set method for interface representation. We show that the finite element implementation of the level-set approach brings some additional benefits as compared to the standard, finite difference level-set realizations. In particular, the use of finite elements permits to localize the interface precisely, without introducing any artificial parameters like the interface thickness; it also allows to maintain the second-order accuracy of the interface normal, curvature and mass conservation. The operator-splitting makes it possible to separate all major difficulties of the problem and enables us to implement the equal-order interpolation for the velocity and pressure. Diverse numerical examples including simulations of bubble dynamics, bifurcating jet flow and Rayleigh-Taylor instability are presented to validate the computational method.

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The Point-Set Method: Front-Tracking without Connectivity

Cited by 141 publications

References 32 publications

Numerical simulation of droplets, bubbles and waves: state of the art

Numerical simulation of droplets, bubbles and waves: state of the art

On stability condition for bifluid flows with surface tension: Application to microfluidics

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

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