Application of the level set method to the finite element solution of two-phase flows

Quecedo, Manuel Pulido; Pastor, Manuel

doi:10.1002/1097-0207(20010130)50:3<645::aid-nme42>3.0.co;2-2

Cited by 37 publications

(23 citation statements)

References 24 publications

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“…Mesh adaptivity, but in quadrilateral grids, is also used by Strain [11] to solve level set equations with a time stepping semi-Lagrangian formulation. More recently, References [19,20] propose the combination of the level set method with ÿnite elements for two-phase ows; Chessa and Belytschko [19] uses an extended ÿnite-element method and Quecedo and Pastor [20] applies the characteristic based scheme of Reference [21].…”

Section: Numerical Formulationmentioning

confidence: 99%

A semi‐Lagrangian level set method for incompressible Navier–Stokes equations with free surface

Gutiérrez

Bermejo

2005

Numerical Methods in Fluids

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In this paper, we formulate a level set method in the framework of ÿnite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier-Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier-Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and exible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the ow past a NACA0012 foil at high Reynolds number.A SEMI-LAGRANGIAN LEVEL SET METHOD 1113 mesh [15], our quasi-monotone interpolation is very general in the sense that it is suitable for any type of mesh without any additional e ort. We should understand quasi-monotone interpolation as positive interpolation or, better perhaps, as a type of essentially non oscillatory interpolation because it can hold oscillations with amplitude O(h p+1 ), where h denotes the mesh size parameter and p the degree of the polynomial interpolation. Moreover, our method to provide quasi-monotonicity is not speciÿcally designed for Lagrange interpolation; on the contrary, it can be executed as well with Hermite interpolation, spline interpolation or even trigonometric interpolation. (ii) We do reinitialization (redistancing) of the level set function by using Sussman and Fatemi algorithm [16] in our semi-Lagrangian framework. The numerical solution of the Navier-Stokes equations is calculated as proposed by Allievi and Bermejo in Reference [12], using the quasi-monotone extension of the conventional semi-Lagrangian interpolation ÿrst introduced in Reference [14].

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Section: Numerical Formulationmentioning

confidence: 99%

A semi‐Lagrangian level set method for incompressible Navier–Stokes equations with free surface

Gutiérrez

Bermejo

2005

Numerical Methods in Fluids

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“…This gives rise to the notion of "level-set approach" that started from the work Osher & Sethian (1988) and has been further developed in Sussman et al (1994), Chang et al (1996), Tornberg (2000), Quecedo & Pastor (2001), Codina & Soto (2002), Iafrati & Campana (2003), see also the books Sethian (1999) and Osher & Fedkiw (2003). A very similar "pseudo-concentration" technique was developed in a parallel manner, see Thompson (1986), Codina et al (1994), Lewis et al (1995), Lock et al (1998).…”

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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“…As an effective alternative, it is possible to use the level set technique, which consists in transforming the indicator function on a distance function (Quecedo & Pastor, 2001). These models are expensive in terms of computer effort, and therefore their use is restricted to cases in which it is necessary to know the fine structure of the flow, forces againt structures, etc.…”

Section: Proposed Model Introductionmentioning

confidence: 99%

Modelling tailings dams and mine waste dumps failures

et al. 2002

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This paper presents a depth-integrated model that can be used to simulate the flowslides, mudflows and debris flows that are caused by the failure of tailing dams, mining waste dumps and other similar structures. The sliding mass is first determined using a coupled elastoplastic finite element code and a suitable constitutive equation. Once failure has been triggered, propagation of the mobilised material is analysed considering flow properties averaged over depth. A simple law of pore pressure dissipation is postulated for cases in which the consolidation and propagation times are of the same order of magnitude.

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Application of the level set method to the finite element solution of two-phase flows

Cited by 37 publications

References 24 publications

A semi‐Lagrangian level set method for incompressible Navier–Stokes equations with free surface

A semi‐Lagrangian level set method for incompressible Navier–Stokes equations with free surface

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

Modelling tailings dams and mine waste dumps failures

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