The constrained reinitialization equation for level set methods

Hartmann, Daniel; Meinke, Matthias; Schröder, Wolfgang

doi:10.1016/j.jcp.2009.10.042

Cited by 129 publications

(69 citation statements)

References 18 publications

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“…Finally, the CR scheme is applied to a three-dimensional problem, a similar formulation of which is discussed in [10]. In this test case, three initially separated spherical interfaces centered at x 1 = (1.0, 1.5, 1.5) T , x 2 = (−1.7, 1.5, 1.5) T , and x 3 = (−0.5, −0.5, −0.5) T at radii r 1 = 1.2, r 2 = 1.0, and r 3 = 0.8 are expanded at the constant speed s = 1.…”

Section: Numerical Experimentsmentioning

confidence: 99%

On accuracy and efficiency of constrained reinitialization

Hartmann

Meinke

Schröder

2010

Numerical Methods in Fluids

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SUMMARYThe reinitialization, which is required to regularize the level set function, can be computationally expensive and hence is a determining factor for the overall efficiency of a level set method. However, it often has a significantly adverse impact on the accuracy of the level set solution. This short note is meant to shed light on the efficiency and accuracy issues of the reinitialization process. Using just one clearly defined level set propagation test case with an analytical solution the solutions obtained using a recently proposed efficient lower-order constrained reinitialization (CR) scheme and standard low-and high-order reinitialization schemes are juxtaposed to evidence the superiority of the novel CR formulation. It is shown that maintaining the location of the zero level set during the reinitialization is crucial for the accuracy and that the displacement caused by standard high-order reinitialization schemes clearly outweighs the benefit of the high-order smoothing of the level set function. Finally, results of a three-dimensional problem are concisely reported to demonstrate the general applicability of the CR scheme.

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Section: Numerical Experimentsmentioning

confidence: 99%

On accuracy and efficiency of constrained reinitialization

Hartmann

Meinke

Schröder

2010

Numerical Methods in Fluids

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“…As has been noted by several authors (e.g. see Hartmann, Meinke, & Schröder, 2010), reinitialization does not preserve the interface location exactly, and its too-frequent application may result in a loss of accuracy and numerical artifacts, as will be seen in subsequent sections of this paper.…”

Section: Methodsmentioning

confidence: 64%

“…see Hartmann et al, 2010). It is postulated that a good solution is to use the convective time step to determine the correct frequency.…”

Section: Remarks On Boundary Conditions and Reinitialization Frequencymentioning

confidence: 99%

Comment on the level-set method used in ‘Numerical study on mobilization of oil slugs in capillary model with level set approach’

Ervik

2016

Engineering Applications of Computational Fluid Mechanics

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This is a comment on a 2014 paper by Dai and Wang. It is argued that the validation in Dai and Wang's paper is an artifact caused by the boundary conditions of the level-set function, meaning that the effects reported in their paper have little physical relevance. Simulations are presented using Dai and Wang's methods to illustrate this claim. Remarks are made on the choice of boundary conditions for the level-set function, as well as the frequency of reinitialization, both of which are important topics that are sometimes overlooked. A simple criterion is proposed for determining the appropriate reinitialization frequency in simulations of highly viscous flows. ARTICLE HISTORY

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“…(8) can displace the zero level set and may lead to substantial errors due to the reinitialization; as a remedy they proposed a fix for the redistance step discretization of Sussman et al (1994). Recently, Hartmann et al (2008Hartmann et al ( , 2010a presented two new improved formulations of the methods of Sussman et al (1994) and Russo and Smereka (2000) for differential equation-based constrained reinitialization of the LS method. Different temporal discretization schemes for solution of Eq.…”

Section: Description Of the Interface Evolutionmentioning

confidence: 99%

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

Wörner

2012

Microfluid Nanofluid

370

197

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This article presents a comprehensive review of numerical methods and models for interface resolving simulations of multiphase flows in microfluidics and micro process engineering. The focus of the paper is on continuum methods where it covers the three common approaches in the sharp interface limit, namely the volumeof-fluid method with interface reconstruction, the level set method and the front tracking method, as well as methods with finite interface thickness such as color-function based methods and the phase-field method. Variants of the mesoscopic lattice Boltzmann method for two-fluid flows are also discussed, as well as various hybrid approaches. The mathematical foundation of each method is given and its specific advantages and limitations are highlighted. For continuum methods, the coupling of the interface evolution equation with the single-field Navier-Stokes equations and related issues are discussed. Methods and models for surface tension forces, contact lines, heat and mass transfer and phase change are presented. In the second part of this article applications of the methods in microfluidics and micro process engineering are reviewed, including flow hydrodynamics (separated and segmented flow, bubble and drop formation, breakup and coalescence), heat and mass transfer (with and without chemical reactions), mixing and dispersion, Marangoni flows and surfactants, and boiling.

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The constrained reinitialization equation for level set methods

Cited by 129 publications

References 18 publications

On accuracy and efficiency of constrained reinitialization

On accuracy and efficiency of constrained reinitialization

Comment on the level-set method used in ‘Numerical study on mobilization of oil slugs in capillary model with level set approach’

Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications

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