On surface tension modelling using the level set method

Abstract

SUMMARYThe paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface-tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two-phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching-off of interfaces, the traditional level set model of surface tension produces an error that results in non-converging solutions for film-like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first-order convergence.

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

“…From the various applications that will be discussed in the second part of this review, FLUENT is used in (Hardt 2005;Taha and Cui 2006a, b;Tanthapanichakoon et al 2006;Abdallah et al 2006;Hardt and Wondra 2008;Ö zkan et al 2007;Zhu et al 2008;Liu and Wang 2008;Urbant et al 2008;Alke and Bothe 2009;Gupta et al 2009bGupta et al , 2010Santos and Kawaji 2010), CFX in (Schönfeld and Rensink 2003;Ndinisa et al 2005;Ö zkan et al 2007;Shao et al 2008;Shepel and Smith 2009;Xiong and Chung 2010), STAR-CD in (Ö zkan et al 2007;Wegener et al 2009), CFD-ACE? in (Kobayashi et al 2004;Rosengarten et al 2006;Saha and Mitra 2009b;Lai et al 2010), TransAT in (Naraynan and Lakehal 2006;Lakehal et al 2008;Narayanan and Lakehal 2008;Chatzikyriakou et al 2009;Gupta et al 2010), COMSOL in (Zagnoni et al 2010;Constantinou and Gavriilidis 2010;Chasanis et al 2010;Kenig et al 2011) and OpenFOAM in (Saha and Mitra 2009a;Kunkelmann and Stephan 2009).…”

“…Essentially, it replaces d C by the local interfacial area concentration a i , which can be interpreted as a smoothed delta function, see also Gada and Sharma (2009). Shepel and Smith (2009) performed simulations with the LS method and compared the performance of this interfacial area concentration surface tension model and a modification of it with that of CSF models based on a regularized Dirac delta function. The authors found that the modified interfacial area concentration model gives superior results for film-like interfaces.…”

A hybrid level-set/moving-mesh interface tracking method

“…The difficulty with level-set two-phase flow simulations is that the implementation of the interfacial jump conditions on a fixed mesh results in at most second-order accuracy [20,30] and more typically first-order accuracy when a regularization of the interfacial discontinuity is used [47]. No level-set methods for two-phase flows with surface tension have surpassed second-order accuracy, including conservative level-set and coupled level-set/volume-of-fluid methods [31,43,45], although there have been many attempts to improve the accuracy [38,40].…”

Simulation of free surface flows using the flux‐difference splitting scheme on the hybrid Cartesian/immersed boundary method

“…Surface fitting methods [1,2] are suitable for simple free surface flows but not for violent free surface flows. The volume of fluid (VOF) type methods [3][4][5][6][7] and the level set method [8][9][10][11] have been adopted 361 by many researchers to simulate free surface flows. However, it is difficult to reconstruct free surfaces or maintain mass conservation of each fluid component as the flow fields become complicated.…”