A new implicit surface tension implementation for interfacial flows

Abstract

SUMMARYA new implementation of surface tension e ects in interfacial ow codes is proposed which is both fully implicit in space, that is the interface never has to be reconstructed, and also semi-implicit in time, with semi-implicit referring to the time integration of the surface tension forces. The main idea is to combine two previously separate techniques to yield a new expression for the capillary forces. The ÿrst is the continuum surface force (CSF) method, which is used to regularize the discontinuous surface tension force term. The regularization can be elegantly implemented with the use of distance functions, which makes the level set method a suitable choice for the interface-tracking algorithm. The second is to use a ÿnite element discretization together with the Laplace-Beltrami operator, which enables simple reformulation of the surface tension term into its semi-implicit equivalent. The performance of the new method is benchmarked against standard explicit methods, where it is shown that the new method is signiÿcantly more robust for the chosen test problems when the time steps exceed the numerical capillary time step restriction. Some improvements are also found in the average number of nonlinear iterations and linear multigrid steps taken while solving the momentum equations.

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

“…Due to the highly non-linear coupling induced by φ in (1)- (2)- (4), implicit treatment of surface tension is not an easy task. A step in this direction was recently performed by Hysing in [15] where he proposed a semi-implicit discretization of the surface tension term (see also preceding works of Bänsch [3]). …”

Quantitative benchmark computations of two‐dimensional bubble dynamics

“…Surface tension effects were incorporated by straight line approximation of the interface contours and direct integration over these line segments instead of using the usual continuum surface force approach. More details on the implementation, solver aspects, and surface tension treatment can be found in References [29,[32][33][34].…”

A semi‐implicit finite volume implementation of the CSF method for treating surface tension in interfacial flows

“…Hysing [2] recently reported a semi-implicit approach to the CSF model, where t ST can be exceeded by at least a factor of 10. He presented his method in a finite element context and incorporated it into an extended version of the FEATFLOW [3] solver, where the level set (LS) method is used to represent fluid interfaces.…”