From level set to volume of fluid and back again at second‐order accuracy

Abstract

Summary We present methods for computing either the level set function or volume fraction field from the other at second‐order accuracy. Both algorithms are optimal in that O(N) computations are needed for N total grid points and both algorithms are easily parallelized. This work includes a novel interface reconstruction algorithm in three dimensions that requires a smaller local block of volume fractions than existing algorithms. A compact local solver leads to better algorithm portability and efficiency: for example, fewer restrictions must be imposed on an adaptive mesh, and fewer grid cells must be communicated between processors in a parallel implementation. We also present a fast sweeping method for computing a unique approximation of the signed distance function to a piecewise linear interface. All of the numerical examples confirm second‐order accuracy on both uniform and tree‐based adaptive grids. Copyright © 2015 John Wiley & Sons, Ltd.

Simulation of liquid composite moulding using a finite volume scheme and the level-set method

“…From Eqs. (11)(12) and Fig. 2, it is noted that as h approaches 0, the estimate of the absolute distance to the interface improves.…”

“…where H i,j is a window function that only includes cells in the narrow band around the interface, and N is the number of cells in the narrow band. The area of the resin domain, S, is calculated using simplices [12] that is 2 nd -order accurate.…”

“…The volumes used for determining the errors are calculated using simplices [12]. As it can be seen in Fig.…”

SAAMPLE: A Segregated Accuracy-driven Algorithm for Multiphase Pressure-Linked Equations

“…where α f denotes the fraction of face f wetted by the corresponding phase. The area fractions are computed in a similar fashion as the volume fractions by using the two-dimensional variant of [27]. For the sake of efficiency, α f is only computed in this way for faces intersected by the Front, i.e.…”

A conservative and well-balanced surface tension model

“…The volume fraction is computed by reconstructing the droplet interface from the level-set information. The interface reconstruction is second-order, where each computational cell is divided into simplexes and the interface intersection points are determined through linear interpolation [6]. The relevant flow parameters are Re = 0.066 and Ca = 0.066.…”