A simple volume-of-fluid reconstruction method for three-dimensional two-phase flows

Abstract

A new PLIC (piecewise linear interface calculation)-type VOF (volume of fluid) method, called APPLIC (approximated PLIC) method, is presented. Although the PLIC method is one of the most accurate VOF methods, the three-dimensional algorithm is complex. Accordingly, it is hard to develop and maintain the computational code. The APPLIC method reduces the complexity using simple approximation formulae. Three numerical tests were performed to compare the accuracy of the SVOF (simplified volume of fluid), VOF/WLIC (weighed line interface calculation), THINC/SW (tangent of hyperbola for interface capturing/slope weighting), THINC/WLIC, PLIC, and APPLIC methods. The results of the tests show that the APPLIC results are as accurate as the PLIC results and are more accurate than the SVOF, VOF/WLIC, THINC/SW, and THINC/WLIC results. It was demonstrated that the APPLIC method is more computationally efficient than the PLIC method.

Analytic Solution to the Piecewise Linear Interface Construction Problem and Its Application in Curvature Calculation for Volume-of-Fluid Simulation Codes

“…The approach is to calculate the volume of the tetrahedral pyramid formed by the plane and the coordinate system axes and, if necessary, subtract the volumes of zero, one, two or all three corners that extend beyond 1. For case (3), an additional condition is required to mutually exclude case (5), in which the bottom four corners of the cube are located beneath the plane.…”

“…which is already considerably more friendly and completes the inverse PLIC formulation in conjunction with Equations ( 2)-( 4), ( 6) and (7). The condition for case (5) is the remaining free sector of the possible range of d mutually excluded by the other four cases. Listing A1 shows the fully optimized C implementation of the inverse PLIC solution.…”

“…The analytic PLIC solution by Scardovelli and Zaleski from 2000 [4] was implemented in Fortran in 2016 by Kawano [5], where it was used as a comparison to the approximative APPLIC method. Here, we focus on the exact SZ solution.…”

“…Figure 1), of which the numbers (1), ( 2) and ( 5) have been already solved in the original 1984 work by Youngs [2], but the cubic polynomial cases (3) and (4)-considered impossible to algebraically invert [3]-in the majority of the literature are approximated by a Newton-Raphson iterative solution. Nevertheless, there does exist an analytic solution by Scardovelli and Zaleski (SZ) [4] and a single documented implementation thereof in Fortran [5], which also includes an approximative version termed APPLIC.…”

Sharp-Interface Phase-Change Model With the Vof Method

“…In this work, a coupling of the geometric VOF method of Kawano [5] with the sharp-interface phase-change model of Sato and Niceno [11] was developed and implemented in the framework of the PSI-BOIL CFD code [8]. The developed method was subjected to the standard procedure of computer code verification and validation to establish its credibility; for verification purposes, several problems including the Stefan problem and the Sucking problem were considered.…”