A finite volume coupled level set and volume of fluid method with a mass conservation step for simulating two‐phase flows

Abstract

This article presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that the interface is calculated in order to satisfy mass conservation with no explicit interface reconstruction step and the mass fluxes across cell-faces are corrected to respect the recovered volume fraction. The mass-conservation correction step proposed here, is utilized using an iterative algorithm which solves a reaction-diffusion equation for the mass correction of the level set. The re-sharpened volume fraction is used for the new volumetric fluxes at each cell which are calculated through the proposed algorithm that guarantees that they satisfy mass conservation. The algorithm is not limited in representing the interface with the 0.5-contour and is applicable for arbitrary polyhedral cells. Good accuracy and mass conservation are achieved when compared to other conservative approaches.

Dynamical Behavior of Nonlinear Coupled Reaction-Diffusion Model: A Numerical Study Utilizing ADI and Staggered Grid Finite Volume Method in Matlab

“…Recently Mas Irfan P. Hidayat et al(2023) introducing a novel meshfree method based on moving Kriging interpolation for efficient and accurate numerical solutions to reaction-diffusion problems [22]. Lyras et al(2022) introduces a finite volume method that employs a level set approach coupled with the volume of fluid method, enabling the simulation of two-phase flows with sharp fluid interfaces [23].…”