Algebraic coupled level set-volume of fluid method for surface tension dominant two-phase flows

In this study, an Algebraic Coupled Level Set-Volume of Fluid (A-CLSVOF) method is proposed for the simulation of interfacial capillary flows. The Volume of Fluid (VOF) method is utilized to incorporate one-way coupling with the Level Set (LS) function in order to improve the accuracy of the surface tension force calculation and to reduce the presence of parasitic currents. In this method, both VOF and LS functions are transported where the new volume fraction determines the interface seed position utilized by the reinitialization procedure for the LS field. Computational efficiency is enhanced through the use of the advected LS field, serving as an initial condition for the reinitialization procedure. The Hamilton-Godunov function is used with a second order (in space and time) discretization scheme to produce a signed distance function. In order to evaluate the performance of the methodology implemented here for capillary dominant flows, four different cases were considered: 1. static droplet; 2. capillary wave relaxation; 3. Rayleigh-Taylor instability and 4. droplet impact on a liquid pool. The simulations demonstrated reduction in spurious currents, accurately predicted capillary pressure and demonstrated overall improvements in efficiency and error reduction owing to the addition of LS advection. The present methodology is tested against previously published experimental results for a droplet impact on a deep liquid pool. Simulation results demonstrate excellent agreement with measured interface height up to and beyond the formation of a Rayleigh-Jet and break-up formation of a secondary daughter drop.