An Application of Modified S-CLSVOF Method to Kelvin-Helmholtz Instability and Comparison with Theoretical Result

This study focuses on validating a two-phase flow solver based on the modified Simple Coupled Level Set and Volume of Fluid method (Uchihashi et al. 2023) through viscous Kelvin-Helmholtz instability simulations. Our numerical simulation results are compared with the ones given by Funada and Joseph (2001) to provide reliable predictions of interface behavior under the influence of viscosity. The primary goal is to accurately assess the solver’s ability to replicate theoretical analysis of interface behaviors under various conditions. First, the wave between two fluids of identical density is calculated. In addition, the effect of surface tension is investigated. By comparing growth rates, numerical simulations obtain well-agreements with the analytical results on the effect of the fluid viscosity, the wave number, and the surface tension. Finally, fluid density is changed to an air-water system. When relative velocity [Formula: see text] is smaller than the criteria of relative velocity [Formula: see text] given by analytical solutions, the wave is not broken. However, waves are splashed into droplets in the condition of [Formula: see text] This result agrees with the analysis by Funada and Joseph (2001). These findings provide a robust framework for applying the solver to more complex two-phase flow problems, supporting advancements in numerical simulations of fluid interfaces.