Numerical Simulation of Capillary Waves: Comparative Study of Volume of Fluid and Level Set Methods

Linear wave theory establishes a relationship between the interfacial tension, viscosity, and capillary wave parameters such as wavelength and decay coefficient. This makes capillary waves an excellent non-intrusive tool for measuring fundamental properties of liquids. But these waves exhibit distinct length scales for their amplitude and wavelength posing significant challenges for numerical simulation. This study investigates numerical simulation methods, Volume of Fluid (VoF) and Level Set (LS), in the context of capillary waves. Both methods are widely used to simulate multiphase flows and differ mainly in numerical implementation and approaches of handling the interface. Accuracy of measuring wave properties heavily relies on precise and reliable interface capturing prompting the need for a comparative investigation. For this study, interIsoFoam (OpenFOAM) and Level Set (COMSOL Multiphysics) solvers are considered. Numerical experiments conducted for a range of parameters show that VoF (average error = 1.09%) performs better than LS (average error = 3.92%). Additionally, VoF provides superior results in other aspects of the wave, including amplitude and sinusoidal appearance. This study also validates linear wave theory in real-world scenarios with finite-amplitude and finite-depth waves with reflections.