Abstract
The two-dimensional Kelvin-Helmholtz instability which arises in two immiscible co-currently moving horizontal liquid layers is studied numerically. Two different methods for capturing the free interface movement are applied, namely the volume-of-fluid method and the level-set method. Both methods are very popular and available within commercial computational fluid dynamics tools. The wave is initialized using two different perturbations implemented into the model. As a case study, a system comprising a toluene layer and an aqueous layer is chosen. Numerical results obtained by both methods are in a good agreement with the linear stability theory for small wave amplitudes. The application of both methods is compared and their advantages and drawbacks are highlighted.