A numerical method for capillarity-dominant free surface flows

The continuum surface force (CSF) method has been extensively employed in the volume-of-fluid (VOF), level set (LS) and front tracking methods to model the surface tension force. It is a robust method requiring relatively easy implementation. However, it is known to generate spurious currents near the interface, which may lead to disastrous interface instabilities and failures of grid convergence. A different surface tension implementation algorithm, referred to as the pressure boundary method (PBM), is introduced in this study. The surface tension force is incorporated into the Navier–Stokes equation via a pressure gradient while the free surface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method. It has been shown that the spurious currents are greatly reduced by the PBM method with the sharp pressure boundary condition preserved. The numerical results of several test cases have been obtained and are in close agreement with data reported in the literature.