A Numerical Method for Capillarity-Driven 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 surface tension force. It is a robust method requiring relatively easy implementation. However, it is known to generate spurious currents near the interface that 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 capillary 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 present method with the sharp pressure boundary condition preserved. The numerical results of several cases have been compared with data reported in the literature and are found to be in a close agreement.