A numerical method for incompressible two-phase flows with open or periodic boundaries

A numerical method for computing unsteady, incompressible two-phase flows with open or periodic boundaries is presented. The method is based on a level set technique for capturing the phase interface, which is combined with a second-order projection method. At the open or periodic boundaries where the normal velocity components are not prescribed, the pressure conditions are calculated iteratively so that the computed flow rate should be equal to a given flow rate. The numerical method is applied for computations of a single Taylor bubble and a train of Taylor bubbles rising in a vertical tube.