A mixed markers and volume-of-fluid method for the reconstruction and advection of interfaces in two-phase and free-boundary flows

In this work we present a new mixed markers and volume-of-fluid (VOF) algorithm for the reconstruction and advection of interfaces in the two-dimensional space. The interface is described by using both the volume fraction function C, as in VOF methods, and surface markers, which locate the interface within the computational cells. The C field and the markers are advected by following the streamlines. New markers are determined by computing the intersections of the advected interface with the grid lines, then other markers are added inside each cut cell to conserve the volume fraction C. A smooth motion of the interface is obtained, typical of the marker approach, with a good volume conservation, as in standard VOF methods. In this article we consider a few typical two-dimensional tests and compare the results of the mixed algorithm with those obtained with VOF methods. Translations, rotations and vortex tests are performed showing that many problems of the VOF technique can be solved and a good accuracy in the geometrical motion and mass conservation can be achieved.