A new VOF unsplit predictor-corrector algorithm for two-phase flow

The accurate advection of each fluid component in a two-phase flow is very important for the conservation of mass and the interface motion. In this work we present a new unsplit Eulerian algorithm in a two-dimensional geometry to compute the fluxing areas across the cell boundary. To simplify the problem we consider a staggered MAC grid with square cells and the velocity components located in the middle of the cell sides. We use a predictor-corrector technique to trace back the position of the four cell vertices and to compute the total fluid area that at the same time will flow across each cell side. We use a fourth-order Runge-Kutta integration scheme to follow the fluid motion along the characteristics, with a bilinear interpolation of velocity field inside the cell from the vertex values. The main improvement with respect to other Eulerian fluxing schemes is that there is no overlapping area and that the mapped lines are continuous.We consider two reconstruction algorithms and present and compare results for the standard single vortex test.