An unsplit lagrangian advection scheme for volume of fluid method

An Unsplit Lagrangian Advection (ULA) scheme for Volume Of Fluid (VOF) method is presented in this article. The ULA scheme is developed based on an algorithm of Piecewise Linear Interface Construction (PLIC). The volume fluxes between cells are calculated through solving the new equation of the linear interfaces in cells in the ULA scheme. The fluxes flowing out from one cell is the inflow fluxes for another cell. In this way the whole fluid volume is conserved strictly without using any redistribution algorithms. The ULA scheme is based on two-dimensional structured rectangular mesh and may be extended to three-dimensional structured mesh with more geometrical efforts. The results from three widely-used benchmark tests show that the ULA scheme can achieve the accuracy higher than Split Lagaragian Advection (SLA) scheme and the Flux-Corrected Transport (FCT) algorithm.