A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surfacetracking algorithm and its verification

Numerical simulation of fluid flow with moving free surface has been performed. For the free surface flow, a volume of fluid (VOF)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface-tracking algorithm based on the donor-acceptor scheme has been proposed. Novel features of the proposed algorithm are characterized by two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems usually encountered in the finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3D free surface flow problems without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the streamline upwind/Petrov-Galerkin (SUPG) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface-tracking scheme and the explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.