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

Abstract

SUMMARYNumerical simulation of uid ow with moving free surface has been performed. For the free surface ow, a volume of uid (VOF)-based algorithm utilizing a ÿxed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a ÿxed 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 uid volume ux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems usually encountered in the ÿnite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3D free surface ow problems without additional e orts. For computation of unsteady incompressible ow, a ÿnite 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 ows. Combination of the proposed free surfacetracking scheme and the explicit fractional step formulation resulted in an e cient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

Diffuse interface tracking of immiscible fluids: Improving phase continuity through free energy density selection

“…Nonetheless, the performance of new interface tracking techniques is frequently benchmarked using free surface flow systems, such as the collapse of a liquid column under gravity (Koshizuka and Oka, 1996;Kim and Lee, 2003;Sochnikov and Efrima, 2003;Yue et al, 2003;Bonet et al, 2004;Cruchaga et al, 2007). Using the experimental data of Cruchaga et al (2007), Koshizuka and Oka (1996) and Martin and Moyce (1952), the interface tracking capabilities of the VOF model built into OpenFOAM Ò and the TVSED function at T R = 0 and T R =1 were compared for the case of a collapsing column of water with initial width, L = 0.114 m, and aspect ratio, A R = H/L =2.…”

Two-Dimensional Non Newtonian Fluid Injection Moulding Filling Improved With a Cvfem/Vof Method

“…In the variable grid methods, known as well as Lagrangian methods, the interface coincides with the front of the moving grid, which has to be redefined after each time step [3,10]. For the fixed grid or Eulerian methods [11,21], the grid is unique and remains constant during the whole calculation process.…”

“…Kim and Lee [10] implemented an explicit formulation of the VOF equation on terms of the actual fractional volume of fluid which is a measure of the wetted area of the boundary of a control volume. In this method, the effective volume of a cell is calculated as a function of the orientation vector of the free surface and the value of the volume fraction in such a cell.…”

A numerical investigation of the resin flow front tracking applied to the RTM process

“…In the great majority of the reported works, the referred Laplace equation is solved using a finite element method, which is the obvious choice for complex geometry discretized domains. The difficulty associated with the use of the Finite Element method regards the evaluation of the mass flow-rate along the grid, which is commonly carried out by creating control volumes around the grid nodes and using the element local system of coordinates to calculate the resin fluxes along the In VOF method the volume fraction f of each fluid volume is determined by solving a transport equation for f, but this solution tends to smear in the volumes close to the moving surface 22 . The gradient of f should be singular at the interface of two inviscid fluids, however it becomes finite in the numerical solution, causing this abnormality.…”