INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (2012) Published online in Wiley Online Library (wileyonlinelibrary.com/journal/nmf). DOI: 10.1002/fld.3723 Two-dimensional non-Newtonian injection molding with a new control volume FEM/volume of fluid method Carlos Salinas 1 , Diego A. Vasco 2 and Nelson O. Moraga 3, * ,† 1 Departamento de Ingeniería Mecánica, Universidad del Bío-Bío, Av. Collao 1202, Concepción, Chile 2 Departamento de Ingeniería Mecánica, Universidad de Santiago de Chile, Av. Lib. Bdo. O’Higgins 3363, Santiago, Chile 3 Departamento de Ingeniería Mecánica, Universidad de La Serena, Av. Benavente 980, La Serena, Chile SUMMARY A new method based on volume of fluid for interface tracking in the simulation of injection molding is presented. The proposed method is comprised of two main stages: accumulation and distribution of the volume fraction. In the first stage the equation for the volume fraction with a noninterfacial flux condition is solved. In the second stage the accumulated volume of fluid that arises as a consequence of the application of the first one is dispersed. This procedure guarantees that the fluid fills the available space without dispersion of the interface. The mathematical model is based on two-phase transport equations that are numerically integrated through the control volume finite element method. The numerical results for the interface position are successfully verified with analytical results and numerical data available in the literature for one-dimensional and two-dimensional domains. The transient position of the advance fronts showed an effective and consistent simulation of an injection molding process. The nondispersive volume of fluid method here proposed is implemented for the simulation of nonisothermal injection molding in two-dimensional cavities. The obtained results are represented as transient interface positions, isotherms and pressure distributions during the injection molding of low density polyethylene. Copyright © 2012 John Wiley & Sons, Ltd. Received 19 March 2012; Revised 21 June 2012; Accepted 23 July 2012 KEY WORDS: free surface; Eulerian; finite volume; non-Newtonian; Navier–Stokes; laminar flow 1. INTRODUCTION Several studies have been focused on the development of efficient methods and algorithms for the accurate prediction of the position of an interface in biphasic (gas–liquid) fluid flow. Although the applications may be numerous, the reported mainly deal with industrial processes such as polymer injection molding [1–3] and metal casting [4–6]. The methods employed for interface tracking are classified according to the domain discretization. In the variable grid methods, known and Lagrangian methods, the interface coincides with the front of the moving grid, which has to be redefined after each time step [7, 8]. Although the implementation of these methods does not require an explicit equation that describes the movement of the interface, the high computational cost for remeshing and the numerical instabilities produced by complex interfaces are two major disadvantages. For the fixed grid methods or Eulerians [9, 10], the grid is unique and remains constant during the whole calculation process. The implementation of fixed grid methods requires lower computational effort; nevertheless, the intrinsic characteristic of the interface being represented by a discontinuous function is missed. On the contrary, the interface is described by a continuous function in a region of the domain. *Correspondence to: Nelson O. Moraga, Departamento de Ingeniería Mecánica, Universidad de La Serena, Av. Benavente 980, La Serena, Chile. † E-mail: nmoraga@userena.cl Copyright © 2012 John Wiley & Sons, Ltd.