Mould filling simulation using finite elements

Abstract

In this paper we consider several aspects related to the application of the pseudo‐concentration techniques to the simulation of mould filling processes. We discuss, in particular, the smoothing of the front when finite elements with interior nodes are employed and the evacuation of air through the introduction of temporary free wall nodes. The basic numerical techniques to solve the incompressible Navier—Stokes equations are also briefly described. The main features of the numerical model are the use of div‐stable velocity—pressure interpolations with discontinuous pressures, the elimination of the pressure via an iterative penalty formulation, the use of the SUPG approach to deal with convection‐dominated problems and the temporal integration using the generalized trapezoidal rule. At the end of the paper we present some numerical results obtained for a two‐dimensional test problem showing the ability of the method to capture complicated flow patterns.

Computation of mould filling processes with a moving Lagrangian interface technique

“…To prevent numerical oscillations that might be generated in solving an advection-dominated problem with a standard Galerkin formulation, methods that stabilize the formulation need to be applied. Among the stabilized methods used for this purpose by other researchers are the Taylor-Galerkin and streamline-upwind=Petrov-Galerkin (SUPG) approaches (see References [3][4][5]). These approaches must be supplemented with techniques that reduce the smearing of the pseudo-concentration proÿle and yield more accurate representation of the interface (see References [2][3][4][5]).…”

“…Among the stabilized methods used for this purpose by other researchers are the Taylor-Galerkin and streamline-upwind=Petrov-Galerkin (SUPG) approaches (see References [3][4][5]). These approaches must be supplemented with techniques that reduce the smearing of the pseudo-concentration proÿle and yield more accurate representation of the interface (see References [2][3][4][5]). In comparison, in the ÿxed-grid ÿnite di erence level set methods (see References [7; 8]), a distance reinitialization procedure is used to redeÿne the pseudo-concentration function, assuring that it does not become too at or too steep near the interface.…”

“…A Galerkin formulation with non-equal-order approximation functions representing the unknowns was used in References [3; 4]. Finite element discretizations with continuous velocity and discontinuous pressure have been applied in Reference [5]. Formulations that use equal-order functions for velocity and pressure have been proposed and extensively employed in a number of contexts (see References [11; 12] and references therein).…”

Finite-element/level-set/operator-splitting (FELSOS) approach for computing two-fluid unsteady flows with free moving interfaces

“…This gives rise to the notion of "level-set approach" that started from the work Osher & Sethian (1988) and has been further developed in Sussman et al (1994), Chang et al (1996), Tornberg (2000), Quecedo & Pastor (2001), Codina & Soto (2002), Iafrati & Campana (2003), see also the books Sethian (1999) and Osher & Fedkiw (2003). A very similar "pseudo-concentration" technique was developed in a parallel manner, see Thompson (1986), Codina et al (1994), Lewis et al (1995), Lock et al (1998).…”

Finite element simulation of the filling of thin moulds

“…Air release. As explained in [4], one of the problems of the VOF formulation as described above is the evacuation of air bubbles. Since we deal with incompressible ows, air cannot shrink and air bubbles near the corners will remain if a method to evacuate them is not devised.…”