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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.

We present in this paper a finite element analysis of Navier‐Stokes equations in a time‐varying domain. The method of weighted residuals is used together with the semi‐discretization approach to obtain the discrete equations. In this approach, where the physical domain is allowed to vary, care is taken to retain the space conservation law property. We describe in detail the transformation of equations between fixed and moving grids. The validity of this method has been tested against two problems which are amenable to analytic solutions. Time accurate results show favorable agreement with analytic solutions. Having verified the applicability of the Galerkin finite element code to problems involving moving grids, we consider the fluid flow in a vessel, where a portion of its boundary moves in time. Results are presented with emphasis on the depiction of vortical flow details.