Numerical simulation of the filling stage for plastic injection moulding based on the Petrov-Galerkin methods

Abstract

Simulation of plastic injection moulding is carried out essentially to solve non-isothermal, viscous, incompressible, and non-Newtonian convection-diffusion flow equations. However, finite element methods present spurious numerical oscillations, which give a failure result associated with the classical Galerkin formulations of viscous incompressible Navier-Stokes equations. The streamline-upwind/Petrov-Galerkin (SUPG) and pressure-stabilizing/Petrov-Galerkin (PSPG) formulations were employed to prevent these potential numerical instabilities by adding to the weighting functions with their derivatives, thus resulting in stabilized finite element formulations using equal-order interpolation functions for velocity and pressure. Numerical experiments showed that the numerical algorithms developed perform in a stable way and give accurate results compared with the well-known commercial software Moldflow.