An RBF meshless method for injection molding modelling

Abstract

Recently, very intensive efforts have been devoted to develop meshless or element free methods that eliminate the need of element connectivity in the solution of PDEs. The motivation is to cut down modelling costs in industrial applications by avoiding the labor intensive step of mesh generation. In addition, these methods are particularly attractive in problems with moving interfaces since no remeshing is necessary. In this paper, we address the problem of injection molding described as a free boundary problem defined by conservation equations for mass, momentum and energy. This model can be dramatically simplified assuming that the mould is thin so that a Hele-Shaw approximation can be used. In this case the momentum equation is just a 2D elliptic equation whose solution yields the pressure distribution in the filled region of the mould. From this pressure field, the velocity distribution can be computed and the location of the advancing front can be updated. Therefore, this problem is very well suited to meshfree techniques and, in this paper, we use a radial basis function (RBF) method which is based on the interpolation and collocation of global shape functions, and for simplicity assume a Newtonian fluid so that the model is linear. In particular, we use multiquadric (MQ) RBFs which have been shown to have exponential convergence. To advance the front we use a level set method which is very efficient for this type of problems because it is very fast and can handle both front collisions and front break-ups without difficulty.