Numerical investigation of non-isothermal viscoelastic filling process by a coupled finite element and discontinuous Galerkin method

Abstract

In this paper, we study the challenging non-isothermal polymer filling process for the cavity with irregular inserts via a coupled finite element method (FEM) and discontinuous Galerkin (DG) method. The non-isothermal eXtended Pom-Pom (XPP) model is utilized to suitably describe the viscoelastic behavior of the branched polymer melt. As for the energy equations, we decouple the convective and diffusive terms to get two sub-equations. It is also able to receive several sub-equations from the momentum equation via splitting scheme. Then the hyperbolic and elliptic type sub-equations are solved via DG and FEM, respectively. The level set method is employed to capture the complicated transient free surface. Due to the pure convective character of the level set and XPP constitutive equations, the Runge-Kutta Discontinous Galerkin (RKDG) is used to deal with them. In this coupled algorithm, it is able to take full advantages of FEM and DG and also avoid the stabilization terms. The non-isothermal filling process of the rectangle cavity with a circular cone insert is first investigated to illustrate the feasibility and validity of the coupled method. Moreover, a more complex mould cavity, the socket with five irregular inserts, is studied as an application case to demonstrate the robustness and practicability of our coupled method. The influences of the inlet melt temperature on the stress and stretch are all analyzed.