Efficient Method for Improving Fully Implicit Scheme in Smoothed Particle Hydrodynamics for Highly Viscous and Non-Newtonian Polymer Flow

Abstract

Smoothed particle hydrodynamics (SPH), a fully Lagrangian particle method, has been widely used in various applications, such as the simulation of incompressible flow with a free surface. For highly viscous flow, which typically appears in polymer processing, a fully implicit scheme, which implicitly treats both the predictor and corrector procedures of the projection method in the SPH framework, is efficient and numerically stable. This study proposes a simple and efficient fully implicit scheme that improves predictive accuracy for highly viscous flow. The proposed scheme utilizes a recently developed scheme for highly viscous flow that performs the pressure calculation before the viscosity diffusion calculation, unlike the conventional projection method. This study further improves the viscosity diffusion calculation by considering a viscous diffusion term that is usually ignored due to the continuity equation. Including this term enables us to correctly perform calculations for non-Newtonian flows. The increase in the computational cost that results from the inclusion of the term is alleviated by introducing a two-step method for calculating the viscous diffusion terms. The developed scheme is applied to injection molding of a polymer melt between two parallel plates. The results show that the proposed two-step implicit scheme reproduces the fountain flow behavior near the advancing front. In addition, a three-dimensional molding simulation of a plate with a hole shows a significant improvement in the prediction of the filling pattern in the mold.