# Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

## TL;DR

This paper introduces a novel 4D simplex space-time discretization method for simulating thermally coupled two-phase flow during mold filling, improving accuracy and efficiency in predicting injection molding defects.

## Contribution

It presents a new discretization approach using simplex space-time meshes for adaptive local refinement in complex mold filling simulations.

## Key findings

- Enhanced numerical accuracy near the melt front
- Efficient local temporal refinement in 4D space-time grids
- Successful application to 2D and 3D benchmark cases

## Abstract

The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.