# Boundary-Conforming Finite Element Methods for Twin-Screw Extruders using Spline-Based Parameterization Techniques

## TL;DR

This paper introduces a spline-based meshing technique for boundary-conforming finite element simulations in twin-screw extruders, enabling efficient, accurate, and adaptable flow and temperature modeling for complex geometries.

## Contribution

The paper presents a novel spline-based meshing method that generates boundary-conforming meshes efficiently at run-time, reducing memory and computational costs for complex screw geometries.

## Key findings

- Effective boundary-conforming meshes generated for complex screw geometries.
- Method reduces re-meshing costs and improves simulation accuracy.
- Demonstrated applicability to 2D and 3D non-Newtonian fluid flows.

## Abstract

This paper presents a novel spline-based meshing technique that allows for usage of boundary-conforming meshes for unsteady flow and temperature simulations in co-rotating twin-screw extruders. Spline-based descriptions of arbitrary screw geometries are generated using Elliptic Grid Generation. They are evaluated in a number of discrete points to yield a coarse classical mesh. The use of a special control mapping allows to fine-tune properties of the coarse mesh like orthogonality at the boundaries. The coarse mesh is used as a 'scaffolding' to generate a boundary-conforming mesh out of a fine background mesh at run-time. Storing only a coarse mesh makes the method cheap in terms of memory storage. Additionally, the adaptation at run-time is extremely cheap compared to computing the flow solution. Furthermore, this method circumvents the need for expensive re-meshing and projections of solutions making it efficient and accurate. It is incorporated into a space-time finite element framework. We present time-dependent test cases of non-Newtonian fluids in 2D and 3D for complex screw designs. They demonstrate the potential of the method also for arbitrarily complex industrial applications.