# Mass conservation analysis of extrusion-based 3D printing simulations based on the level-set method

## TL;DR

This paper evaluates the mass conservation performance of the conservative level-set method in extrusion-based 3D printing simulations, highlighting how parameter tuning improves accuracy and efficiency.

## Contribution

It provides a systematic analysis of how interface thickness and reinitialization parameters affect mass conservation, offering a validated parameter tuning strategy for simulations.

## Key findings

- Reducing interface thickness improves mass conservation accuracy.
- Tuning reinitialization parameters enhances simulation reliability.
- Validated across various materials and geometries.

## Abstract

Accurate numerical simulation of material extrusion additive manufacturing requires reliable tracking of evolving material interfaces while preserving mass conservation. Inaccurate mass conservation can lead to significant discrepancies between simulated and deposited strand geometries, undermining the predictive capability of the model. In this work, we investigate the mass conservation performance of the conservative level-set (CLS) method in extrusion-based 3D printing simulations. A systematic parametric study is conducted to quantify the influence of the interface thickness and reinitialization parameters on mass conservation, using the steady-state cross-sectional area of deposited strands as a quantitative metric. Simulated cross-sections are compared against reference values obtained from analytical mass balance relations. The results show that reducing both the interface thickness and the reinitialization parameter improves mass conservation accuracy, although diminishing returns and increased computational cost are observed beyond certain thresholds. In addition, appropriate tuning of the interface thickness can relax mesh refinement requirements while maintaining acceptable accuracy. The proposed parameter selection strategy is validated across a range of printing conditions, materials, and nozzle geometries, including multilayer deposition of viscoplastic fluids. The simulations show reasonable agreement with experimentally validated data from the literature, confirming that careful CLS parameter tuning enables accurate and computationally efficient prediction of strand geometry in extrusion-based 3D printing.