Document Type

Article

Journal/Book Title/Conference

AppliedMath

Author ORCID Identifier

Zilong Song:  https://orcid.org/0000-0002-2823-199X

Volume

6

Issue

9

Publisher

MDPI AG

Publication Date

9-5-2026

Journal Article Version

Version of Record

First Page

1

Last Page

29

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Abstract

Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments have been adopted for the POD and DEIM models: the introduction of preconditioner matrices to avoid large condition numbers and the use of indicator matrices to generate the non-linear data. For different cases regarding operating parameters, the results show that the DEIM model dramatically speeds up the computation (e.g., over 250 times faster compared with the full model) while maintaining accuracy. This makes simulations of the FSW process more accessible and easily combined with machine learning techniques in future study.

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