Open Access

ARTICLE

The Local Radial Basis Function Collocation Method for Evaluating the Non-Fourier Heat Transfer in Thermal Metamaterials

Anyu Hong¹, Zheng-Yang Li^2,*

1 School of Infrastructure Engineering, Nanchang University, Nanchang, China
2 National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing, China

* Corresponding Author: Zheng-Yang Li. Email:

Computer Modeling in Engineering & Sciences 2026, 148(2), 10 https://doi.org/10.32604/cmes.2026.084527

Received 24 April 2026; Accepted 24 July 2026; Issue published 28 August 2026

Abstract

The simulation of non-Fourier heat conduction poses significant computational challenges, particularly in periodic structures such as thermal wave crystals or thermal metamaterials. This paper employs the Local Radial Basis Function Collocation Method (LRBFCM) to evaluate the wave-like propagation characteristics inherent to the non-Fourier heat transfer process. Utilizing LRBFCM, the complex band structure of thermal wave crystals is calculated, and these findings are validated against temperature responses in the frequency domain. Finally, this study introduces a robust methodology for predicting non-Fourier heat conduction behavior in thermal metamaterials. In a word, this paper investigates the application of the LRBFCM method in calculating the abnormal properties of thermal wave crystals, which the LRBFCM has not been applied to such problems before. The results show that the calculations of the thermal wave crystals and thermal metamaterials with complex geometries and novel heat conduction phenomena can be calculated based on the LRBFCM. While the LRBFCM can achieve the same computational efficiency as the analytical method. The LRBFCM paves a robust method for dealing with ultrafast thermal processing such as laser hardening, laser cladding, metal additive manufacturing, and so on.

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Keywords

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