Space–time method for analyzing transient heat conduction in functionally graded materials

Abstract

In this study, a novel approach is presented for simulating transient heat conduction in functionally graded materials (FGM) with varying material properties only in the z direction. The proposed collocation method employs a meshless localized space–time radial basis function (LSTRBF), which yields a linear sparse matrix system, offering advantages over the global method in terms of scalability and suitability for multidimensional problems. Additionally, a novel shape parameter strategy, known as variable leave-one-out cross-validation (LOOCV), is introduced to enhance accuracy while overcoming conventional LOOCV limitations. Four benchmark numerical examples are utilized to demonstrate the simplicity, efficiency, accuracy, and stability of the method. Overall, the proposed LSTRBF method presents a promising alternative for efficiently and accurately simulating transient heat conduction in FGMs.

Keywords:

• 3D transient heat transfer
• functionally graded materials
• localized space–time radial basis function
• meshless method
• multiquadrics
• shape parameter

Disclosure Statement

No potential conflict of interest was reported by the author(s)

Acknowledgments

We would like to express our sincere gratitude to the reviewers for their valuable and constructive feedback. We gratefully acknowledge the financial support of the Ministry of Science and Technology (MOST) of Taiwan under grant numbers 111-2811-E002-062 and 109-2221-E002-006-MY3. This article was subsidized for English editing by National Taiwan University under the Excellence Improvement Program for the Data-Driven Constitutive Model Free Computational Mechanics program. Authors are also grateful for the computational resources and support from the NTUCE-NCREE Joint Artificial Intelligence Research Center and the National Center of High-performance Computing (NCHC).