A Localized Method of Fundamental Solution for Numerical Simulation of Nonlinear Heat Conduction

Feng Wang, Yan-Cheng Liu and Hui Zheng
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Feng Wang: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Yan-Cheng Liu: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China
Hui Zheng: School of Civil Engineering and Architecture, Nanchang University, Nanchang 330031, China

Mathematics, 2022, vol. 10, issue 5, 1-15

Abstract: In this study, an efficient localized method of fundamental solution (LMFS) is applied to nonlinear heat conduction with mixed boundary conditions. Since the thermal conductivity is temperature-dependent, the Kirchhoff transformation is used to transform the nonlinear partial differential equations (PDEs) into Laplace equations with nonlinear boundary conditions. Then the LMFS is applied to the governing equation, and the nonlinear equations are treated by the fictitious time integration method (FTIM). Both 2D and 3D numerical examples are proposed to verify the effectiveness of the LMFS.

Keywords: nonlinear heat conduction; Kirchhoff transformation; localized method of fundamental solutions; fictitious time integration method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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