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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Feng Wang & Yan-Cheng Liu & Hui Zheng, 2022. "A Localized Method of Fundamental Solution for Numerical Simulation of Nonlinear Heat Conduction," Mathematics, MDPI, vol. 10(5), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:773-:d:760736
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    Cited by:

    1. Oswaldo González-Gaxiola & Anjan Biswas & Yakup Yıldırım & Luminita Moraru, 2022. "Highly Dispersive Optical Solitons in Birefringent Fibers with Polynomial Law of Nonlinear Refractive Index by Laplace–Adomian Decomposition," Mathematics, MDPI, vol. 10(9), pages 1-12, May.

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