Application of the meshless generalized finite difference method to inverse heat source problems

•Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data. The generalized finite difference method (GFDM) is a relatively new...

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Bibliographic Details
Published in:	International journal of heat and mass transfer Vol. 108; pp. 721 - 729
Main Authors:	Gu, Yan, Wang, Lei, Chen, Wen, Zhang, Chuanzeng, He, Xiaoqiao
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.05.2017
Subjects:	Generalized finite difference method Inverse heat source problem Meshless method Steady-state heat conduction Steady-state heat conduction Generalized finite difference method Inverse heat source problem Meshless method
ISSN:	0017-9310, 1879-2189
Online Access:	Get full text
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Summary:	•Extending the GFDM to solve the fourth-order partial differential equations.•Making the first attempt to apply the GFDM to inverse heat source problems.•Promising results retrieved for heat sources were obtained with 2% noise data. The generalized finite difference method (GFDM) is a relatively new domain-type meshless method for the numerical solution of certain boundary value problems. This paper documents the first attempt to apply the method for recovering the heat source in steady-state heat conduction problems. In order to guarantee the uniqueness of the solution, the heat source here is assumed to satisfy a second-order partial differential equation, and thereby transforming the problem into a fourth-order partial differential equation, which can be solved conveniently and stably by using the GFDM. Numerical analysis are presented on three benchmark test problems with both smooth and piecewise smooth geometries. The stability and sensitivity of the scheme with respect to the amount of noise added into the input data are analyzed. The numerical results obtained show that the proposed algorithm is accurate, computationally efficient and numerically stable for the numerical solution of inverse heat source problems.
ISSN:	0017-9310 1879-2189
DOI:	10.1016/j.ijheatmasstransfer.2016.12.084