An extended method of time-dependent fundamental solutions for inhomogeneous heat conduction

• Published in: Engineering analysis with boundary elements Vol. 33; no. 5; pp. 717 - 725
• Main Author: Dong, C.F.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-05-2009; Elsevier
• Subjects: Approximation; Boundary element method; Boundary-integral methods; Computational techniques; Conduction; Effectiveness; Eigenvalues; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat conduction; Heat transfer; Inhomogeneous heat conduction; Inhomogeneous media; Mathematical analysis; Mathematical methods in physics; Mathematical models; Method of fundamental solutions; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Physics; Transient heat conduction; Method of fundamental solutions; Inhomogeneous heat conduction; Transient heat conduction; Transient response; Point sources; Particular solution; Modelling; Eigenvalue problem; Collocation method; Heat transfer; Thermal conduction
• ISSN: 0955-7997; 1873-197X
• DOI: 10.1016/j.enganabound.2008.09.006

In this paper, the method of time-dependent fundamental solutions is extended to solving transient heat conduction problems in inhomogeneous media. The solution of the problem under investigation is split into two parts, namely the particular and homogenous solutions. The novelty of the proposed approach lies in that an approximation of the particular solution is derived by using the fundamental solutions of the associated eigenvalue equations. Numerical results for one- and two-dimensional geometries are presented to verify the efficacy of the proposed method. The effects of the numbers of source and collocation points, the eigenvalues and the parameter
T on the accuracy of the numerical solution are also investigated.