A Novel Localized Meshless Method for Solving Transient Heat Conduction Problems in Complicated Domains

Abstract

This paper first attempts to solve the transient heat conduction problem by combining the recently proposed local knot method (LKM) with the dual reciprocity method (DRM). Firstly, the temporal derivative is discretized by a finite difference scheme, and thus the governing equation of transient heat transfer is transformed into a non-homogeneous modified Helmholtz equation. Secondly, the solution of the non-homogeneous modified Helmholtz equation is decomposed into a particular solution and a homogeneous solution. And then, the DRM and LKM are used to solve the particular solution of the non-homogeneous equation and the homogeneous solution of the modified Helmholtz equation, respectively. The LKM is a recently proposed local radial basis function collocation method with the merits of being simple, accurate, and free of mesh and integration. Compared with the traditional domain-type and boundary-type schemes, the present coupling algorithm could be treated as a really good alternative for the analysis of transient heat conduction on high-dimensional and complicated domains. Numerical experiments, including two-and three-dimensional heat transfer models, demonstrated the effectiveness and accuracy of the new methodology.

Noninvasive reconstruction of internal heat source in biological tissue using adaptive simulated annealing algorithm

“…The shape function in finite element method uses a unified polynomial function, which is convenient and simple. However, most mesh free methods require shape functions for points, which may be different and complex according to different points, resulting in a huge amount of computation for the corresponding matrix 17 – 19 . For these reasons, the numerical methods mentioned above are not suitable for the the modeling and simulation of bio-heat conduction reverse problems on account of the complexity of biological tissue and organs, and also face great difficulties in the clinical applications such as the real-time detection of temperature field in lesions and its’ surrounding tissues during tumor hyperthermia, the thermal analysis and diagnosis of diseases 20 .…”