Open Access

ARTICLE

A Coupled BEM-MLPG Technique for the Thermal Analysis of Non-Homogeneous Media

A. Tadeu¹, P. Stanak², J. Sladek², V. Sladek², J. Prata¹, N. Simões¹

1 ITeCons, University of Coimbra, Pólo II, Rua Pedro Hispano, 3030-289, Coimbra, Portugal.
2 Institute of Construction and Architecture, Slovak Academy of Sciences, 84503 Bratislava, Slovakia.

Computer Modeling in Engineering & Sciences 2013, 93(6), 489-516. https://doi.org/10.3970/cmes.2013.093.489

Abstract

This paper presents a technique that couples the boundary element method (BEM) with the meshless local Petrov-Galerkin (MLPG) method, formulated in the frequency domain. It is then used to study the transient heat diffusion through a two-dimensional unbounded medium containing confined subdomains where the material properties vary from point to point. To exploit the advantages of each method, the BEM is used for the homogeneous unbounded domain and the MLPG method is used for the non-homogeneous confined subdomains. The nodal points placed at the interface between the confined subdomains and the unbounded homogenous medium are used to couple the BEM and the MPLG method. The MLPG method is formulated using the moving leastsquares (MLS) approximation as the trial function and the Heaviside step function as the test function in local integral equations defined over small local sub-domains. The coupled BEM-MLPG approach is verified against the results provided by an analytical solution developed for a circular confined subdomain, in which the thermal diffusivity within the circular non-homogeneous region is assumed to vary in the radial direction. The proposed model is finally used to solve the case of a pair of non-homogeneous confined subdomains for which analytical solutions are not known. The analysis of time domain temperature responses is presented, which illustrates the applicability of the model.

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Keywords

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