Coupling BEM/TBEM and MFS for the simulation of transient conduction heat transfer

Abstract

SUMMARYThe coupling between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS) is proposed for the transient analysis of conduction heat transfer in the presence of inclusions, thereby overcoming the limitations posed by each method. The full domain is divided into sub-domains, which are modeled using the BEM/TBEM and the MFS, and the coupling of the sub-domains is achieved by imposing the required boundary conditions.The accuracy of the proposed algorithms, using different combinations of BEM/TBEM and MFS formulations, is checked by comparing the resulting solutions against referenced solutions.The applicability of the proposed methodology is shown by simulating the thermal behavior of a solid ring incorporating a crack or a thin inclusion in its wall. The crack is assumed to have null thickness and does not allow diffusion of energy; hence, the heat fluxes are null along its boundary. The thin inclusion is modeled as filled with thermal insulating material.

IR thermography used to detect thin defects versus numerical simulation results

“…The numerical formulations are based on the coupling between the boundary element method (BEM)/the traction boundary element method (TBEM) and the method of fundamental solutions (MFS) [17] . The approach is implemented to solve 2D systems subjected to transient heat diffusion in presence of thin inclusions.…”

“…The authors of the present paper have proposed several numerical formulations to simulate transient heat propagation using a frequency domain approach, particularly in the presence of stratified media with or without embedded inclusions [ [14] - [17]]. Some of these numerical formulations have later been validated using experimental results ( [18], [19]).…”

2.5D elastic wave propagation in non-homogeneous media coupling the BEM and MLPG methods

“…A similar technique was also used for the acoustic analysis of non-homogeneous inclusions [38]. Other examples include combinations of the BEM with the method of fundamental solutions (MFS) [39,40], BEM with meshless Kansa's method [41], FEM with EFG method [42,43] and BEM with EFG method [44]. Alves Costa et al [45] proposed a coupled FEM-BEM approach for the 2.5D analysis of track-ground vibrations.…”

Directional Method of Fundamental Solutions for Three-dimensional Laplace Equation

“…The method of fundamental solutions (MFS) is one of the most powerful meshless techniques that belongs to the category as the boundary-type meshless methods, which has been applied to many engineering problems Tadeu et al, 2010;Lin et al, 2014;. The key idea of the MFS is to represent the solution by a linear combination of fundamental solutions with respect to the source points located outside the domain to avoid the singularity of fundamental solutions.…”