Coupling the BEM and analytical solutions for the numerical simulation of transient heat conduction in a heterogeneous solid medium

This paper simulates the three-dimensional transient heat diffusion conduction in a solid medium containing multi-layered cylindrical circular heterogeneities using a coupling formulation between the boundary element method (BEM) and analytical solutions. The analytical solutions are incorporated as Green's functions, thereby making the discretization of the interfaces of the multi-layered system unnecessary; this improves the efficiency of the algorithm. The coupling is enforced by imposing the continuity of temperature and heat fluxes at virtual interfaces created around each heterogeneity. The solution is first computed in the frequency domain, for a wide range of frequencies and axial wavenumbers, using complex frequencies to avoid aliasing phenomenon. Time series can then be obtained by means of a (fast) inverse Fourier transform. The accuracy, efficiency, and stability of the proposed algorithms are confirmed by comparing the results against reference solutions. The transient analysis of heat diffusion in a solid medium in the presence of multi-layered inclusions is used to illustrate the potential of the proposed coupling formulation.