Iterative simulation of 3D heat diffusion in a medium with multiple cracks

This paper presents an iterative three-dimensional (3D) normal-derivative equation model (TBEM) to simulate 3D heat diffusion generated by a point heat source in the presence of 3D cracks embedded in an unbounded spatially uniform solid medium. The method is intended to reduce the processing time (CPU time) needed to compute 3D heat diffusion using a TBEM formulation.In the proposed formulation each inclusion is modelled individually and successively. The first crack is submitted to an incident heat field and produces a disturbance. Each one of the cracks analyzed next is reached by a heat field generated by the previous one, which is seen as an incident field. The iterative process is stopped when the heat field disturbance generated by each inclusion is negligible. The final solution is the sum of all the contributions (disturbances in the heat field).Performance of the iterative approach proposed in this study is evaluated by comparing results generated using the full 3D TBEM and using the iterative model, in terms of temperature results, CPU time required for a given frequency, as well as number of iterations. The applicability of the proposed method is illustrated via a numerical example of heat field in time domain computation.