Semi-analytical source (SAS) method for 3-D transient heat conduction problems with moving heat source of arbitrary shape

Abstract

In this study, the semi-analytical source method, which has recently developed by the authors, is implemented for a 3-D fully-transient heat conduction problem with a moving heat source. The method utilizes the exact Green’s function for a diffusion problem with a piecewise constant heat source meaning that the heat source term is defined as the superposition of piece-wise constant contributions in each time interval and in each spatial interval. This approach allows the modeling of any arbitrary spatial distribution of heating with time varying power. Moreover, the method is not limited to straight-line motion of the heat source, and can include internal heating as well as surface heating. One important aspect of the method is that spatial discretization is required only on the path of the heating source and at the observation locations of interest, consequently the discretization of the entire domain is not required as in the case of fully-numerical methods. To verify the semi-analytical source method, an experimental setup was constructed and experiments were conducted with a fiber laser, and satisfactory agreement is achieved. Several case studies are also demonstrated with a Gaussian heat source. The semi-analytical source method is particularly well-suited for parallel computing. To explore this aspect, the parallelization of the method is explored using the Message Passing Interface (MPI) and domain decomposition with up to 800 processors on Stampede2. The parallelization results reveal that semi-analytical method is very suitable for parallel computation. For a strong scaling, the method shows an ideal linear scaling with increasing number of processors with a proper load balance. The weak scaling reveals that the parallelization performance exponentially increases with the increasing time domain due to convolution nature of the method in time.