Efficient solutions for transient thermal processes involving moving heat sources

Many industrial processes involve transient heat transfer problems where the heat source moves over the domain. For instance, the Automated Tape Placement (ATP) in the context of composites manufacturing may be considered. In this process, the composite piece is built up by adding different layers successively, which are welded on the substrate by means of a local heat source, typically a laser, which moves all over the boundary. If one is interested in monitoring or controlling the process, some thermocouples need to be installed where knowing the temperature is of interest. However from a numerical point of view, having a moving heat source poses several problems. Classically, even when the problem remains linear, it would be needed to solve the transient problem by performing an appropriate time stepping, needing for the solution to solve many algebraic problems. In order to overcome these limitations, this work proposes solving the problem in the frequency domain because in this case it can be proved that the reciprocity principle is satisfied. Then, a unitary heat source may be applied where the temperature measurement is performed giving place to a transfer function which relates the measurement point and the boundary, where the heat flux applies. However this transfer function is only valid for a single frequency, and thus if the heat flux signal contains several frequencies, many transfer functions need to be computed. Instead, we prefer to compute a generalized transfer function by using the PGD method, i.e. the frequency is included as an extra-coordinate, like the physical space. Once this generalized transfer function has been computed, a simple and computationally cheap postprocessing suffices for obtaining the temperature response at the point of interest, for any heat source path on the boundary.