A spatiotemporal two-level method for high-fidelity thermal analysis of laserpowder bed fusion

Numerical simulation of the laser powder bed fusion (LPBF) procedure for additive manufacturing (AM) is difficult due to the presence of multiple scales in both time and space, ranging from the part scale (order of millimeters/seconds) to the powder scale (order of microns/milliseconds). This difficulty is compounded by the fact that the regions of small-scale behavior are not fixed, but change in time as the geometry is produced. While much work in recent years has been focused on resolving the problem of multiple scales in space, there has been less work done on multiscale approaches for the temporal discretization of LPBF problems. In the present contribution, we extend on a previously introduced two-level method in space by combining it with a multiscale time integration method. The unique transfer of information through the transmission conditions allows for interaction between the space and time scales while reducing computational costs. At the same time, all of the advantages of the two-level method in space (namely its geometrical flexibility and the ease in which one may deploy structured, uniform meshes) remain intact. Adopting the proposed multiscale time integration scheme, we observe a computational speed-up by a factor $\times 2.44$ compared to the same two-level approach with uniform time integration, when simulating a laser source traveling on a bare plate of nickel-based superalloy material following an alternating scan path of fifty laser tracks.