On accurate time integration for temperature evolutions in additive manufacturing

We investigate two numerical challenges in thermal finite element simulations of laser powder bed fusion (LPBF) processes. First, we compare the behavior of first‐ and second‐order implicit time‐stepping schemes on a fixed domain. While both methods yield comparable accuracies in the pre‐asymptotic regime, the second‐order method eventually outperforms the first‐order method. However, the oscillations present in the pre‐asymptotic range of the second‐order method can render it less suitable for simulating LPBF processes. Then, we consider sudden domain extensions resulting from subsequently adding new layers of material with ambient temperature. We model this extension on the continuous level in an energy conservative manner. The discontinuities introduced here reduce the convergence order for both time‐stepping schemes to 0.75. First and second order accuracy could only be achieved by strongly grading the time‐steps towards the domain expansion.