
Moving beyond forward Euler: advanced explicit schemes to accelerate conduction-based simulations in additive manufacturing
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Despite significant progress over the past decade, predictive modeling of additive manufacturing processes remains a computationally intensive task. Even when restricting the analysis to conduction-based simulations (i.e., excluding hydrodynamic effects), achieving accurate modeling at the part scale is sometimes intractable. This challenge arises due to the multiple time scales inherent in these processes and the numerous associated nonlinearities (e.g., phase changes, the temperature dependence of material properties, or thermal radiation). To reduce computational costs without compromising accuracy, we recently highlighted the advantages of the forward Euler explicit scheme over the conventional backward Euler implicit scheme in the specific case of conduction-based modeling of powder bed fusion. Among the many benefits of the former, one can cite the absence of nonlinear iterations and its ease of parallelization. As a result, this strategy is gaining increasing adoption within the additive manufacturing community and has helped push the boundaries of what is computationally feasible. However, the forward Euler scheme is not without drawbacks when applied to additive manufacturing. For instance, we have demonstrated that its significant advantages over implicit schemes in powder bed fusion are considerably reduced when applied to directed energy deposition processes. Moreover, due to its conditional stability, the efficiency of the forward Euler scheme is greatly diminished when modeling highly conductive materials such as aluminum or copper. Furthermore, it performs poorly compared to unconditionally stable implicit schemes when cooling effects need to be captured. As a result, switching from the forward Euler scheme to the backward Euler scheme becomes necessary when transitioning from heating to cooling, adding complexity to an already intricate numerical implementation for additive manufacturing modeling. In this talk, I will demonstrate how one can retain the advantages of explicit schemes (ease of parallelization, simplicity of implementation) while significantly mitigating the three aforementioned drawbacks.