Speeding up mesoscale thermal simulations of powder bed additive manufacturing thanks to the forward Euler time-integration scheme: A critical assessment

Essongue, Simon; Ledoux, Yann; Ballu, Alex

doi:10.1016/j.finel.2022.103825

Cited by 19 publications

(9 citation statements)

References 41 publications

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“…A more detailed discussion of stability limits in the context of explicit time integration for PBFAM problems can be found in [46]. In addition to (19), the admissible time step size is also limited by the velocity 𝑣 scan of the moving heat source: we do not want the heat source to travel further than the radius 𝑅 of the laser beam in one time step and therefore require:…”

Section: Time Integration and Solution Proceduresmentioning

confidence: 99%

“…Importantly, the time step limitation due to the moving heat source is required for accuracy and not stability: it holds for explicit and implicit schemes, and thus can be considered an inherent characteristic of the physical problem when modeled in a scan-resolved manner. This consideration has also been stated independently of the authors in the very recent contribution [46]. Explicit time stepping has been used for the simulation of PBFAM in [47], directed energy deposition in [48] and wire arc AM in [49].…”

Section: Introductionmentioning

confidence: 99%

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A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

Proell,

Munch,

Kronbichler

et al. 2024

Additive Manufacturing

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Section: Time Integration and Solution Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

Proell,

Munch,

Kronbichler

et al. 2024

Additive Manufacturing

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“…It has been shown that explicit approaches can be more effective even when tiny time step sizes are required [20]. Moreover, various ingenious combinations of explicit and implicit methods, such as semi-explicit or semi-implicit methods, have also been presented [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges

et al. 2023

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Several previous experiments showed that the leapfrog–hopscotch and the adapted Dufort–Frankel methods are the most efficient among the explicit and stable numerical methods to solve heat transfer problems in building walls. In this paper, we extensively measure the running times of the most successful methods and compare them to the performance of other available solvers, for example, ANSYS transient thermal analysis and the built-in routines of MATLAB, where three different mesh resolutions are used. We show that the running time of our methods changes linearly with mesh size, unlike in the case of other methods. After that, we make a long-term simulation (one full winter month) of two-dimensional space systems to test the two best versions of the methods. The real-life engineering problem we solve is the examination of thermal bridges with different shapes in buildings to increase energy efficiency.

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“…The improved AFEM with drilling DOFs will be referred to as the stabilised augmented finite element method (SAFEM) in this work. Numerical experiments conducted with an in-house code [16,17] demonstrate that the SAFEM outperforms the AFEM when cracks are traction-free. The results obtained with cohesive cracks are of similar accuracy.…”

Section: Introductionmentioning

confidence: 99%

On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method

Essongue,

Couégnat,

Martin

2023

Applied Mechanics

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The augmented finite element method (AFEM) embeds cracks within solid elements. These cracks are modelled without additional degrees of freedom thanks to a dedicated static condensation process. However, static condensation can induce a lack of constraint problem, resulting in singular stiffness matrices. To address this issue, we propose a new method called the stabilised augmented finite element method (SAFEM), which produces non-singular stiffness matrices. We conducted 2D experiments involving stationary traction-free cracks and propagating cohesive discontinuities to compare the performance of the SAFEM with the AFEM. The SAFEM outperforms the AFEM in modelling traction-free cracks.

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Speeding up mesoscale thermal simulations of powder bed additive manufacturing thanks to the forward Euler time-integration scheme: A critical assessment

Cited by 19 publications

References 41 publications

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

A highly efficient computational approach for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

Comparison of the Performance of New and Traditional Numerical Methods for Long-Term Simulations of Heat Transfer in Walls with Thermal Bridges

On the Use of Drilling Degrees of Freedom to Stabilise the Augmented Finite Element Method

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