MEchanics GAthering -MEGA- Seminar: Front tracking with a twist: the eXtreme mesh deformation approach (X-MESH)
Event details
| Date | 06.02.2025 |
| Hour | 16:15 › 17:05 |
| Speaker | Prof. Nicolas Moës, Applied mechanics and mathematics, Institute of Mechanics, Materials and Civil Engineering, UCLouvain |
| Location | Online |
| Category | Conferences - Seminars |
| Event Language | English |
Abstract: The arbitrary Eulerian Lagrangian (ALE) formulation is a common approach for tracking fronts in finite element simulations. It is, however, difficult to track fronts over long distances, as the mesh density generally becomes too low on one side of the front (increasingly large elements). Moreover, traditional ALE front tracking cannot cope with
changes in the front topology. To remedy the above problems (at least the first one), remeshing is required from time to time to maintain correct mesh approximation
capability on both sides of the front. This remeshing requires projection of the field and updating of the database in the simulation, which is detrimental to the speed and
accuracy.
We introduce a new approach in which the set of nodes located on the front evolves over time allowing the front to migrate through the mesh. Topological changes are easily taken into account. For example, a front can nucleate, propagate and merge with other fronts as it propagates. For the new approach to work properly, we have to accept that some elements become very small and possibly of zero measure. This means that the elements can deform in extreme ways, hence the acronym X-MESH. Surprisingly, as we shall show, this situation does not prevent simulations from being carried out. In short, X-MESH simply uses node movements to propagate fronts over long distances, even in the event of topological changes. The mesh topology remains unchanged during simulation. The size and sparsity of the finite element matrices are therefore fixed throughout the simulation, and no field projection is required. As the simulation progresses, nodes arrive and depart from the front. X-MESH's capability will be demonstrated for several important applications in mechanics and physics, such as front tracking in the Stefan phase change model or the simulation of immiscible two-phase flows. The work is funded by a European Research Council (ERC) Synergy Grant whose co-PI is Professor J-F. Remacle also at UCLouvain.
- N. Moës, J.-F. Remacle, J. Lambrechts, B. Lé and N. Chevaugeon (2023). The eXtreme Mesh Deformation Approach (X-MESH) for the Stefan Phase Change Model. Journal of Computational Physics, 477, 111878.
- A. Quiriny, J. Lambrechts, N. Moës and J.-F. Remacle (2024), X-Mesh: A new approach for the simulation of two-phase flow with sharp interface, Journal of Computational Physics, 112775
- Quiriny, A., Kucera, V., Lambrechts, J., Moës, N., & Remacle, J. F. (2024). The tempered finite element method. arXiv preprint : 2411.17564
- Chemin, A., Lambrechts, J., Moës, N., & Remacle, J. F. (2025). The eXteme Mesh deformation approach (X-Mesh) applied to the Porous Medium Equation. arXiv preprint: 2501.03083
Bio: Dr. Nicolas Moës is a Professor at UCLouvain in Belgium, co-leading the ERC Synergy Grant project on simulating front propagation using extreme mesh deformation (X-MESH). He joined UCLouvain in 2024 after a distinguished career in computational mechanics. Dr. Moës obtained his Engineering Degree from the University of Liège and his Ph.D. from École Normale Supérieure de Cachan in 1996. He then conducted postdoctoral research at the University of Texas at Austin and Northwestern University, where he co-developed the eXtended Finite Element Method (X-FEM) in 1999, a groundbreaking technique for modeling crack propagation without remeshing. Dr. Moës further advanced X-FEM for fracture, material interfaces, and free boundaries, and actively collaborated with industry, including Snecma Moteurs and EDF R&D. In 2001, he became a full professor at École Centrale de Nantes, where he focused on fracture mechanics and damage modeling. He received an ERC Advanced Grant (2012-2017) for his work on fracture modeling with level sets. Dr. Moës is also a Fellow of the International Association for Computational Mechanics (IACM), where he has been on the executive committee since 2014. He was elected to the French Academy of Science in 2020.
changes in the front topology. To remedy the above problems (at least the first one), remeshing is required from time to time to maintain correct mesh approximation
capability on both sides of the front. This remeshing requires projection of the field and updating of the database in the simulation, which is detrimental to the speed and
accuracy.
We introduce a new approach in which the set of nodes located on the front evolves over time allowing the front to migrate through the mesh. Topological changes are easily taken into account. For example, a front can nucleate, propagate and merge with other fronts as it propagates. For the new approach to work properly, we have to accept that some elements become very small and possibly of zero measure. This means that the elements can deform in extreme ways, hence the acronym X-MESH. Surprisingly, as we shall show, this situation does not prevent simulations from being carried out. In short, X-MESH simply uses node movements to propagate fronts over long distances, even in the event of topological changes. The mesh topology remains unchanged during simulation. The size and sparsity of the finite element matrices are therefore fixed throughout the simulation, and no field projection is required. As the simulation progresses, nodes arrive and depart from the front. X-MESH's capability will be demonstrated for several important applications in mechanics and physics, such as front tracking in the Stefan phase change model or the simulation of immiscible two-phase flows. The work is funded by a European Research Council (ERC) Synergy Grant whose co-PI is Professor J-F. Remacle also at UCLouvain.
- N. Moës, J.-F. Remacle, J. Lambrechts, B. Lé and N. Chevaugeon (2023). The eXtreme Mesh Deformation Approach (X-MESH) for the Stefan Phase Change Model. Journal of Computational Physics, 477, 111878.
- A. Quiriny, J. Lambrechts, N. Moës and J.-F. Remacle (2024), X-Mesh: A new approach for the simulation of two-phase flow with sharp interface, Journal of Computational Physics, 112775
- Quiriny, A., Kucera, V., Lambrechts, J., Moës, N., & Remacle, J. F. (2024). The tempered finite element method. arXiv preprint : 2411.17564
- Chemin, A., Lambrechts, J., Moës, N., & Remacle, J. F. (2025). The eXteme Mesh deformation approach (X-Mesh) applied to the Porous Medium Equation. arXiv preprint: 2501.03083
Bio: Dr. Nicolas Moës is a Professor at UCLouvain in Belgium, co-leading the ERC Synergy Grant project on simulating front propagation using extreme mesh deformation (X-MESH). He joined UCLouvain in 2024 after a distinguished career in computational mechanics. Dr. Moës obtained his Engineering Degree from the University of Liège and his Ph.D. from École Normale Supérieure de Cachan in 1996. He then conducted postdoctoral research at the University of Texas at Austin and Northwestern University, where he co-developed the eXtended Finite Element Method (X-FEM) in 1999, a groundbreaking technique for modeling crack propagation without remeshing. Dr. Moës further advanced X-FEM for fracture, material interfaces, and free boundaries, and actively collaborated with industry, including Snecma Moteurs and EDF R&D. In 2001, he became a full professor at École Centrale de Nantes, where he focused on fracture mechanics and damage modeling. He received an ERC Advanced Grant (2012-2017) for his work on fracture modeling with level sets. Dr. Moës is also a Fellow of the International Association for Computational Mechanics (IACM), where he has been on the executive committee since 2014. He was elected to the French Academy of Science in 2020.
Practical information
- General public
- Free
Organizer
- MEGA.Seminar Organizing Committee, Jean-François Molinari