cea-03954894
https://cea.hal.science/cea-03954894
[CEA] CEA - Commissariat à l'énergie atomique
[INSMI] CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions
[DEN] Direction des énergies
[TDS-MACS] Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes
[DEN-CAD] DES Cadarache
[CEA-CAD] CEA Cadarache
[MAP-CEA] MAP-contributeur
Multilevel Adaptive Mesh Refinement with controlled accuracy for nonlinear quasi-static mechanics
Koliesnikova, Daria
Ramiere, Isabelle
Lebon, Frédéric
[PHYS.MECA.SOLID] Physics [physics]/Mechanics [physics]/Solid mechanics [physics.class-ph]
[SPI.MECA.STRU] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph]
[INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]
[MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP]
COMM
We propose an adaptive mesh refinement (AMR) algorithm dedicated to the simulation of nonlinearquasi-static solid mechanics problems with phenomena localized at the structural scale [1]. The proposedmethod allows us to follow in time the evolution of studied phenomena in a fully-automatic (thanks to ana posteriori error estimator [2]), precise (respecting user-prescribed accuracies) and efficient (in terms ofmemory space and computational time) way.We adopt the multilevel Local Defect Correction (LDC) refinement method [3] for its great potentialitiesfor solving elliptic problems [4]. We propose an algorithmic extension of the LDC method to nonlinearquasi-static problems and provide key aspects associated to its practical implementation. We highlightits efficiency in the nonlinear context and show its natural ability to generate a hierarchy of meshes oflimited sizes that dynamically follow the evolution over time of studied phenomena.We address generic AMR-related questions associated to dynamic mesh adaptation, such as fields trans-fer between time steps as well as the discretization error control over time. We propose a straightforwardand efficient equilibration strategy lying on the introduction of the initial non equilibrated residual as asource term of the problem. We also develop a reliable remeshing algorithm aiming to limit the numberof mesh regeneration over time while guaranteeing the fulfillment of prescribed errors.Several numerical experiments, in 2D and 3D, with different types of material behavior as well as variableloadings are proposed to validate the efficiency of the developed algorithm.REFERENCES[1] Koliesnikova, D., Ramière, I. and Lebon, F. Fully automatic multigrid adaptive mesh refinementstrategy with controlled accuracy for nonlinear quasi-static problems. in progress.[2] Verfürth, R. A review of a posteriori error estimation and adaptive mesh-refinement techniques.Wiley, Chichester. (1996).[3] Hackbusch, W. Local Defect Correction method and Domain Decomposition techniques, In: DefectCorrection Methods. Springer, Vienna (1984) 89-113.[4] Koliesnikova, D., Ramière, I. and Lebon, F. A unified framework for the computational comparisonof adaptive mesh refinement strategies for all-quadrilateral and all-hexahedral meshes: Locallyadaptive multigrid methods versus h-adaptive methods. J. of Computational Physics (2021) 110310.
2022-07-31
en
WCCM 2022
Yokohama, Japan