A modular reduced-order modeling strategy for coupled multiphysics problems

Since most modern industrial systems involve interactions between multiple physical phenomena (e.g., mechanical, thermal, or electromagnetic), their high-fidelity simulation requires accounting for their multiphysical behavior [1]. Whenever the coupling of several physics is considered, the nature of the model representing each one is crucial. Indeed, it may be relevant to couple models of different types [2] (e.g., simplified/fine model, data-based/finite element model). This contribution proposes a suitable framework for the multimodel simulation of strongly coupled multiphysics problems, including powerful reduced-order modeling (ROM) techniques. This work focuses on the LATIN-PGD method, initially developed for nonlinear evolution problems. In order to deal with multiphysics problems, the method relies on extending the notion of material interface between substructures found in domain decomposition to an interface between physics [3]. Consequently, the different physics only communicate through this interface (on which the coupled equations are satisfied), whereas the single-physics admissibility equations are solved separately for each physics. Moreover, the LATIN solver provides an approximation of the solution over the whole domain and the entire time interval at each iteration. Thus, applying the Proper Generalized Decomposition (PGD) [4] ROM technique to each decoupled problem is highly relevant and allows significant computational cost reduction. A first implementation in the case of strongly coupled 3D thermo-mechanics is presented herein and deals with coupling a full-order model (FOM) with a simplified one (ROM or even analytical). Special attention is paid to the accommodation of these models on the interface between physics. Numerical examples show great potential in terms of modularity. REFERENCES [1] Keyes, D.E., McInnes, L.C., Woodward, C, et al. Multiphysics simulations: Challenges and opportunities. The International Journal of High Performance Computing Applications (2013) 27(1):4-83. [2] Néron, D., Ben Dhia, H. and Cottereau, R. A decoupled strategy to solve reduced-order multimodel problems in the PGD and Arlequin frameworks. Computational Mechanics (2016) 57(4):509–521. [3] Néron, D. and Dureisseix, D. A computational strategy for thermo-poroelastic structures with a time-space interface coupling. International Journal for Numerical Methods in Engineering (2008) 75(9):1053–1084. [4] Chinesta, F., Ladeveze, P. and Cueto, E. A Short Review on Model Order Reduction Based on Proper Generalized Decomposition. Archives of Computational Methods in Engineering (2011) 18(4):395–404