Data-driven kinematics-consistent model-order reduction of fluid–structure interaction problems: application to deformable microcapsules in a Stokes flow

Abstract

In this paper, we present a generic approach of a dynamical data-driven model-order reduction technique for three-dimensional fluid–structure interaction problems. A low-order continuous linear differential system is identified from snapshot solutions of a high-fidelity solver. The reduced-order model uses different ingredients, such as proper orthogonal decomposition, dynamic mode decomposition and Tikhonov-based robust identification techniques. An interpolation method is used to predict the capsule dynamics for any values of the governing non-dimensional parameters that are not in the training database. Then a dynamical system is built from the predicted solution. Numerical evidence shows the ability of the reduced model to predict the time evolution of the capsule deformation from its initial state, whatever the parameter values. Accuracy and stability properties of the resulting low-order dynamical system are analysed numerically. The numerical experiments show very good agreement, measured in terms of modified Hausdorff distance between capsule solutions of the full-order and low-order models, in the case of both confined and unconfined flows. This work is a first milestone to move towards real-time simulation of fluid–structure problems, which can be extended to nonlinear low-order systems to account for strong material and flow nonlinearities. It is a valuable innovation tool for rapid design and for the development of innovative devices.