Hybrid reduced-order methods for segregated fluid-structure interaction solvers in an ALE approach using the Finite Volume Method.

This dissertation intends to construct hybrid reduced-order models (ROMs) for segregated Fluid-structure interactions solvers in an Arbitrary Lagrangian-Eulerian (ALE) framework both in laminar and turbulent regime. The ROM methodology developed is based on full order solvers which make use of the Finite Volume Discretization method. The hybrid ROMs are built by combining data-driven techniques and classic model reduction approaches, such as proper orthogonal decomposition combined with Galerkin projection. This combination seems like a natural evolutionary process for engineering applications. The resulting hybrid ROMs, allow for both scalability and physics-based modelling. In this hybrid model, Proper Orthogonal Decomposition (POD) primarily calculates low-dimensional projections/features that can be evolved over time through the simultaneous use of classical Galerkin projection, neural networks/ recurrent neural networks, or radial basis functions. In this recipe, the Partial Differential Equations (PDEs) associated to mass and momentum balance are treated using a standard POD-Galerkin projection approach, while Radial Basis Functions (RBF) networks are used for the grid motion interpolation and Neural Networks (NNs) are employed for the approximation of the eddy viscosity field. Incorporating data-driven techniques, the reduced-order models are able to achieve higher accuracy, efficiency and flexibility of use, making them powerful tools for simulating complex Fluid-structure interactions problems which could be useful in industrial applications and in the development of digital twins. In this work, we tested the hybrid ROMs on two different test cases. The first test is that of the flow around an oscillating cylinder in laminar regime (Re = 200) and the second test case on the Flow Induced Vibration (FIV) of a pitch-plunge airfoil at a high Reynolds number (Re = 10000000). The results confirm that in each test case the ROM methodology developed is able to reproduce the wake dynamics of the flow around the moving body and all the response characteristics of the system such as the lift and drag forces, amplitude/ frequency/phase of the displacement, and the features of the original dynamical system. The results show good convergence properties without any necessity of additional stabilization for what concerns pressure solutions. This is due to the fact that, even at the reduced order level, we use a segregated scheme which reproduces the full order model algorithm used to deal with the saddle-point structure of the Navier–Stokes equations. Finally, to circumvent the expensive computational cost associated with the Galerkin projection methods, we introduce an additional hyper-reduction methodology based on Empiral Lagrangian Interpolation Method (ELIM) leveraging on the identification of some points at optimal locations in the domain of interest. Preliminary results on the reconstruction part of the algorithm are presented for the test case of Burger’s equation over a backward facing step.