@article {2023, title = {An optimisation{\textendash}based domain{\textendash}decomposition reduced order model for the incompressible Navier-Stokes equations}, volume = {151}, year = {2023}, month = {2023/12/01/}, pages = {172 - 189}, abstract = {

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain{\textendash}decomposition (DD) methods and reduced{\textendash}order modelling (ROM). In particular, we consider an optimisation{\textendash}based domain{\textendash}decomposition algorithm for the parameter{\textendash}dependent stationary incompressible Navier{\textendash}Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal{\textendash}control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward{\textendash}facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain{\textendash}decomposition algorithm.

}, keywords = {Computational fluid dynamics, Domain decomposition, Optimal control, Proper orthogonal decomposition, Reduced order modelling}, isbn = {0898-1221}, url = {https://www.sciencedirect.com/science/article/pii/S0898122123004248}, author = {Ivan Prusak and Monica Nonino and Davide Torlo and Francesco Ballarin and Gianluigi Rozza} } @article {2022, title = {Model order reduction for bifurcating phenomena in fluid-structure interaction problems}, journal = {International Journal for Numerical Methods in FluidsInternational Journal for Numerical Methods in FluidsInt J Numer Meth Fluids}, volume = {n/a}, year = {2022}, month = {2022/05/23}, abstract = {

Abstract This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coand? effect, in a multi-physics setting involving fluid and solid media. Taking into consideration a fluid-structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch-wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper-elastic law delays the bifurcation w.r.t.\ the standard model, while the same effect is even magnified when considering linear elastic solid.

}, keywords = {Bifurcation theory, Coand{\u a} effect, continuum mechanics, fluid dynamics, monolithic method, parametrized fluid-structure interaction problem, Proper orthogonal decomposition, reduced order modeling}, isbn = {0271-2091}, url = {https://doi.org/10.1002/fld.5118}, author = {Moaad Khamlich and Federico Pichi and Gianluigi Rozza} } @article {2022, title = {A POD-Galerkin reduced order model for the Navier{\textendash}Stokes equations in stream function-vorticity formulation}, year = {2022}, month = {2022/06/14/}, pages = {105536}, abstract = {

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier{\textendash}Stokes equations in the stream function-vorticity formulation. Unlike previous works, we choose different reduced coefficients for the vorticity and stream function fields. In addition, for parametric studies we use a global POD basis space obtained from a database of time dependent full order snapshots related to sample points in the parameter space. We test the performance of our ROM strategy with the well-known vortex merger benchmark and a more complex case study featuring the geometry of the North Atlantic Ocean. Accuracy and efficiency are assessed for both time reconstruction and physical parametrization.

}, keywords = {Galerkin projection, Navier{\textendash}Stokes equations, Proper orthogonal decomposition, Reduced order model, Stream function-vorticity formulation}, isbn = {0045-7930}, url = {https://www.sciencedirect.com/science/article/pii/S0045793022001645}, author = {Michele Girfoglio and Annalisa Quaini and Gianluigi Rozza} } @article {2021, title = {On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis}, journal = {Computers \& Fluids}, volume = {216}, year = {2021}, pages = {104819}, abstract = {

In this work, Dynamic Mode Decomposition (DMD) and Proper Orthogonal Decomposition (POD) methodologies are applied to hydroacoustic dataset computed using Large Eddy Simulation (LES) coupled with Ffowcs Williams and Hawkings (FWH) analogy. First, a low-dimensional description of the flow fields is presented with modal decomposition analysis. Sensitivity towards the DMD and POD bases truncation rank is discussed, and extensive dataset is provided to demonstrate the ability of both algorithms to reconstruct the flow fields with all the spatial and temporal frequencies necessary to support accurate noise evaluation. Results show that while DMD is capable to capture finer coherent structures in the wake region for the same amount of employed modes, reconstructed flow fields using POD exhibit smaller magnitudes of global spatiotemporal errors compared with DMD counterparts. Second, a separate set of DMD and POD modes generated using half the snapshots is employed into two data-driven reduced models respectively, based on DMD mid cast and POD with Interpolation (PODI). In that regard, results confirm that the predictive character of both reduced approaches on the flow fields is sufficiently accurate, with a relative superiority of PODI results over DMD ones. This infers that, discrepancies induced due to interpolation errors in PODI is relatively low compared with errors induced by integration and linear regression operations in DMD, for the present setup. Finally, a post processing analysis on the evaluation of FWH acoustic signals utilizing reduced fluid dynamic fields as input demonstrates that both DMD and PODI data-driven reduced models are efficient and sufficiently accurate in predicting acoustic noises.

}, keywords = {Dynamic mode decomposition, Ffowcs Williams and Hawkings, Hydroacoustics, Large eddy simulation, Model reduction, Proper orthogonal decomposition}, issn = {0045-7930}, doi = {https://doi.org/10.1016/j.compfluid.2020.104819}, url = {https://www.sciencedirect.com/science/article/pii/S0045793020303893}, author = {Mahmoud Gadalla and Marta Cianferra and Marco Tezzele and Giovanni Stabile and Andrea Mola and Gianluigi Rozza} } @article {2020, title = {Reduced order methods for parametric optimal flow control in coronary bypass grafts, toward patient-specific data assimilation}, journal = {International Journal for Numerical Methods in Biomedical EngineeringInternational Journal for Numerical Methods in Biomedical EngineeringInt J Numer Meth Biomed Engng}, volume = {n/a}, year = {2020}, month = {2020/05/27}, pages = {e3367}, abstract = {

Abstract Coronary artery bypass grafts (CABG) surgery is an invasive procedure performed to circumvent partial or complete blood flow blockage in coronary artery disease. In this work, we apply a numerical optimal flow control model to patient-specific geometries of CABG, reconstructed from clinical images of real-life surgical cases, in parameterized settings. The aim of these applications is to match known physiological data with numerical hemodynamics corresponding to different scenarios, arisen by tuning some parameters. Such applications are an initial step toward matching patient-specific physiological data in patient-specific vascular geometries as best as possible. Two critical challenges that reportedly arise in such problems are: (a) lack of robust quantification of meaningful boundary conditions required to match known data as best as possible and (b) high computational cost. In this work, we utilize unknown control variables in the optimal flow control problems to take care of the first challenge. Moreover, to address the second challenge, we propose a time-efficient and reliable computational environment for such parameterized problems by projecting them onto a low-dimensional solution manifold through proper orthogonal decomposition-Galerkin.

}, keywords = {coronary artery bypass grafts, data assimilation, flow control, Galerkin methods, hemodynamics modeling, Optimization, patient-specific simulations, Proper orthogonal decomposition, reduced order methods}, isbn = {2040-7939}, doi = {https://doi.org/10.1002/cnm.3367}, url = {https://onlinelibrary.wiley.com/doi/10.1002/cnm.3367?af=R}, author = {Zakia Zainib and F. Ballarin and Stephen E. Fremes and Piero Triverio and Laura Jim{\'e}nez-Juan and Gianluigi Rozza} }