Model order reduction in aerodynamics: Review and applications

Abstract

The need of the aerospace industry, at national or European level, of faster yet reliable computational fluid dynamics models is the main drive for the application of model reduction techniques. This need is linked to the time cost of high-fidelity models, rendering them inefficient for applications like multi-disciplinary optimization. With the goal of testing and applying model reduction to computational fluid dynamics models applicable to lifting surfaces, a bibliographical research covering reduction of nonlinear, dynamic, or steady models was conducted. This established the prevalence of projection and least mean squares methods, which rely on solutions of the original high-fidelity model and their proper orthogonal decomposition to work. Other complementary techniques such as adaptive sampling, greedy sampling, and hybrid models are also presented and discussed. These projection and least mean squares methods are then tested on simple and documented benchmarks to estimate the error and speed-up of the reduced order models thus generated. Dynamic, steady, nonlinear, and multiparametric problems were reduced, with the simplest version of these methods showing the most promise. These methods were later applied to single parameter problems, namely the lid-driven cavity with incompressible Navier–Stokes equations and varying Reynolds number, and the elliptic airfoil at varying angles of attack for compressible Euler flow. An analysis of the performance of these methods is given at the end of this article, highlighting the computational speed-up obtained with these techniques, and the challenges presented by multiparametric problems and problems showing point singularities in their domain.

Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution

“…Given the abundance of data and data‐driven tools, the development of ROMs is gaining increasing popularity nowadays. As highlighted in our introduction, there are a great number of review articles available concerning various aspects of model order reduction and its applications [23,29,37,38,44,45,52, 54‐56,67,71,95,105,106,118,165,169,183,202,204,210,220,224,225,245,262,278,287,317‐319,328,344,351,356,358,364], and more relevant to our discussion, the enabling role of model order reduction approaches in developing next generation DT systems has been also discussed [136,277]. Of particular interest, MPC [113,139,218] originated in the late seventies and has since then evolved considerably.…”

“…In this perspective letter, we aim to provide an overview of HAM strategies relevant to scientific and engineering applications. The topic spans a wide spectrum, and there are a great number of review articles on relevant discussions, methodologies, and applications [23,29,37,38,44,45,52,54‐56,67,71,95,105,106,118,165,169,183,202,204,210,220,224,225,245,262,278,287,317‐319,328,344, 351,356,358,364]. Therefore, it is not our intention to give a complete biography, but rather somehow present our subjective perspectives with an emphasis on the emerging methodologies and enabling technologies from modeling perspectives.…”

A Study on the Surrogate-Based Optimization of Flexible Wings Considering a Flutter Constraint

“…Therefore, searching for more computationally efficient solutions that are able to maximize wing performance without reaching flutter within the flight envelope is required. With this goal in mind, different approaches are considered in the literature, namely, multi-fidelity models [3,4], conventional [5] and machine learning-based surrogate models [6], and reduced-order models [7].…”

On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues

“…The main objective of this study is to provide an overview of data-driven reduced order modeling strategies relevant to fluid dynamics applications. The topic spans a wide spectrum, and there are many review articles on pertinent discussions, methodologies, and applications in fluids [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] as well as closely related fields . Therefore, it is not our intention to include a detailed discussion, but rather to survey one important ROM research area, closure modeling, and provide our subjective perspectives on how data-driven modeling has made an impact in this area.…”