This paper deals with an extension of dynamic mode decomposition (DMD), which is appropriate to treat general periodic and quasi-periodic dynamics, transients decaying attractors, including cases (not accessible standard DMD) that show limited spatial complexity but a very large number involved frequencies. The extension, labeled as higher order decomposition, uses time-lagged snapshots can be seen superimposed DMD in sliding window. new method illustrated clarified using some toy model the...

Modal-decomposition techniques are computational frameworks based on data aimed at identifying a low-dimensional space for capturing dominant flow features: the so-called modes. We propose deep probabilistic-neural-network architecture learning minimal and near-orthogonal set of non-linear modes from high-fidelity turbulent-flow useful analysis, reduced-order modeling control. Our approach is β-variational autoencoders (β-VAEs) convolutional neural networks (CNNs), which enable extracting...

This article shows the capability of using a higher order dynamic mode decomposition (HODMD) algorithm both to identify flow patterns and extrapolate transient solution attractor region. Numerical simulations are carried out for three-dimensional around circular cylinder, standard (DMD) DMD applied non-converged solution. The good performance HODMD is proved, showing that this method guesses converged from numerical in transitional obtained can be extrapolated fact sheds light on finding...

This study proposes an improvement in the performance of reduced-order models (ROMs) based on dynamic mode decomposition to model flow dynamics attractor from a transient solution. By combining higher order (HODMD) with efficient selection criterion, HODMD criterion (HODMDc) ROM is able identify dominant patterns high accuracy. helps us develop more parsimonious structure, allowing better predictions dynamics. The method tested solution NACA0012 airfoil buffeting transonic flow, and its good...

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There several modal techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode (DMD) considered the most demanded methods, especially field of fluid dynamics. Following magnificent performance on various applications fields, numerous extensions these have been developed. In this work we present an ambitious review comparing eight different including established...

Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady time-periodic three-dimensional flows, which are inhomogeneous in two (and periodic one) all three directions.After a brief exposition theory, some recent advances reported.First, results presented on implementation Jacobian-free Newton-Krylov time-stepping method into standard finite-volume aerodynamic code to obtain global flows industrial...

Solving computational fluid dynamics problems requires using large resources. The time and memory requirements to solve realistic vary from a few hours several weeks with processors working in parallel. Motivated by the need of reducing such amount resources (improving industrial applications which plays key role), this article introduces new predictive Reduced Order Model (ROM) applied problems. model is based on physical principles combines modal decompositions deep learning architectures....

This work presents a new application of higher order dynamic mode decomposition (HODMD) for the analysis reactive flows. Due to high complexity data analysed, consisting more than 80 variables (i.e., temperature and chemically reacting species) extension HODMD has been developed combining multi-dimensional algorithm with classical preprocessing techniques generally used in machine learning analyses, such as principal component (PCA). methodology proved be suitable identify main patterns...

Understanding flow structures in urban areas is widely recognized as a challenging concern due to its effect on development, air quality, and pollutant dispersion. In this study, state-of-the-art data-driven methods for modal analysis of simplified flows are used study the dominant processes these environments. Higher order dynamic mode decomposition (HODMD), highly-efficient method analyze turbulent flows, together with traditional techniques such proper-orthogonal (POD) high-fidelity...

This article presents an innovative open-source software named ModelFLOWs-app,1 written in Python, which has been created and tested to generate precise robust hybrid reduced order models (ROMs) fully data-driven. By integrating modal decomposition deep learning diverse ways, the uncovers fundamental patterns dynamic systems. acquired knowledge is then employed enrich comprehension of underlying physics, reconstruct databases from limited measurements, forecast progression system dynamics....

We develop a reduced order model to represent the complex flow behaviour around vertical axis wind turbines. First, we simulate turbines using an accurate high discontinuous Galerkin–Fourier Navier–Stokes Large Eddy Simulation solver with sliding meshes and extract snapshots in time. Subsequently, construct based on dynamic mode decomposition approach that selects modes frequency. show only few are necessary reconstruct of original simulation, even for blades rotating turbulent regimes....

This article presents a new method to predict the wind velocity upstream horizontal axis turbine from set of light detection and ranging (LiDAR) measurements. The uses higher order dynamic mode decomposition (HODMD) construct reduced model (ROM) that can be extrapolated in space. LiDAR measurements have been carried out at six different planes perpendicular axis. HODMD-based ROM predicts with high accuracy during timespan 24 h plane is more than 225 m far away turbine. Moreover, technique...

This article presents a review on two methods based dynamic mode decomposition and its multiple applications, focusing higher order (which provides purely temporal Fourier‐like decomposition) spatiotemporal Koopman gives decomposition). These are data‐driven, using either numerical or experimental data, permit reconstructing the given data identifying growth rates frequencies involved in dynamics spatial wavenumbers case of decomposition. Thus, they may be used to identify extrapolate from...