Data-driven modal decomposition methods as feature detection techniques for flow problems: a critical assessment

Modal decomposition techniques are showing a fast growth in popularity for their good properties as data-driven tools. There are several modal decomposition techniques, yet Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) are considered the most demanded methods, especially in the field of fluid dynamics. Following their magnificent performance on various applications in several fields, numerous extensions of these techniques have been developed. In this work we present an ambitious review comparing eight different modal decomposition techniques, including most established methods: POD, DMD and Fast Fourier Trasform (FFT), extensions of these classical methods: based on time embedding systems, Spectral POD (SPOD) and Higher Order DMD (HODMD), based on scales separation, multi-scale POD (mPOD), multi-resolution DMD (mrDMD), and based on the properties of the resolvent operator, the data-driven Resolvent Analysis (RA). The performance of all these techniques will be evaluated on three different testcases: the laminar wake around cylinder, a turbulent jet flow, and the three dimensional wake around cylinder in transient regime. First, we show a comparison between the performance of the eight modal decomposition techniques when the datasets are shortened. Next, all the results obtained will be explained in details, showing both the conveniences and inconveniences of all the methods under investigation depending on the type of application and the final goal (reconstruction or identification of the flow physics). In this contribution we aim on giving a -- as fair as possible -- comparison of all the techniques investigated. To the authors knowledge, this is the first time a review paper gathering all this techniques have been produced, clarifying to the community what is the best technique to use for each application

An entropy-variables-based formulation of residual distribution schemes for non-equilibrium flows

In this paper we present an extension of Residual Distribution techniques for the simulation of compressible flows in non-equilibrium conditions. The latter are modeled by means of a state-of-the-art multi-species and two-temperature model. An entropy-based variable transformation that symmetrizes the projected advective Jacobian for such a thermophysical model is introduced. Moreover, the transformed advection Jacobian matrix presents a block diagonal structure, with mass-species and electronic-vibrational energy being completely decoupled from the momentum and total energy sub-system. The advantageous structure of the transformed advective Jacobian can be exploited by contour-integration-based Residual Distribution techniques: established schemes that operate on dense matrices can be substituted by the same scheme operating on the momentum–energy subsystem matrix and repeated application of scalar scheme to the mass-species and electronic-vibrational energy terms. Finally, the performance gain of the symmetrizing-variables formulation is quantified on a selection of representative testcases, ranging from subsonic to hypersonic, in inviscid or viscous conditions.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Wavy Walls, a Passive Way to Control the Transition to Turbulence. Detailed Simulation and Physical Explanation

Inducing spanwise motions in the vicinity of solid boundaries alters the energy, mass and/or momentum transfer. Under some conditions, these motions are such that drag is reduced and/or transition to turbulence is delayed. There are several possibilities to induce those spanwise motions, be it through active imposition a predefined velocity distribution at the walls or by careful design of the wall shape, which corresponds to passive control.In this contribution, we investigate the effect that wavy walls might have on delaying transition to turbulence. Direct Numerical Simulation of both planar and wavy-walled channel flows at laminar and turbulent regimes are conducted. A pseudo laminar regime that remains stable until a Reynolds number 20% higher that the critical is found for the wavy-walled simulations. Dynamic Mode Decomposition applied to the simulation data reveals that in these configurations, modes with wavelength and frequency compatible with the surface undulation pattern appear. We explain and visualize the appearance of these modes. At higher Reynolds numbers we show that these modes remain present but are not dominant anymore. This work is an initial demonstration that flow control strategies that trigger underlying stable modes can keep or conduct the flow to new configurations more stable than the original one

A stability analysis of the compressible boundary layer flow over indented surfaces

This contribution presents a stability analysis for compressible boundary layer flows over indented surfaces. Specifically, the effects of increasing depth D/δ* and Ma∞ number on perturbation time-decay rates and spatial amplification factors are quantified and compared with those of an unindented configuration. The indented surfaces represent aeronautical lifting surfaces endowed with the smooth gap resulting when a filler material applied at the junction of leading-edge and wing-box components retracts upon its curing process. Since the configuration considered is such that the parallel/weakly-parallel assumptions are necessarily compromised, a global temporal stability analysis is considered in this study. Our analysis does not require a parallel flow constrain, and hence it is believed to be valid when two dimensional effects are relevant

Higher order dynamic mode decomposition: From fluid dynamics to heart disease analysis

In this work, we study in detail the performance of Higher Order Dynamic Mode Decomposition (HODMD) technique when applied to echocardiography images. HODMD is a data-driven method generally used in fluid dynamics and in the analysis of complex non-linear dynamical systems modeling several complex industrial applications. In this paper we apply HODMD, for the first time to the authors knowledge, for patterns recognition in echocardiography, specifically, echocardiography data taken from several mice, either in healthy conditions or afflicted by different cardiac diseases. We exploit the HODMD advantageous properties in dynamics identification and noise cleaning to identify the relevant frequencies and coherent patterns for each one of the diseases. The echocardiography datasets consist of video loops taken with respect to a long axis view (LAX) and a short axis view (SAX), where each video loop covers at least three cardiac cycles, formed by (at most) 300 frames each (called snapshots). The proposed algorithm, using only a maximum quantity of 200 snapshots, was able to capture two branches of frequencies, representing the heart rate and respiratory rate. Additionally, the algorithm provided a number of modes, which represent the dominant features and patterns in the different echocardiography images, also related to the heart and the lung. Six datasets were analyzed: one echocardiography taken from a healthy subject and five different sets of echocardiography taken from subjects with either Diabetic Cardiomyopathy, Obesity, SFSR4 Hypertrophy, TAC Hypertrophy or Myocardial Infarction. The results show that HODMD is robust and a suitable tool to identify characteristic patterns able to classify the different pathologies studied.MICINNDepto. de Medicina y Cirugía AnimalFac. de VeterinariaTRUEpu

A novel data-driven method for the analysis and reconstruction of cardiac cine MRI

Cardiac cine magnetic resonance imaging (MRI) can be considered the optimal criterion for measuring cardiac function. This imaging technique can provide us with detailed information about cardiac structure, tissue composition and even blood flow, which makes it highly used in medical science. But due to the image time acquisition and several other factors the MRI sequences can easily get corrupted, causing radiologists to misdiagnose 40 million people worldwide each and every single year. Hence, the urge to decrease these numbers, researchers from different fields have been introducing novel tools and methods in the medical field. Aiming to the same target, we consider in this work the application of the higher order dynamic mode decomposition (HODMD) technique. The HODMD algorithm is a linear method, which was originally introduced in the fluid dynamics domain, for the analysis of complex systems. Nevertheless, the proposed method has extended its applicability to numerous domains, including medicine. In this work, HODMD in used to analyze sets of MR images of a heart, with the ultimate goal of identifying the main patterns and frequencies driving the heart dynamics. Furthermore, a novel interpolation algorithm based on singular value decomposition combined with HODMD is introduced, providing a three-dimensional reconstruction of the heart. This algorithm is applied (i) to reconstruct corrupted or missing images, and (ii) to build a reduced order model of the heart dynamics.SIMOPAIR, SpainThe European Union’s Horizon 2020The Marie Skłodowska-CurieCentro Nacional de Investigaciones Cardiovasculares Carlos III. (CNIC), Madrid, SpainMinisterio de Ciencia e Innovación (MCIN). Madrid, SpainThe Pro CNIC Foundation. Severo Ochoa Center of ExcellenceThe European UnionDepto. de Medicina y Cirugía AnimalFac. de VeterinariaTRUEpu