A non-linear observer for unsteady three-dimensional flows

Buffoni, Marcelo; Camarri, Simone; Iollo, Angelo; Lombardi, Edoardo; Salvetti, Maria Vittoria

doi:10.1016/j.jcp.2007.11.005

Cited by 15 publications

(12 citation statements)

References 22 publications

(38 reference statements)

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“…The model may be linear, for example, based on dynamic mode decomposition (DMD) [22,23,24,25], with an estimate maintained by Kalman filtering [16,48,49]. The model could also be nonlinear, based on a Galerkin projection of the Navier-Stokes equations onto a set of POD modes [50,51,52], or the result of model identification [53,54]. Recent work has investigated the use of data assimilation techniques (e.g.…”

Section: Prior Work In Flow Field Reconstructionmentioning

confidence: 99%

Robust flow reconstruction from limited measurements via sparse representation

Callaham¹,

Maeda²,

Brunton³

2019

Phys. Rev. Fluids

140

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In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the minimum-energy solution that is consistent with the measured data. However, this approach may be prone to overfitting and sensitive to noise. To address these challenges we instead seek a sparse representation of the data in a library of examples. Sparse representation has been widely used for image recognition and reconstruction, and it is well-suited to structured data with limited, corrupt measurements. We explore sparse representation for flow reconstruction on a variety of fluid data sets with a wide range of complexity, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows. In addition, we compare several measurement strategies and consider various types of noise and corruption over a range of intensities. We find that sparse representation has considerably improved estimation accuracy and robustness to noise and corruption compared with least squares methods. We also introduce a sparse estimation procedure on local spatial patches for complex multiscale flows that preclude a global sparse representation. Based on these results, sparse representation is a promising framework for extracting useful information from complex flow fields with realistic measurements.

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Section: Prior Work In Flow Field Reconstructionmentioning

confidence: 99%

Robust flow reconstruction from limited measurements via sparse representation

Callaham¹,

Maeda²,

Brunton³

2019

Phys. Rev. Fluids

140

View full text Add to dashboard Cite

show abstract

“…The role of the projection matrix P can be also viewed from a more generic system theory‐related standpoint. In general, for low‐order models constructed from the full‐field data, the problem of estimating the state of the system from wall measurement arises, resulting in techniques as the linear stochastic estimation, see Bonnet et al , and references therein, and its variants or in more rigorous methods for nonlinear dynamic systems . From this standpoint, the quantity P i j can be understood as an output equation that relates the observed outputs of the system

a_{i}^{τ}

, which are, fundamentally, appropriate linear combinations of the sensor readings, to the internal states

a_{j}^{ω}

.…”

Section: Comparison With Full‐field Pod Analysismentioning

confidence: 99%

Wall‐based reduced‐order modelling

Lasagna

Tutty

2015

Numerical Methods in Fluids

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In this work we propose a novel approach to model order reduction for incompressible fluid flows that focuses on the spatio-temporal description of the stresses on the surface of a body, i.e. of the wall shear stress and of the wall pressure. The spatial representation of these two variables is given by a compact set of "wall basis functions", i.e. elementary basis functions defined on the wall. In this paper, these are derived using the well-known Proper Orthogonal Decomposition, to represent optimally the fluctuation energy of the pressure and shear stress. On the other hand, the functional structure of the dynamic model is derived from first principles using the vorticity form of the Navier-Stokes equations, yielding a set of nonlinear ordinary differential equations for the time-varying amplitudes of the wall shear stress basis functions. Coefficients of this model are then identified from simulation data. To complete the system, we show that the surface pressure distribution, i.e. the time-varying amplitudes of the wall pressure basis functions, can be derived from a quadratic model of the wall shear stress temporal coefficients, stemming from the Poisson equation for the pressure. This further step is crucial for the correct representation of the aerodynamic forces. As a paradigmatic example, we present our approach for the modelling of the free dynamics of the separated flow around a circular cylinder in the laminar regime, at Re = 200. Further implications and potentialities of the proposed approach are discussed.

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“…Combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) with a linear combination, Suzuki et al have developed a method that obtains unmeasurable quantities of an unsteady flow such as pressure fields and vorticity distributions [2], and have evaluated the data-assimilation capabilities of the method [3]. Buffoni et al have proposed an estimation method of a velocity field based on a non-linear low-dimensional model of the flow with velocity or shear stress measurement, treating an unsteady flow around a square cylinder with a low Reynolds number [4]. Recently, the methodology combining measurement and simulation has been used to obtain the velocity in regions where no velocity information is available in particle image velocimetry (PIV) [5], and to estimate time-resolved velocity fields from non-time-resolved PIV data [6].…”

Section: Introductionmentioning

confidence: 99%

Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

Yamagata¹,

Hayase²

2016

JFCMV

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The purpose of this study was to clarify grid convergence property of three-dimensional measurement-integrated (3D-MI) simulation for a flow behind a square cylinder with Karman vortex street. Measurement-integrated (MI) simulation is a kind of the observer in the dynamical system theory by using CFD scheme as a mathematical model of the system. In a former study, two-dimensional MI (2D-MI) simulation with a coarse grid system showed a fairly good result in comparison with a 2D ordinary (2D-O) simulation, but the results were degraded with grid refinement. In this study, 3D-MI simulation and three-dimensional ordinary (3D-O) simulation were performed with three grid systems of different grid resolutions, and their grid convergence properties were compared. As a result, all 3D-MI simulations reproduced the vortex shedding frequency identical to that of the experiment, and the flow fields obtained were very close, within 5% difference between the results, while the results of the 3D-O simulations showed variation of the solution under convergence. It is shown that the grid convergence property of 3D-MI simulation is monotonic and better than that of 3D-O simulation, whereas those of 2D-O and 2D-MI simulations for streamwise velocity fluctuation are divergent. The solution of 3D-MI simulation with a relatively coarse grid system properly reproduces the basic three-dimensional structure of the wake flow as well as the drag and lift coefficients.

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A non-linear observer for unsteady three-dimensional flows

Cited by 15 publications

References 22 publications

Robust flow reconstruction from limited measurements via sparse representation

Robust flow reconstruction from limited measurements via sparse representation

Wall‐based reduced‐order modelling

Grid Convergence Property of Three-Dimensional Measurement-Integrated Simulation for Unsteady Flow behind a Square Cylinder with Karman Vortex Street

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