Fast simulation of nonstationary wind velocity fields by proper orthogonal decomposition interpolation

Thermal distortion is a critical design consideration for the Haystack Ultrawide-band Satellite Imaging Radar (HUSIR) with respect to its performance at W-band. This design consideration is needed due to the thermal distortion effects on the surface accuracy of a parabolic reflector. For example, a tight surface tolerance of ∼100 microns root-mean-squared is required to obtain 85 percent antenna performance efficiency for the 37 meter (120 foot) diameter reflector. An understanding of the temperature and velocity fields aids compensation of these losses. Computational fluid dynamics models (CFD) are too computationally expensive to implement in a control algorithm. Therefore, this work applies proper orthogonal decomposition (POD) to simulated CFD data and creates a reduced order model of the fluid system that characterizes the dominant features of both the temperature and velocity fields. A case study of the HUSIR’s convective flow inside a dome is illustrated.

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Spatio-Temporal Analysis of Photospheric Turbulent Velocity Fields Using the Proper Orthogonal Decomposition

Helioseismology, Asteroseismology, and MHD Connections ◽

10.1007/978-0-387-89482-9_13 ◽

2008 ◽

pp. 163-178 ◽

Cited By ~ 1

Author(s):

A. Vecchio ◽

V. Carbone ◽

F. Lepreti ◽

L. Primavera ◽

L. Sorriso-Valvo ◽

...

Keyword(s):

Proper Orthogonal Decomposition ◽

Temporal Analysis ◽

Velocity Fields ◽

Orthogonal Decomposition ◽

Turbulent Velocity ◽

Spatio Temporal ◽

Proper Orthogonal

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A tale of two airfoils: resolvent-based modelling of an oscillator versus an amplifier from an experimental mean

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.747 ◽

2019 ◽

Vol 881 ◽

pp. 51-83 ◽

Cited By ~ 8

Author(s):

Sean Symon ◽

Denis Sipp ◽

Beverley J. McKeon

Keyword(s):

Proper Orthogonal Decomposition ◽

Resolvent Operator ◽

Stokes Equations ◽

Velocity Fields ◽

Orthogonal Decomposition ◽

Low Rank ◽

Experimental Measurements ◽

Mean Velocity ◽

Proper Orthogonal ◽

The Resolvent Operator

The flows around a NACA 0018 airfoil at a chord-based Reynolds number of $Re=10\,250$ and angles of attack of $\unicode[STIX]{x1D6FC}=0^{\circ }$ and $\unicode[STIX]{x1D6FC}=10^{\circ }$ are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity fields are data assimilated so that they are solutions of the incompressible Reynolds-averaged Navier–Stokes equations forced by Reynolds stress terms which are derived from experimental data. Resolvent analysis of the data-assimilated mean velocity fields reveals low-rank behaviour only in the vicinity of the shedding frequency for $\unicode[STIX]{x1D6FC}=0^{\circ }$ and none of its harmonics. The resolvent operator for the $\unicode[STIX]{x1D6FC}=10^{\circ }$ case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by spectral proper orthogonal decomposition. It is also shown that the second linear mechanism, corresponding to the Kelvin–Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as an input for resolvent analysis due to missing data near the leading edge. For both cases, resolvent modes resemble those from spectral proper orthogonal decomposition when the resolvent operator is low rank. The $\unicode[STIX]{x1D6FC}=0^{\circ }$ case is classified as an oscillator and its harmonics, where the resolvent operator is not low rank, are modelled using parasitic modes as opposed to classical resolvent modes which are the most amplified. The $\unicode[STIX]{x1D6FC}=10^{\circ }$ case behaves more like an amplifier and its nonlinear forcing is far less structured. The two cases suggest that resolvent-based modelling can be achieved for more complex flows with limited experimental measurements.

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Data-Targeted Prior Distribution for Variational AutoEncoder

Fluids ◽

10.3390/fluids6100343 ◽

2021 ◽

Vol 6 (10) ◽

pp. 343

Author(s):

Nissrine Akkari ◽

Fabien Casenave ◽

Thomas Daniel ◽

David Ryckelynck

Keyword(s):

Probability Distribution ◽

Proper Orthogonal Decomposition ◽

Prior Distribution ◽

Posterior Probability ◽

Fluid Flows ◽

Velocity Fields ◽

Orthogonal Decomposition ◽

Training Data ◽

Inference Model ◽

Proper Orthogonal

Bayesian methods were studied in this paper using deep neural networks. We are interested in variational autoencoders, where an encoder approaches the true posterior and the decoder approaches the direct probability. Specifically, we applied these autoencoders for unsteady and compressible fluid flows in aircraft engines. We used inferential methods to compute a sharp approximation of the posterior probability of these parameters with the transient dynamics of the training velocity fields and to generate plausible velocity fields. An important application is the initialization of transient numerical simulations of unsteady fluid flows and large eddy simulations in fluid dynamics. It is known by the Bayes theorem that the choice of the prior distribution is very important for the computation of the posterior probability, proportional to the product of likelihood with the prior probability. Hence, we propose a new inference model based on a new prior defined by the density estimate with the realizations of the kernel proper orthogonal decomposition coefficients of the available training data. We numerically show that this inference model improves the results obtained with the usual standard normal prior distribution. This inference model was constructed using a new algorithm improving the convergence of the parametric optimization of the encoder probability distribution that approaches the posterior. This latter probability distribution is data-targeted, similarly to the prior distribution. This new generative approach can also be seen as an improvement of the kernel proper orthogonal decomposition method, for which we do not usually have a robust technique for expressing the pre-image in the input physical space of the stochastic reduced field in the feature high-dimensional space with a kernel inner product.

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