POD-Galerkin Projection ROM for the Flow Passing A Rotating Elliptical Airfoil

Xu, Bolun; Hu, Gao; Wei, Mingjun; Hrynuk, John

doi:10.2514/6.2020-3082

Cited by 2 publications

(1 citation statement)

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“…To this end, building upon our recent works on the hybrid analysis and modeling (HAM) framework [9][10][11], we present a data assimilation-empowered approach to utilize a machine learning methodology to fuse computationally-light physics-based models with the available real-time measurement data to provide more accurate and reliable predictions of wake-vortex transport and decay. In particular, we build a surrogate reduced order model (ROM), by combining proper orthogonal decomposition (POD) for basis construction [12][13][14][15][16][17] and Galerkin projection to model the dynamical evolution on the corresponding low-order subspace [18][19][20][21][22][23][24][25][26]. Although ROMs based on Galerkin projection (denoted as GROMs in the present study) have been traditionally considered the standard approach for reduced order modeling, they often become inaccurate and unstable for long-term predictions of convection-dominated flows with strong nonlinearity [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction

et al. 2021

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In this paper, we put forth a long short-term memory (LSTM) nudging framework for the enhancement of reduced order models (ROMs) of fluid flows utilizing noisy measurements for air traffic improvements. Toward emerging applications of digital twins in aviation, the proposed approach allows for constructing a realtime predictive tool for wake-vortex transport and decay systems. We build on the fact that in realistic application, there are uncertainties in initial and boundary conditions, model parameters, as well as measurements. Moreover, conventional nonlinear ROMs based on Galerkin projection (GROMs) suffer from imperfection and solution instabilities, especially for advection-dominated flows with slow decay in the Kolmogorov width. In the presented LSTM nudging (LSTM-N) approach, we fuse forecasts from a combination of imperfect GROM and uncertain state estimates, with sparse Eulerian sensor measurements to provide more reliable predictions in a dynamical data assimilation framework. We illustrate our concept by solving a two-dimensional vorticity transport equation. We investigate the effects of measurements noise and state estimate uncertainty on the performance of the LSTM-N behavior. We also demonstrate that it can sufficiently handle different levels of temporal and spatial measurement sparsity, and offer a huge potential in developing next-generation digital twin technologies.

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