Approximate deconvolution reduced order modeling

Xie, Xuping; Wells, David; Wang, Zhu; Iliescu, Traian

doi:10.1016/j.cma.2016.10.005

Cited by 68 publications

(62 citation statements)

References 59 publications

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“…In ROMs, spatial filtering has been used as a preprocessing step, to filter out the noise in the snapshot data and, thus, in the generation of the POD modes (see, e.g., Section 5 in [25] for a survey of relevant work). Two types of explicit ROM spatial filters are considered in this section: a POD projection (Section 3.1) and a POD DF (Section 3.2; see [37] for a related, but different, approach). Indeed, in the preprocessing spatial filtering used in [25], the snapshots (i.e., the input data) are spatially filtered, but the ROMs (i.e., the mathematical models) are not.…”

Section: The Galerkin Rom (G-rom)mentioning

confidence: 99%

“…In Reg-ROMs, on the other hand, some of the ROM terms are explicitly filtered, and thus, the mathematical model is modified. Two types of explicit ROM spatial filters are considered in this section: a POD projection (Section 3.1) and a POD DF (Section 3.2; see [37] for a related, but different, approach). The properties of these explicit ROM spatial filters are discussed in Section 3.3.…”

Section: The Galerkin Rom (G-rom)mentioning

confidence: 99%

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An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

Wells

Wang

Xie

et al. 2017

Numerical Methods in Fluids

118

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Summary In this paper, we propose a new evolve‐then‐filter reduced order model (EF‐ROM). This is a regularized ROM (Reg‐ROM), which aims to add numerical stabilization to proper orthogonal decomposition (POD) ROMs for convection‐dominated flows. We also consider the Leray ROM (L‐ROM). These two Reg‐ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a POD differential filter (DF). The four Reg‐ROM/filter combinations are tested in the numerical simulation of the three‐dimensional flow past a circular cylinder at a Reynolds number Re=1000. Overall, the most accurate Reg‐ROM/filter combination is EF‐ROM‐DF. Furthermore, the spatial filter has a higher impact on the Reg‐ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF‐ROM and L‐ROM. Finally, the CPU times of the four Reg‐ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS. Copyright © 2017 John Wiley & Sons, Ltd.

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Section: The Galerkin Rom (G-rom)mentioning

confidence: 99%

Section: The Galerkin Rom (G-rom)mentioning

confidence: 99%

An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

Wells

Wang

Xie

et al. 2017

Numerical Methods in Fluids

118

View full text Add to dashboard Cite

show abstract

“…However, it has been observed that the discarded modes often contribute to the evolving dynamics of large-scale complex turbulent flow systems, like the geophysical flows [36], resulting in instabilities and modeling errors in the solution [25,[37][38][39]. Thus, several research efforts have been devoted to improve the stability of ROM-GP frameworks by addressing the truncated modes contributions [40][41][42][43][44]. Noack et al [45] proposed an extra 'shift-mode' for accurate representation of the unstable steady solution.…”

Section: Introductionmentioning

confidence: 99%

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

et al. 2019

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In this study, we present a non-intrusive reduced order modeling (ROM) framework for largescale quasi-stationary systems. The framework proposed herein exploits the time series prediction capability of long short-term memory (LSTM) recurrent neural network architecture such that: (i) in the training phase, the LSTM model is trained on the modal coefficients extracted from the highresolution data snapshots using proper orthogonal decomposition (POD) transform, and (ii) in the testing phase, the trained model predicts the modal coefficients for the total time recursively based on the initial time history. Hence, no prior information about the underlying governing equations is required to generate the ROM. To illustrate the predictive performance of the proposed framework, the mean flow fields and time series response of the field values are reconstructed from the predicted modal coefficients by using an inverse POD transform. As a representative benchmark test case, we consider a two-dimensional quasi-geostrophic (QG) ocean circulation model which, in general, displays an enormous range of fluctuating spatial and temporal scales. We first illustrate that the conventional Galerkin projection based reduced order modeling of such systems requires a high number of POD modes to obtain a stable flow physics. In addition, ROM-GP does not seem to capture the intermittent bursts appearing in the dynamics of the first few most energetic modes. However, the proposed non-intrusive ROM framework based on LSTM (ROM-LSTM) yields a stable solution even for a small number of POD modes. We also observe that the ROM-LSTM model is able to capture quasi-periodic intermittent bursts accurately, and yields a stable and accurate mean flow dynamics using the time history of a few previous time states, denoted as the lookback time-window in this paper. Throughout the paper, we demonstrate our findings in terms of time series evolution of the field values and mean flow patterns, which suggest that the proposed fully non-intrusive ROM framework is robust and capable of predicting noisy nonlinear fluid flows in an extremely efficient way compared to the conventional projection based ROM framework.

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“…We emphasize, however, that the F-ROM (18) is not a closed system of equations, since the ROM stress tensor SFS r (which is used in the definition of ; see (19)) depends on u d (see (17)). Thus, to close the F-ROM (18), we need to solve the ROM closure problem, 30,33,[59][60][61] ie, to find a formula ≈ (a). The explicit formula for (see (17) and (19)) allows for the first time the use of data-driven modeling of the entire missing ROM information.…”

Section: Data-driven Correction Rommentioning

confidence: 99%

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

Mohebujjaman

Rebholz

Iliescu

2018

Numerical Methods in Fluids

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Summary We have recently proposed a data‐driven correction reduced‐order model (DDC‐ROM) framework for the numerical simulation of fluid flows, which can be formally written as follows. The new DDC‐ROM was constructed by using reduced‐order model spatial filtering and data‐driven reduced‐order model closure modeling (for the Correction term) and was successfully tested in the numerical simulation of a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. In this paper, we propose a physically constrained DDC‐ROM (CDDC‐ROM), which aims at improving the physical accuracy of the DDC‐ROM. The new physical constraints require that the CDDC‐ROM operators satisfy the same type of physical laws (ie, the Correction term's linear component should be dissipative, and the Correction term's nonlinear component should conserve energy) as those satisfied by the fluid flow equations. To implement these physical constraints, in the data‐driven modeling step, we replace the unconstrained least squares problem with a constrained least squares problem. We perform a numerical investigation of the new CDDC‐ROM and standard DDC‐ROM for a two‐dimensional channel flow past a circular cylinder at Reynolds numbers Re = 100,Re = 500, and Re = 1000. To this end, we consider a reproductive regime as well as a predictive (ie, cross‐validation) regime in which we use as little as 50% of the original training data. The numerical investigation clearly shows that the new CDDC‐ROM is significantly more accurate than the DDC‐ROM in both regimes.

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Approximate deconvolution reduced order modeling

Cited by 68 publications

References 59 publications

An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

An evolve‐then‐filter regularized reduced order model for convection‐dominated flows

Nonintrusive reduced order modeling framework for quasigeostrophic turbulence

Physically constrained data‐driven correction for reduced‐order modeling of fluid flows

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