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Fluids
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Reduced Order Modeling of Fluid Flows
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Reduced Order Modeling of Fluid Flows

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (15 August 2018) | Viewed by 32718

Special Issue Editors

Dr. Omer San

E-Mail Website
Guest Editor
Mechanical and Aerospace Engineering, Oklahoma State University, 201 General Academic Building, Stillwater, OK 74078-5016, USA
Interests: fluid mechanics; complex systems; pattern formation; partial differential equations; non-Newtonian fluids; fluid–structure interaction; hydrodynamic stability; non-equilibrium thermodynamics; vortex induced oscillations; rheology; pathological flows; network analysis; philosophy of science; sustainability and science and creativity in mathematics and science
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Goodarz Ahmadi

E-Mail Website
Guest Editor
Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699-5725, USA
Interests: computational fluid dynamics (CFD); turbulence; multiphase flows; aerosols transport and deposition; respiratory flows; heat and mass transfer
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The ever-increasing need for computational efficiency and improved accuracy of many applications in fluids leads to very large-scale dynamical systems, whose simulations and analyses make excessive and unmanageable demands on computational resources. Since the computational cost of traditional full-order numerical simulations is extremely prohibitive, many successful model order reduction approaches have been introduced. The purpose of such approaches is to reduce this computational burden and serve as surrogate models for efficient computational analysis fluid systems, especially in settings where the traditional methods require repeated model evaluations over a large range of parameter values. Simplifying computational complexity of the underlying mathematical model, these reduced order models offer promises in many prediction, identification, design, optimization, and control applications. However, they are neither robust with respect to the parameter changes nor low-cost to handle nonlinear dependence for complex nonlinear dynamical systems with temporal and stochastic parameters. Therefore, reduced order modeling remains an open challenge and the development of efficient and reliable model order reduction techniques is of paramount importance for both fundamental and applied fluid dynamics research. Topics in this call include, but are not limited to: projection-based approaches, reduced subspace or basis generation methods, regularization algorithms, coarse-grained simulations, data-driven methods, compressive or sparse sampling ideas and their implementations for fast predictive modeling, parameter identification, data assimilation, design, control, optimization and uncertainty quantification problems arising in fluid dynamics applications.

Dr. Omer San
Prof. Dr. Goodarz Ahmadi
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • parametric model reduction methods

  • proper orthogonal decomposition

  • dynamic mode decomposition

  • Koopman operators

  • radial basis functions

  • rational interpolation methods

  • empirical interpolation methods

  • manifold interpolation methods

  • balanced truncation

  • closure modeling

  • regularization algorithms

  • scale-aware basis selection

  • Krylov subspace methods

  • Volterra series

  • nonlinear kernel-based methods

  • data-driven methods

  • spatiotemporal patterns extraction

  • predictability quantification

  • non-projection based model reduction

  • machine learning enabled reduced-order models

  • high-dimensional parameter subspace characterization

  • tensor techniques

  • non-intrusive models

  • compressive sensing

  • greedy sampling algorithms

  • reduced-order adaptive flow controller for fluid flows

Published Papers (6 papers)

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Research

11 pages, 10111 KiB  
Article
Computing Functional Gains for Designing More Energy-Efficient Buildings Using a Model Reduction Framework
by Imran Akhtar, Jeff Borggaard and John Burns
Fluids 2018, 3(4), 97; https://doi.org/10.3390/fluids3040097 - 23 Nov 2018
Cited by 1 | Viewed by 2691
Abstract
We discuss developing efficient reduced-order models (ROM) for designing energy-efficient buildings using computational fluid dynamics (CFD) simulations. This is often the first step in the reduce-then-control technique employed for flow control in various industrial and engineering problems. This approach computes the proper orthogonal [...] Read more.
We discuss developing efficient reduced-order models (ROM) for designing energy-efficient buildings using computational fluid dynamics (CFD) simulations. This is often the first step in the reduce-then-control technique employed for flow control in various industrial and engineering problems. This approach computes the proper orthogonal decomposition (POD) eigenfunctions from high-fidelity simulations data and then forms a ROM by projecting the Navier-Stokes equations onto these basic functions. In this study, we develop a linear quadratic regulator (LQR) control based on the ROM of flow in a room. We demonstrate these approaches on a one-room model, serving as a basic unit in a building. Furthermore, the ROM is used to compute feedback functional gains. These gains are in fact the spatial representation of the feedback control. Insight of these functional gains can be used for effective placement of sensors in the room. This research can further lead to developing mathematical tools for efficient design, optimization, and control in building management systems. Full article
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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35 pages, 2907 KiB  
Article
Extreme Learning Machines as Encoders for Sparse Reconstruction
by S M Abdullah Al Mamun, Chen Lu and Balaji Jayaraman
Fluids 2018, 3(4), 88; https://doi.org/10.3390/fluids3040088 - 01 Nov 2018
Cited by 14 | Viewed by 3984
Abstract
Reconstruction of fine-scale information from sparse data is often needed in practical fluid dynamics where the sensors are typically sparse and yet, one may need to learn the underlying flow structures or inform predictions through assimilation into data-driven models. Given that sparse reconstruction [...] Read more.
Reconstruction of fine-scale information from sparse data is often needed in practical fluid dynamics where the sensors are typically sparse and yet, one may need to learn the underlying flow structures or inform predictions through assimilation into data-driven models. Given that sparse reconstruction is inherently an ill-posed problem, the most successful approaches encode the physics into an underlying sparse basis space that spans the manifold to generate well-posedness. To achieve this, one commonly uses a generic orthogonal Fourier basis or a data specific proper orthogonal decomposition (POD) basis to reconstruct from sparse sensor information at chosen locations. Such a reconstruction problem is well-posed as long as the sensor locations are incoherent and can sample the key physical mechanisms. The resulting inverse problem is easily solved using l 2 minimization or if necessary, sparsity promoting l 1 minimization. Given the proliferation of machine learning and the need for robust reconstruction frameworks in the face of dynamically evolving flows, we explore in this study the suitability of non-orthogonal basis obtained from extreme learning machine (ELM) auto-encoders for sparse reconstruction. In particular, we assess the interplay between sensor quantity and sensor placement in a given system dimension for accurate reconstruction of canonical fluid flows in comparison to POD-based reconstruction. Full article
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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12 pages, 1019 KiB  
Article
Evolve Filter Stabilization Reduced-Order Model for Stochastic Burgers Equation
by Xuping Xie, Feng Bao and Clayton G. Webster
Fluids 2018, 3(4), 84; https://doi.org/10.3390/fluids3040084 - 26 Oct 2018
Cited by 4 | Viewed by 2935
Abstract
In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical [...] Read more.
In this paper, we introduce the evolve-then-filter (EF) regularization method for reduced order modeling of convection-dominated stochastic systems. The standard Galerkin projection reduced order model (G-ROM) yield numerical oscillations in a convection-dominated regime. The evolve-then-filter reduced order model (EF-ROM) aims at the numerical stabilization of the standard G-ROM, which uses explicit ROM spatial filter to regularize various terms in the reduced order model (ROM). Our numerical results are based on a stochastic Burgers equation with linear multiplicative noise. The numerical result shows that the EF-ROM is significantly better than G-ROM. Full article
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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26 pages, 11423 KiB  
Article
A Hybrid Analytics Paradigm Combining Physics-Based Modeling and Data-Driven Modeling to Accelerate Incompressible Flow Solvers
by Sk. Mashfiqur Rahman, Adil Rasheed and Omer San
Fluids 2018, 3(3), 50; https://doi.org/10.3390/fluids3030050 - 18 Jul 2018
Cited by 12 | Viewed by 8211
Abstract
Numerical solution of the incompressible Navier–Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this divergence-free constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, [...] Read more.
Numerical solution of the incompressible Navier–Stokes equations poses a significant computational challenge due to the solenoidal velocity field constraint. In most computational modeling frameworks, this divergence-free constraint requires the solution of a Poisson equation at every step of the underlying time integration algorithm, which constitutes the major component of the computational expense. In this study, we propose a hybrid analytics procedure combining a data-driven approach with a physics-based simulation technique to accelerate the computation of incompressible flows. In our approach, proper orthogonal basis functions are generated to be used in solving the Poisson equation in a reduced order space. Since the time integration of the advection–diffusion equation part of the physics-based model is computationally inexpensive in a typical incompressible flow solver, it is retained in the full order space to represent the dynamics more accurately. Encoder and decoder interface conditions are provided by incorporating the elliptic constraint along with the data exchange between the full order and reduced order spaces. We investigate the feasibility of the proposed method by solving the Taylor–Green vortex decaying problem, and it is found that a remarkable speed-up can be achieved while retaining a similar accuracy with respect to the full order model. Full article
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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23 pages, 10280 KiB  
Article
One Dimensional Model for Droplet Ejection Process in Inkjet Devices
by Huicong Jiang and Hua Tan
Fluids 2018, 3(2), 28; https://doi.org/10.3390/fluids3020028 - 23 Apr 2018
Cited by 10 | Viewed by 6901
Abstract
In recent years, physics-based computer models have been increasingly applied to design the drop-on-demand (DOD) inkjet devices. The initial design stage for these devices often requires a fast turnaround time of computer models, because it usually involves a massive screening of a large [...] Read more.
In recent years, physics-based computer models have been increasingly applied to design the drop-on-demand (DOD) inkjet devices. The initial design stage for these devices often requires a fast turnaround time of computer models, because it usually involves a massive screening of a large number of design parameters. Thus, in the present study, a 1D model is developed to achieve the fast prediction of droplet ejection process from DOD devices, including the droplet breakup and coalescence. A popular 1D slender-jet method (Egger, 1994) is adopted in this study. The fluid dynamics in the nozzle region is described by a 2D axisymmetric unsteady Poiseuille flow model. Droplet formation and nozzle fluid dynamics are coupled, and hence solved together, to simulate the inkjet droplet ejection. The arbitrary Lagrangian–Eulerian method is employed to solve the governing equations. Numerical methods have been proposed to handle the breakup and coalescence of droplets. The proposed methods are implemented in an in-house developed MATLAB code. A series of validation examples have been carried out to evaluate the accuracy and the robustness of the proposed 1D model. Finally, a case study of the inkjet droplet ejection with different Ohnesorge number (Oh) is presented to demonstrate the capability of the proposed 1D model for DOD inkjet process. Our study has shown that 1D model can significantly reduce the computational time (usually less than one minute) yet with acceptable accuracy, which makes it very useful to explore the large parameter space of inkjet devices in a short amount of time. Full article
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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32 pages, 13334 KiB  
Article
Multiscale Stuart-Landau Emulators: Application to Wind-Driven Ocean Gyres
by Dmitri Kondrashov, Mickaël D. Chekroun and Pavel Berloff
Fluids 2018, 3(1), 21; https://doi.org/10.3390/fluids3010021 - 06 Mar 2018
Cited by 22 | Viewed by 5610
Abstract
The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), [...] Read more.
The multiscale variability of the ocean circulation due to its nonlinear dynamics remains a big challenge for theoretical understanding and practical ocean modeling. This paper demonstrates how the data-adaptive harmonic (DAH) decomposition and inverse stochastic modeling techniques introduced in (Chekroun and Kondrashov, (2017), Chaos, 27), allow for reproducing with high fidelity the main statistical properties of multiscale variability in a coarse-grained eddy-resolving ocean flow. This fully-data-driven approach relies on extraction of frequency-ranked time-dependent coefficients describing the evolution of spatio-temporal DAH modes (DAHMs) in the oceanic flow data. In turn, the time series of these coefficients are efficiently modeled by a family of low-order stochastic differential equations (SDEs) stacked per frequency, involving a fixed set of predictor functions and a small number of model coefficients. These SDEs take the form of stochastic oscillators, identified as multilayer Stuart–Landau models (MSLMs), and their use is justified by relying on the theory of Ruelle–Pollicott resonances. The good modeling skills shown by the resulting DAH-MSLM emulators demonstrates the feasibility of using a network of stochastic oscillators for the modeling of geophysical turbulence. In a certain sense, the original quasiperiodic Landau view of turbulence, with the amendment of the inclusion of stochasticity, may be well suited to describe turbulence. Full article
(This article belongs to the Special Issue Reduced Order Modeling of Fluid Flows)
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