A dynamic closure modeling framework for model order reduction of geophysical flows
Abstract
Here in this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing generalizability, the proposed reduced order modeling (ROM) framework is first constructed by Galerkin projection of the single-layer quasigeostrophic equation, a standard prototype of large-scale general circulation models, onto a set of dominant proper orthogonal decomposition modes. We then propose an eddy viscosity closure approach to stabilize the resulting surrogate model considering the analogy between large eddy simulation (LES) and truncated modal projection. Our efforts, in particular, include the translation of the dynamic subgrid-scale model into our ROM setting by defining a test truncation similar to the test filtering in LES. Finally, the a posteriori analysis shows that our approach is remarkably accurate, allowing us to integrate simulations over long time intervals at a nominally small computational overhead.
- Authors:
-
- Oklahoma State Univ., Stillwater, OK (United States). School of Mechanical and Aerospace Engineering
- Publication Date:
- Research Org.:
- Oklahoma State Univ., Stillwater, OK (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1593561
- Alternate Identifier(s):
- OSTI ID: 1509520
- Grant/Contract Number:
- SC0019290
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Fluids
- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 4; Journal ID: ISSN 1070-6631
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Turbulence modeling; Geophysical flows; Reduced order modeling; Proper orthogonal decomposition; Galerkin projection; Dynamic eddy viscosity closure
Citation Formats
Rahman, Sk. M., Ahmed, S. E., and San, O. A dynamic closure modeling framework for model order reduction of geophysical flows. United States: N. p., 2019.
Web. doi:10.1063/1.5093355.
Rahman, Sk. M., Ahmed, S. E., & San, O. A dynamic closure modeling framework for model order reduction of geophysical flows. United States. https://doi.org/10.1063/1.5093355
Rahman, Sk. M., Ahmed, S. E., and San, O. Fri .
"A dynamic closure modeling framework for model order reduction of geophysical flows". United States. https://doi.org/10.1063/1.5093355. https://www.osti.gov/servlets/purl/1593561.
@article{osti_1593561,
title = {A dynamic closure modeling framework for model order reduction of geophysical flows},
author = {Rahman, Sk. M. and Ahmed, S. E. and San, O.},
abstractNote = {Here in this paper, a dynamic closure modeling approach has been derived to stabilize the projection-based reduced order models in the long-term evolution of forced-dissipative dynamical systems. To simplify our derivation without losing generalizability, the proposed reduced order modeling (ROM) framework is first constructed by Galerkin projection of the single-layer quasigeostrophic equation, a standard prototype of large-scale general circulation models, onto a set of dominant proper orthogonal decomposition modes. We then propose an eddy viscosity closure approach to stabilize the resulting surrogate model considering the analogy between large eddy simulation (LES) and truncated modal projection. Our efforts, in particular, include the translation of the dynamic subgrid-scale model into our ROM setting by defining a test truncation similar to the test filtering in LES. Finally, the a posteriori analysis shows that our approach is remarkably accurate, allowing us to integrate simulations over long time intervals at a nominally small computational overhead.},
doi = {10.1063/1.5093355},
journal = {Physics of Fluids},
number = 4,
volume = 31,
place = {United States},
year = {Fri Apr 26 00:00:00 EDT 2019},
month = {Fri Apr 26 00:00:00 EDT 2019}
}
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Works referenced in this record:
A Reduced-Order Method for Simulation and Control of Fluid Flows
journal, July 1998
- Ito, K.; Ravindran, S. S.
- Journal of Computational Physics, Vol. 143, Issue 2
Modeling Mesoscale Turbulence in the Barotropic Double-Gyre Circulation
journal, November 2003
- Holm, Darryl D.; Nadiga, Balasubramanya T.
- Journal of Physical Oceanography, Vol. 33, Issue 11
An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications
journal, October 2004
- Vreman, A. W.
- Physics of Fluids, Vol. 16, Issue 10
A proposed modification of the Germano subgrid‐scale closure method
journal, March 1992
- Lilly, D. K.
- Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 3
Non-linear dynamics and statistical theories for basic geophysical flows
book, January 2006
- Majda, Andrew; Wang, Xiaoming
Dispersive–Dissipative Eddy Parameterization in a Barotropic Model
journal, August 2001
- Nadiga, Balasubramanya T.; Margolin, Len G.
- Journal of Physical Oceanography, Vol. 31, Issue 8
Reduced-order subscales for POD models
journal, July 2015
- Baiges, Joan; Codina, Ramon; Idelsohn, Sergio
- Computer Methods in Applied Mechanics and Engineering, Vol. 291
The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
journal, January 1993
- Berkooz, G.
- Annual Review of Fluid Mechanics, Vol. 25, Issue 1
Artificial viscosity proper orthogonal decomposition
journal, January 2011
- Borggaard, Jeff; Iliescu, Traian; Wang, Zhu
- Mathematical and Computer Modelling, Vol. 53, Issue 1-2
A Short Review on Model Order Reduction Based on Proper Generalized Decomposition
journal, October 2011
- Chinesta, Francisco; Ladeveze, Pierre; Cueto, Elías
- Archives of Computational Methods in Engineering, Vol. 18, Issue 4
Numerical Simulations of a Two-Layer Quasi-Geostrophic Equation of the Ocean
journal, January 2000
- Medjo, T. Tachim
- SIAM Journal on Numerical Analysis, Vol. 37, Issue 6
Identification strategies for model-based control
journal, July 2013
- Cordier, Laurent; Noack, Bernd R.; Tissot, Gilles
- Experiments in Fluids, Vol. 54, Issue 8
A dynamic subgrid‐scale eddy viscosity model
journal, July 1991
- Germano, Massimo; Piomelli, Ugo; Moin, Parviz
- Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 7
On the stability and convergence of a Galerkin reduced order model (ROM) of compressible flow with solid wall and far-field boundary treatment
journal, August 2010
- Kalashnikova, I.; Barone, M. F.
- International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10
Efficiency of a POD-based reduced second-order adjoint model in 4D-Var data assimilation
journal, January 2007
- Daescu, D. N.; Navon, I. M.
- International Journal for Numerical Methods in Fluids, Vol. 53, Issue 6
Model Reduction for Flow Analysis and Control
journal, January 2017
- Rowley, Clarence W.; Dawson, Scott T. M.
- Annual Review of Fluid Mechanics, Vol. 49, Issue 1
Approximate deconvolution reduced order modeling
journal, January 2017
- Xie, Xuping; Wells, David; Wang, Zhu
- Computer Methods in Applied Mechanics and Engineering, Vol. 313
On Low-Dimensional Galerkin Models for Fluid Flow
journal, June 2000
- Rempfer, D.
- Theoretical and Computational Fluid Dynamics, Vol. 14, Issue 2
Modal Analysis of Fluid Flows: An Overview
journal, December 2017
- Taira, Kunihiko; Brunton, Steven L.; Dawson, Scott T. M.
- AIAA Journal, Vol. 55, Issue 12
A New Closure Strategy for Proper Orthogonal Decomposition Reduced-Order Models
journal, April 2012
- Akhtar, Imran; Wang, Zhu; Borggaard, Jeff
- Journal of Computational and Nonlinear Dynamics, Vol. 7, Issue 3
pyMOR -- Generic Algorithms and Interfaces for Model Order Reduction
journal, January 2016
- Milk, René; Rave, Stephan; Schindler, Felix
- SIAM Journal on Scientific Computing, Vol. 38, Issue 5
Evaluating Data Assimilation Algorithms
journal, November 2012
- Law, K. J. H.; Stuart, A. M.
- Monthly Weather Review, Vol. 140, Issue 11
Sparse reduced-order modelling: sensor-based dynamics to full-state estimation
journal, April 2018
- Loiseau, Jean-Christophe; Noack, Bernd R.; Brunton, Steven L.
- Journal of Fluid Mechanics, Vol. 844
An evolve-then-filter regularized reduced order model for convection-dominated flows: EVOLVE-THEN-FILTER REGULARIZED REDUCED ORDER MODEL
journal, February 2017
- Wells, D.; Wang, Z.; Xie, X.
- International Journal for Numerical Methods in Fluids, Vol. 84, Issue 10
A reduced-order approach to four-dimensional variational data assimilation using proper orthogonal decomposition
journal, January 2007
- Cao, Yanhua; Zhu, Jiang; Navon, I. M.
- International Journal for Numerical Methods in Fluids, Vol. 53, Issue 10
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
journal, January 2015
- Benner, Peter; Gugercin, Serkan; Willcox, Karen
- SIAM Review, Vol. 57, Issue 4
A spectral viscosity method for correcting the long-term behavior of POD models
journal, February 2004
- Sirisup, S.; Karniadakis, G. E.
- Journal of Computational Physics, Vol. 194, Issue 1
Spectral proper orthogonal decomposition
journal, March 2016
- Sieber, Moritz; Paschereit, C. Oliver; Oberleithner, Kilian
- Journal of Fluid Mechanics, Vol. 792
Observing the Ocean in the 1990s
journal, October 1982
- Munk, W.; Wunsch, C.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 307, Issue 1499
Proper orthogonal decomposition and low-dimensional models for driven cavity flows
journal, July 1998
- Cazemier, W.; Verstappen, R. W. C. P.; Veldman, A. E. P.
- Physics of Fluids, Vol. 10, Issue 7
pyROM: A computational framework for reduced order modeling
journal, January 2019
- Puzyrev, Vladimir; Ghommem, Mehdi; Meka, Shiv
- Journal of Computational Science, Vol. 30
On a Physical Basis for Numerical Prediction of Large-Scale Motions in the Atmosphere
journal, December 1949
- Charney, J. G.
- Journal of Meteorology, Vol. 6, Issue 6
Proper orthogonal decomposition closure models for turbulent flows: A numerical comparison
journal, September 2012
- Wang, Zhu; Akhtar, Imran; Borggaard, Jeff
- Computer Methods in Applied Mechanics and Engineering, Vol. 237-240
Stabilization of projection-based reduced-order models: STABILIZATION OF PROJECTION-BASED REDUCED-ORDER MODELS
journal, February 2012
- Amsallem, David; Farhat, Charbel
- International Journal for Numerical Methods in Engineering, Vol. 91, Issue 4
Wind-driven ocean circulation and equilibrium statistical mechanics
journal, August 1989
- Griffa, Annalisa; Salmon, Rick
- Journal of Marine Research, Vol. 47, Issue 3
Numerical analysis of the Leray reduced order model
journal, January 2018
- Xie, Xuping; Wells, David; Wang, Zhu
- Journal of Computational and Applied Mathematics, Vol. 328
Stabilization of projection-based reduced order models of the Navier–Stokes
journal, August 2012
- Balajewicz, Maciej; Dowell, Earl H.
- Nonlinear Dynamics, Vol. 70, Issue 2
Low-dimensional modelling of high-Reynolds-number shear flows incorporating constraints from the Navier–Stokes equation
journal, July 2013
- Balajewicz, Maciej J.; Dowell, Earl H.; Noack, Bernd R.
- Journal of Fluid Mechanics, Vol. 729
Two-level discretizations of nonlinear closure models for proper orthogonal decomposition
journal, January 2011
- Wang, Z.; Akhtar, I.; Borggaard, J.
- Journal of Computational Physics, Vol. 230, Issue 1
Evolution of three-dimensional coherent structures in a flat-plate boundary layer
journal, February 1994
- Rempfer, Dietmar; Fasel, Hermann F.
- Journal of Fluid Mechanics, Vol. 260
The Quantum Limit to Moore's Law
journal, August 2008
- Powell, James R.
- Proceedings of the IEEE, Vol. 96, Issue 8
Physically constrained data‐driven correction for reduced‐order modeling of fluid flows
journal, October 2018
- Mohebujjaman, M.; Rebholz, L. G.; Iliescu, T.
- International Journal for Numerical Methods in Fluids, Vol. 89, Issue 3
POD-Galerkin approximations in PDE-constrained optimization
journal, October 2010
- Sachs, Ekkehard W.; Volkwein, Stefan
- GAMM-Mitteilungen, Vol. 33, Issue 2
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body
journal, April 2014
- Östh, Jan; Noack, Bernd R.; Krajnović, Siniša
- Journal of Fluid Mechanics, Vol. 747
Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part I
journal, August 1966
- Arakawa, Akio
- Journal of Computational Physics, Vol. 1, Issue 1
A coarse-grid projection method for accelerating incompressible flow computations
journal, January 2013
- San, Omer; Staples, Anne E.
- Journal of Computational Physics, Vol. 233
Approximate deconvolution large eddy simulation of a barotropic ocean circulation model
journal, January 2011
- San, Omer; Staples, Anne E.; Wang, Zhu
- Ocean Modelling, Vol. 40, Issue 2
Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations
journal, October 2010
- Carlberg, Kevin; Bou-Mosleh, Charbel; Farhat, Charbel
- International Journal for Numerical Methods in Engineering, Vol. 86, Issue 2
Model reduction for compressible flows using POD and Galerkin projection
journal, February 2004
- Rowley, Clarence W.; Colonius, Tim; Murray, Richard M.
- Physica D: Nonlinear Phenomena, Vol. 189, Issue 1-2
A survey of model reduction methods for large-scale systems
book, January 2001
- Antoulas, A. C.; Sorensen, D. C.; Gugercin, S.
- Contemporary Mathematics
Four-Gyre Circulation in a Barotropic Model with Double-Gyre Wind Forcing
journal, June 2000
- Greatbatch, Richard J.; Nadiga, B. T.
- Journal of Physical Oceanography, Vol. 30, Issue 6
The chips are down for Moore’s law
journal, February 2016
- Waldrop, M. Mitchell
- Nature, Vol. 530, Issue 7589
An intrinsic stabilization scheme for proper orthogonal decomposition based low-dimensional models
journal, May 2007
- Kalb, Virginia L.; Deane, Anil E.
- Physics of Fluids, Vol. 19, Issue 5
Wind-Driven Currents in a Baroclinic Ocean; with Application to the Equatorial Currents of the Eastern Pacific
journal, November 1947
- Sverdrup, H. U.
- Proceedings of the National Academy of Sciences, Vol. 33, Issue 11
A Hybrid Approach for Model Order Reduction of Barotropic Quasi-Geostrophic Turbulence
journal, October 2018
- Rahman, Sk.; San, Omer; Rasheed, Adil
- Fluids, Vol. 3, Issue 4
Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses
journal, April 2012
- Chen, Kevin K.; Tu, Jonathan H.; Rowley, Clarence W.
- Journal of Nonlinear Science, Vol. 22, Issue 6, p. 887-915
Enablers for robust POD models
journal, February 2009
- Bergmann, M.; Bruneau, C. -H.; Iollo, A.
- Journal of Computational Physics, Vol. 228, Issue 2
Stability Properties of POD-Galerkin Approximations for the Compressible Navier-Stokes Equations
journal, March 2000
- Iollo, A.; Lanteri, S.; Désidéri, J. -A.
- Theoretical and Computational Fluid Dynamics, Vol. 13, Issue 6
A stabilized proper orthogonal decomposition reduced-order model for large scale quasigeostrophic ocean circulation
journal, May 2015
- San, Omer; Iliescu, Traian
- Advances in Computational Mathematics, Vol. 41, Issue 5
Optimal nonlinear eddy viscosity in Galerkin models of turbulent flows
journal, February 2015
- Protas, Bartosz; Noack, Bernd R.; Östh, Jan
- Journal of Fluid Mechanics, Vol. 766
Data Assimilation for Numerical Weather Prediction: A Review
book, January 2009
- Navon, Ionel M.
- Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications
Turbulence and the dynamics of coherent structures. I. Coherent structures
journal, January 1987
- Sirovich, Lawrence
- Quarterly of Applied Mathematics, Vol. 45, Issue 3
An Example of Eddy-Induced Ocean Circulation
journal, July 1980
- Holland, William R.; Rhines, Peter B.
- Journal of Physical Oceanography, Vol. 10, Issue 7
Inertial gyres in decaying and forced geostrophic turbulence
journal, November 1992
- Cummins, Patrick F.
- Journal of Marine Research, Vol. 50, Issue 4
On the structure of dynamical systems describing the evolution of coherent structures in a convective boundary layer
journal, March 1994
- Rempfer, D.
- Physics of Fluids, Vol. 6, Issue 3
Spectral proper orthogonal decomposition
text, January 2016
- Sieber, Moritz; Paschereit, Christian Oliver; Oberleithner, Kilian
- Technische Universität Berlin
Computational Design for Long-Term Numerical Integration of the Equations of Fluid Motion: Two-Dimensional Incompressible Flow. Part I
journal, August 1997
- Arakawa, Akio
- Journal of Computational Physics, Vol. 135, Issue 2
Fundamentals of engineering numerical analysis
journal, April 2002
- Moin, Parviz
- Canadian Journal of Civil Engineering, Vol. 29, Issue 2
Data Assimilation: A Mathematical Introduction
book, January 2015
- Law, Kody; Stuart, Andrew; Zygalakis, Konstantinos
- Texts in Applied Mathematics
Approximate deconvolution large eddy simulation of a barotropic ocean circulation model
text, January 2011
- San, Omer; Staples, Anne E.; Wang, Zhu
- arXiv
Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
text, January 2011
- Wang, Zhu; Akhtar, Imran; Borggaard, Jeff
- arXiv
A coarse-grid projection method for accelerating incompressible flow computations
text, January 2012
- San, Omer; Staples, Anne E.
- arXiv
On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
text, January 2013
- Östh, Jan; Noack, Bernd R.; Krajnović, Siniša
- arXiv
Optimal Nonlinear Eddy Viscosity in Galerkin Models of Turbulent Flows
text, January 2014
- Protas, Bartosz; Noack, Bernd R.; Östh, Jan
- arXiv
pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
text, January 2015
- Milk, René; Rave, Stephan; Schindler, Felix
- arXiv
Modal Analysis of Fluid Flows: An Overview
preprint, January 2017
- Taira, Kunihiko; Brunton, Steven L.; Dawson, Scott T. M.
- arXiv
Sparse reduced-order modeling : Sensor-based dynamics to full-state estimation
text, January 2017
- Loiseau, Jean-Christophe; Noack, Bernd R.; Brunton, Steven L.
- arXiv
Stabilization of projection-based reduced-order models: STABILIZATION OF PROJECTION-BASED REDUCED-ORDER MODELS
journal, February 2012
- Amsallem, David; Farhat, Charbel
- International Journal for Numerical Methods in Engineering, Vol. 91, Issue 4
Stabilization of projection-based reduced order models of the Navier–Stokes
journal, August 2012
- Balajewicz, Maciej; Dowell, Earl H.
- Nonlinear Dynamics, Vol. 70, Issue 2
A spectral viscosity method for correcting the long-term behavior of POD models
journal, February 2004
- Sirisup, S.; Karniadakis, G. E.
- Journal of Computational Physics, Vol. 194, Issue 1
An Example of Eddy-Induced Ocean Circulation
journal, July 1980
- Holland, William R.; Rhines, Peter B.
- Journal of Physical Oceanography, Vol. 10, Issue 7
pyMOR - Generic Algorithms and Interfaces for Model Order Reduction
text, January 2015
- Milk, René; Rave, Stephan; Schindler, Felix
- arXiv
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- Physics of Fluids, Vol. 31, Issue 12
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journal, November 2019
- Rahman, Sk. M.; Pawar, S.; San, O.
- Physical Review E, Vol. 100, Issue 5
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- arXiv