Augmented proper orthogonal decomposition for problems with moving discontinuities

Brenner, Thomas A.; Fontenot, Raymond L.; Cizmas, Paul G. A.; O’Brien, Thomas J.; Breault, Ronald W.

doi:10.1016/j.powtec.2010.03.032

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…where D is the dimension of the domain and J is a nonlinear functional consisting of the combinations of the time coefficients and basis functions of each approximated state variable. The approximated governing equations, (10) or (12), were projected along the POD basis functions,…”

Section: Reduced-order Modelmentioning

confidence: 99%

“…The FOM ( 13) was used to generate the snapshots for the ROM. It is important to note that while the governing equations of the FOM used the characteristic variables, the ROM used the zeta-variables (10). A grid convergence study was performed for the steady flow through the nozzle by using 51, 101, and 201 nodes.…”

Section: Quasi-one-dimensional Nozzle Flowmentioning

confidence: 99%

“…Proper Orthogonal Decomposition was developed by Karhunen and Loeve [3,4] and applied to fluid dynamics by Lumley [5]. The POD method is a common model reduction procedure used to develop ROMs, and has been used for many applications such as turbomachinery [6,7], cavity [8], and multiphase [9,10] flows. Other model reduction methods have also been explored such as the Balanced POD [11], dynamic mode decomposition [12], and biorthogonal decomposition [13].…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Proper Orthogonal Decomposition based Reduced-Order Model

Krath,

Carpenter,

Cizmas

et al. 2020

Preprint

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This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy equations were written using specific volume instead of density. This substitution allowed for the pre-computation of the coefficients of the system of ODEs that make up the reduced-order model. Several methods were employed to enhance the stability of the ODE solver: the penalty method to enforce boundary conditions, artificial dissipation, and a method that modifies the number of modes used in the POD approximation. This new POD-based reduced-order model was validated for four cases at both on-and off-reference conditions: a quasi-one-dimensional nozzle, a two-dimensional channel, a threedimensional axisymmetric nozzle, and a transonic fan. The speedup obtained by using the POD-based ROM vs. the full-order model exceeded four orders of magnitude in all cases tested.

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Section: Reduced-order Modelmentioning

confidence: 99%

Section: Quasi-one-dimensional Nozzle Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Proper Orthogonal Decomposition based Reduced-Order Model

Krath,

Carpenter,

Cizmas

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…The timeevolution of each modes' weight can then be calculated with a truncated Galerkin projection approach (Aubry et al (1988); Berkooz et al (1993); Lumley et al (1996); Sirovich (1987)). This procedure has proven to be a powerful simulation tool for various fluid mechanical problems (Akhtar et al (2009) ;Bergmann et al (2005); Cazemier et al (1998); Deane et al (1991); Liakopoulos et al (1997); Rempfer and Fasel (1994); Siegel et al (2008); Singh et al (2001); Wang et al (2012b)) including multiphase flows (Brenner et al (2010(Brenner et al ( , 2012; Cizmas et al (2003); Yuan et al (2005)). However, it is well-known that long-time integration of POD-modes may predict spurious asymptotic behavior (Foias et al (1991); Rempfer (2000); Sirisup and Karniadakis (2004)).…”

Section: Introductionmentioning

confidence: 99%

Recurrence CFD – A novel approach to simulate multiphase flows with strongly separated time scales

Lichtenegger

Pirker

2016

Chemical Engineering Science

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Classical Computational Fluid Dynamics (CFD) of long-time processes with strongly separated time scales is computationally extremely demanding if not impossible. Consequently, the state-of-the-art description of such systems is not capable of real-time simulations or online process monitoring.In order to bridge this gap, we propose a new method suitable to decouple slow from fast degrees of freedom in many cases. Based on the recurrence statistics of unsteady flow fields, we deduce a recurrence process which enables the generic representation of pseudo-periodic motion at high spatial and temporal resolution.Based on these fields, passive scalars can be traced by recurrence CFD. While a first, Eulerian Model A solves a passive transport equation in a classical implicit finite-volume environment, a second, Lagrangian Model B propagates fluid particles obeying a stochastic differential equation explicitly.Finally, this new concept is tested by two multiphase processes -a lab scale oscillating bubble column and an industrial scale steelmaking converter. Results of tracer distribution obtained by recurrence CFD are in very good agreement with full CFD simulations, while computational times are dramatically reduced. Actually, recurrence CFD is a promising candidate for online simulations of passive transport processes at full CFD resolution, which opens the door towards improved process monitoring.

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“…Then, the POD basis is used to approximate the solution of original problems. The POD-based dimensionality reduction method has found numerous successful applications in various fields, such as data analysis, numerical heat transfer and computational fluid dynamics, and more discussions can be found in [1][2][3][4][5][6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Temperature field reconstruction from the partial measurement data using the gappy proper orthogonal decomposition

Lei

Shi

2013

IET Science, Measurement & Technology

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Fast reconstruction of the temperature field from the partial temperature measurement data is highly desirable in the field of thermal engineering, in which reconstruction algorithms play a crucial role in real applications. Based on the gappy proper orthogonal decomposition technique, a promising approach that integrates the numerical simulation information and the measurement information is proposed in this study for the temperature field reconstruction from the partial measurement data, where the original reconstruction problem is formulated into an optimisation problem. An objective functional, which simultaneously considers the outliers in the measurement data and the model approximation distortions, is presented. Based on the split Bregman iteration technique, an iterative scheme is developed for solving the proposed objective functional. Numerical simulations are implemented to demonstrate the feasibility and effectiveness of the proposed algorithm.

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Augmented proper orthogonal decomposition for problems with moving discontinuities

Cited by 12 publications

References 16 publications

An Efficient Proper Orthogonal Decomposition based Reduced-Order Model

An Efficient Proper Orthogonal Decomposition based Reduced-Order Model

Recurrence CFD – A novel approach to simulate multiphase flows with strongly separated time scales

Temperature field reconstruction from the partial measurement data using the gappy proper orthogonal decomposition

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