Construction of reduced order models for the non-linear Navier-Stokes equations using the proper orthogonal fecomposition (POD)/Galerkin method.

Fike, Jeffrey A.

doi:10.2172/1096504

Cited by 2 publications

(4 citation statements)

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“…More detail on the content described in this chapter can be found in the following journal articles and SAND reports, written during the time of this LDRD project: [59,55,35,18,60,61].…”

Section: Chapter 5 Stable Roms Via Continuous Projectionmentioning

confidence: 99%

“…The reader is referred to the following SAND reports and articles written during the time of this LDRD project for more details on the topics described in this report: [55,59,60,61,35].…”

Section: Introductionmentioning

confidence: 99%

“…35) is the unique symmetric (at least) positive semi-definite solution of the Lyapunov equationAP + PA T + BB T = 0. A T t C T Ce At dt, (A.37)is the unique symmetric (at least) positive semi-definite solution of the Lyapunov equationA T Q + QA + C T C = 0.…”

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confidence: 99%

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Reduced Order Modeling for Prediction and Control of Large-Scale Systems.

Kalashnikova

Arunajatesan²,

Barone³

et al. 2014

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This report describes work performed from June 2012 through May 2014 as a part of a Sandia Early Career Laboratory Directed Research and Development (LDRD) project led by the first author. The objective of the project is to investigate methods for building stable and efficient proper orthogonal decomposition (POD)/Galerkin reduced order models (ROMs): models derived from a sequence of high-fidelity simulations but having a much lower computational cost. Since they are, by construction, small and fast, ROMs can enable real-time simulations of complex systems for onthe-spot analysis, control and decision-making in the presence of uncertainty. Of particular interest to Sandia is the use of ROMs for the quantification of the compressible captive-carry environment, simulated for the design and qualification of nuclear weapons systems. It is an unfortunate reality that many ROM techniques are computationally intractable or lack an a priori stability guarantee for compressible flows. For this reason, this LDRD project focuses on the development of techniques for building provably stable projection-based ROMs. Model reduction approaches based on continuous as well as discrete projection are considered.

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“…More detail on the content described in this chapter can be found in the following journal articles and SAND reports, written during the time of this LDRD project: [59,55,35,18,60,61].…”

Section: Chapter 5 Stable Roms Via Continuous Projectionmentioning

confidence: 99%

“…The reader is referred to the following SAND reports and articles written during the time of this LDRD project for more details on the topics described in this report: [55,59,60,61,35].…”

Section: Introductionmentioning

confidence: 99%

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Reduced Order Modeling for Prediction and Control of Large-Scale Systems.

Kalashnikova

Arunajatesan²,

Barone³

et al. 2014

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“…The online time-integration of the ROM system (4) (with the ROM coefficient matrix computed within Spirit and written to disk) is then performed using a fourth-order Runge-Kutta scheme in MATLAB. For more information on the Spirit code, the reader is referred to [55,54].…”

Section: Stability-preserving Discrete Implementationmentioning

confidence: 99%

Construction of energy-stable projection-based reduced order models

Kalashnikova

Barone

Arunajatesan

et al. 2014

Applied Mathematics and Computation

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a r t i c l e i n f o Keywords: Reduced order model (ROM) Proper orthogonal decomposition (POD)/ Galerkin projection Linear hyperbolic/incompletely parabolic systems Linear time-invariant (LTI) systems Numerical stability Lyapunov equation a b s t r a c tAn approach for building energy-stable Galerkin reduced order models (ROMs) for linear hyperbolic or incompletely parabolic systems of partial differential equations (PDEs) using continuous projection is developed. This method is an extension of earlier work by the authors specific to the equations of linearized compressible inviscid flow. The key idea is to apply to the PDEs a transformation induced by the Lyapunov function for the system, and to build the ROM in the transformed variables. For linear problems, the desired transformation is induced by a special inner product, termed the ''symmetry inner product'', which is derived herein for several systems of physical interest. Connections are established between the proposed approach and other stability-preserving model reduction methods, giving the paper a review flavor. More specifically, it is shown that a discrete counterpart of this inner product is a weighted L 2 inner product obtained by solving a Lyapunov equation, first proposed by Rowley et al. and termed herein the ''Lyapunov inner product''. Comparisons between the symmetry inner product and the Lyapunov inner product are made, and the performance of ROMs constructed using these inner products is evaluated on several benchmark test cases.Published by Elsevier Inc.

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Construction of reduced order models for the non-linear Navier-Stokes equations using the proper orthogonal fecomposition (POD)/Galerkin method.

Cited by 2 publications

References 4 publications

Reduced Order Modeling for Prediction and Control of Large-Scale Systems.

Reduced Order Modeling for Prediction and Control of Large-Scale Systems.

Construction of energy-stable projection-based reduced order models

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