Bayesian identification of a projection-based Reduced Order Model for Computational Fluid Dynamics Computers and Fluids

Giovanni Stabile, Bojana Rosic

Research output: Contribution to journalArticleAcademic

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Abstract

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.
Original languageEnglish
JournalComputers and fluids
Publication statusSubmitted - 25 Oct 2019

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Identification (control systems)
Computational fluid dynamics
Fluids
Turbulence models
Inverse problems
Ordinary differential equations
Chaos theory
Sensitivity analysis
Polynomials
Decomposition

Keywords

  • math.NA
  • cs.NA

Cite this

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Bayesian identification of a projection-based Reduced Order Model for Computational Fluid Dynamics Computers and Fluids. / Stabile, Giovanni; Rosic, Bojana.

In: Computers and fluids, 25.10.2019.

Research output: Contribution to journalArticleAcademic

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T1 - Bayesian identification of a projection-based Reduced Order Model for Computational Fluid Dynamics Computers and Fluids

AU - Stabile, Giovanni

AU - Rosic, Bojana

PY - 2019/10/25

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N2 - In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.

AB - In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.

KW - math.NA

KW - cs.NA

M3 - Article

JO - Computers and fluids

JF - Computers and fluids

SN - 0045-7930

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