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

    3 Downloads (Pure)

    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

    Fingerprint

    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

    @article{022010279fdd43dbb6e9d4da2b4667ae,
    title = "Bayesian identification of a projection-based Reduced Order Model for Computational Fluid Dynamics Computers and Fluids",
    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.",
    keywords = "math.NA, cs.NA",
    author = "Giovanni Stabile and Bojana Rosic",
    year = "2019",
    month = "10",
    day = "25",
    language = "English",
    journal = "Computers and fluids",
    issn = "0045-7930",
    publisher = "Elsevier",

    }

    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

    TY - JOUR

    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

    Y1 - 2019/10/25

    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

    ER -