Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations

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    15 Citations (Scopus)

    Abstract

    Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space–time (ST) computational methods in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

    Original languageEnglish
    Pages (from-to)1-18
    Number of pages18
    JournalComputational Mechanics
    DOIs
    Publication statusAccepted/In press - 2018 Apr 4

    Fingerprint

    Discontinuity
    Stabilization
    Incompressible flow
    Discretization
    Space-time
    Finite Element
    Compressible flow
    Advection
    Advection-diffusion Equation
    Computational methods
    Finite Element Discretization
    Incompressible Flow
    Navier-Stokes Equations
    Stabilized Methods
    Compressible Flow
    Computational Methods
    Spacing
    Target
    Dependent
    Term

    Keywords

    • Advection–diffusion equation
    • Discontinuity-capturing parameter
    • Finite element discretization
    • Incompressible-flow Navier–Stokes equations
    • Isogeometric discretization
    • Space–time computational methods
    • Stabilization parameter

    ASJC Scopus subject areas

    • Ocean Engineering
    • Mechanical Engineering
    • Computational Theory and Mathematics
    • Computational Mathematics
    • Applied Mathematics

    Cite this

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    title = "Stabilization and discontinuity-capturing parameters for space–time flow computations with finite element and isogeometric discretizations",
    abstract = "Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space–time (ST) computational methods in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.",
    keywords = "Advection–diffusion equation, Discontinuity-capturing parameter, Finite element discretization, Incompressible-flow Navier–Stokes equations, Isogeometric discretization, Space–time computational methods, Stabilization parameter",
    author = "Kenji Takizawa and Tezduyar, {Tayfun E.} and Yuto Otoguro",
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    AU - Otoguro, Yuto

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    AB - Stabilized methods, which have been very common in flow computations for many years, typically involve stabilization parameters, and discontinuity-capturing (DC) parameters if the method is supplemented with a DC term. Various well-performing stabilization and DC parameters have been introduced for stabilized space–time (ST) computational methods in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible and compressible flows. These parameters were all originally intended for finite element discretization but quite often used also for isogeometric discretization. The stabilization and DC parameters we present here for ST computations are in the context of the advection–diffusion equation and the Navier–Stokes equations of incompressible flows, target isogeometric discretization, and are also applicable to finite element discretization. The parameters are based on a direction-dependent element length expression. The expression is outcome of an easy to understand derivation. The key components of the derivation are mapping the direction vector from the physical ST element to the parent ST element, accounting for the discretization spacing along each of the parametric coordinates, and mapping what we have in the parent element back to the physical element. The test computations we present for pure-advection cases show that the parameters proposed result in good solution profiles.

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