Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation

    Research output: Book/ReportReportProfessional

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    Abstract

    A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherNumerical Analysis and Computational Mechanics (NACM)
    Number of pages42
    ISBN (Print)0169-2690
    Publication statusPublished - 2001

    Publication series

    NameMemorandum
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1599
    ISSN (Print)0169-2690

    Keywords

    • EWI-3419
    • MSC-76N15
    • MSC-65P25
    • multigrid technique
    • pseudo-time integration method
    • Arbitrary Lagrangian Eulerian (ALE)technique
    • Dynamic grid motion
    • Gas dynamics
    • Discontinuous Galerkin finite element method
    • Local mesh refinement
    • IR-65786
    • METIS-201429

    Cite this

    van der Vegt, J. J. W., & van der Ven, H. (2001). Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation. (Memorandum; No. 1599). Enschede: Numerical Analysis and Computational Mechanics (NACM).
    van der Vegt, Jacobus J.W. ; van der Ven, H. / Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation. Enschede : Numerical Analysis and Computational Mechanics (NACM), 2001. 42 p. (Memorandum; 1599).
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    title = "Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation",
    abstract = "A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.",
    keywords = "EWI-3419, MSC-76N15, MSC-65P25, multigrid technique, pseudo-time integration method, Arbitrary Lagrangian Eulerian (ALE)technique, Dynamic grid motion, Gas dynamics, Discontinuous Galerkin finite element method, Local mesh refinement, IR-65786, METIS-201429",
    author = "{van der Vegt}, {Jacobus J.W.} and {van der Ven}, H.",
    note = "Imported from MEMORANDA",
    year = "2001",
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    isbn = "0169-2690",
    series = "Memorandum",
    publisher = "Numerical Analysis and Computational Mechanics (NACM)",
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    van der Vegt, JJW & van der Ven, H 2001, Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation. Memorandum, no. 1599, Numerical Analysis and Computational Mechanics (NACM), Enschede.

    Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation. / van der Vegt, Jacobus J.W.; van der Ven, H.

    Enschede : Numerical Analysis and Computational Mechanics (NACM), 2001. 42 p. (Memorandum; No. 1599).

    Research output: Book/ReportReportProfessional

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    AU - van der Vegt, Jacobus J.W.

    AU - van der Ven, H.

    N1 - Imported from MEMORANDA

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    Y1 - 2001

    N2 - A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.

    AB - A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method.

    KW - EWI-3419

    KW - MSC-76N15

    KW - MSC-65P25

    KW - multigrid technique

    KW - pseudo-time integration method

    KW - Arbitrary Lagrangian Eulerian (ALE)technique

    KW - Dynamic grid motion

    KW - Gas dynamics

    KW - Discontinuous Galerkin finite element method

    KW - Local mesh refinement

    KW - IR-65786

    KW - METIS-201429

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    SN - 0169-2690

    T3 - Memorandum

    BT - Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation

    PB - Numerical Analysis and Computational Mechanics (NACM)

    CY - Enschede

    ER -

    van der Vegt JJW, van der Ven H. Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation. Enschede: Numerical Analysis and Computational Mechanics (NACM), 2001. 42 p. (Memorandum; 1599).