Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows

    Research output: Contribution to journalArticleAcademicpeer-review

    33 Citations (Scopus)

    Abstract

    A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux calculations, which is generally the most expensive part of the algorithm. In addition a detailed discussion of the truncation error of the presented algorithm is given. The discretization of the Euler equations is combined with anisotropic grid refinement of an unstructured, hexahedron-type grid to achieve optimal resolution in areas with shocks, vortices, and other localized flow phenomena. The data structure and searching algorithms necessary for efficient calculation on highly irregular grids obtained with local grid refinement are discussed in detail. The method is demonstrated with calculations of the supersonic flow over a 10? ramp and the ONERA M6 wing under transsonic flow conditions
    Original languageUndefined
    Pages (from-to)46-77
    Number of pages32
    JournalJournal of computational physics
    Volume141
    Issue number1
    DOIs
    Publication statusPublished - 20 Mar 1998

    Keywords

    • Discontinuous Galerkin finite element methods
    • Gas dynamics
    • EWI-16349
    • Anisotropic grid adaptation
    • IR-73718
    • METIS-206721

    Cite this

    @article{a7bd3d21e35640b3a80dd4833473d2fa,
    title = "Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows",
    abstract = "A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux calculations, which is generally the most expensive part of the algorithm. In addition a detailed discussion of the truncation error of the presented algorithm is given. The discretization of the Euler equations is combined with anisotropic grid refinement of an unstructured, hexahedron-type grid to achieve optimal resolution in areas with shocks, vortices, and other localized flow phenomena. The data structure and searching algorithms necessary for efficient calculation on highly irregular grids obtained with local grid refinement are discussed in detail. The method is demonstrated with calculations of the supersonic flow over a 10? ramp and the ONERA M6 wing under transsonic flow conditions",
    keywords = "Discontinuous Galerkin finite element methods, Gas dynamics, EWI-16349, Anisotropic grid adaptation, IR-73718, METIS-206721",
    author = "{van der Vegt}, {Jacobus J.W.} and {van der Ven}, H.",
    year = "1998",
    month = "3",
    day = "20",
    doi = "10.1006/jcph.1998.5904",
    language = "Undefined",
    volume = "141",
    pages = "46--77",
    journal = "Journal of computational physics",
    issn = "0021-9991",
    publisher = "Academic Press Inc.",
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    }

    Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows. / van der Vegt, Jacobus J.W.; van der Ven, H.

    In: Journal of computational physics, Vol. 141, No. 1, 20.03.1998, p. 46-77.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows

    AU - van der Vegt, Jacobus J.W.

    AU - van der Ven, H.

    PY - 1998/3/20

    Y1 - 1998/3/20

    N2 - A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux calculations, which is generally the most expensive part of the algorithm. In addition a detailed discussion of the truncation error of the presented algorithm is given. The discretization of the Euler equations is combined with anisotropic grid refinement of an unstructured, hexahedron-type grid to achieve optimal resolution in areas with shocks, vortices, and other localized flow phenomena. The data structure and searching algorithms necessary for efficient calculation on highly irregular grids obtained with local grid refinement are discussed in detail. The method is demonstrated with calculations of the supersonic flow over a 10? ramp and the ONERA M6 wing under transsonic flow conditions

    AB - A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux calculations, which is generally the most expensive part of the algorithm. In addition a detailed discussion of the truncation error of the presented algorithm is given. The discretization of the Euler equations is combined with anisotropic grid refinement of an unstructured, hexahedron-type grid to achieve optimal resolution in areas with shocks, vortices, and other localized flow phenomena. The data structure and searching algorithms necessary for efficient calculation on highly irregular grids obtained with local grid refinement are discussed in detail. The method is demonstrated with calculations of the supersonic flow over a 10? ramp and the ONERA M6 wing under transsonic flow conditions

    KW - Discontinuous Galerkin finite element methods

    KW - Gas dynamics

    KW - EWI-16349

    KW - Anisotropic grid adaptation

    KW - IR-73718

    KW - METIS-206721

    U2 - 10.1006/jcph.1998.5904

    DO - 10.1006/jcph.1998.5904

    M3 - Article

    VL - 141

    SP - 46

    EP - 77

    JO - Journal of computational physics

    JF - Journal of computational physics

    SN - 0021-9991

    IS - 1

    ER -