Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm

W.E.H. Sollie, Onno Bokhove, Jacobus J.W. van der Vegt

    Research output: Book/ReportReportProfessional

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    Abstract

    A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages53
    Publication statusPublished - Nov 2009

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1909
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • Level set
    • Front tracking
    • Cut-cell
    • EWI-16496
    • Two fluid flow
    • Space-time discontinuous Galerkin
    • IR-68559
    • METIS-264145

    Cite this

    Sollie, W. E. H., Bokhove, O., & van der Vegt, J. J. W. (2009). Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm. (Memorandum / Department of Applied Mathematics; No. 1909). Enschede: University of Twente, Department of Applied Mathematics.
    Sollie, W.E.H. ; Bokhove, Onno ; van der Vegt, Jacobus J.W. / Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm. Enschede : University of Twente, Department of Applied Mathematics, 2009. 53 p. (Memorandum / Department of Applied Mathematics; 1909).
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    abstract = "A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative.",
    keywords = "Level set, Front tracking, Cut-cell, EWI-16496, Two fluid flow, Space-time discontinuous Galerkin, IR-68559, METIS-264145",
    author = "W.E.H. Sollie and Onno Bokhove and {van der Vegt}, {Jacobus J.W.}",
    year = "2009",
    month = "11",
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    series = "Memorandum / Department of Applied Mathematics",
    publisher = "University of Twente, Department of Applied Mathematics",
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    Sollie, WEH, Bokhove, O & van der Vegt, JJW 2009, Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm. Memorandum / Department of Applied Mathematics, no. 1909, University of Twente, Department of Applied Mathematics, Enschede.

    Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm. / Sollie, W.E.H.; Bokhove, Onno; van der Vegt, Jacobus J.W.

    Enschede : University of Twente, Department of Applied Mathematics, 2009. 53 p. (Memorandum / Department of Applied Mathematics; No. 1909).

    Research output: Book/ReportReportProfessional

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    N2 - A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative.

    AB - A novel numerical method for two fluid flow computations is presented, which combines the space-time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space-time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local {\it hp}-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative.

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    KW - METIS-264145

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    Sollie WEH, Bokhove O, van der Vegt JJW. Two fluid space-time discontinuous Galerkin finite element method. Part I: Numerical algorithm. Enschede: University of Twente, Department of Applied Mathematics, 2009. 53 p. (Memorandum / Department of Applied Mathematics; 1909).