Space-time discontinuous Galerkin finite element method for two-fluid flows

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

    Research output: Contribution to journalArticleAcademicpeer-review

    24 Citations (Scopus)

    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 disconti- nuities and a very local stencil, making it relatively easy to combine with local hp-refine- ment. 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 con- servative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.
    Original languageUndefined
    Pages (from-to)789-817
    Number of pages29
    JournalJournal of computational physics
    Volume230
    Issue number3
    DOIs
    Publication statusPublished - 2011

    Keywords

    • METIS-277506
    • Space–time discontinuous Galerkin
    • IR-75791
    • Level set
    • Front tracking
    • Two fluid flow
    • Cut-cell
    • EWI-19409

    Cite this

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    title = "Space-time discontinuous Galerkin finite element method for two-fluid flows",
    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 disconti- nuities and a very local stencil, making it relatively easy to combine with local hp-refine- ment. 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 con- servative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.",
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    Space-time discontinuous Galerkin finite element method for two-fluid flows. / Sollie, W.E.H.; Bokhove, Onno; van der Vegt, Jacobus J.W.

    In: Journal of computational physics, Vol. 230, No. 3, 2011, p. 789-817.

    Research output: Contribution to journalArticleAcademicpeer-review

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    AU - Sollie, W.E.H.

    AU - Bokhove, Onno

    AU - van der Vegt, Jacobus J.W.

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    PY - 2011

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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 disconti- nuities and a very local stencil, making it relatively easy to combine with local hp-refine- ment. 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 con- servative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.

    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 disconti- nuities and a very local stencil, making it relatively easy to combine with local hp-refine- ment. 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 con- servative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.

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