Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension

Onno Bokhove

    Research output: Book/ReportReportOther research output

    9 Downloads (Pure)

    Abstract

    Free boundaries in shallow-water equations demarcate the time-dependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous finite element discretization of the one-dimensional or symmetric shallow-water equations is presented. The algorithm uses fixed Eulerian flooded elements and one mixed Eulerian-Lagrangian element at each free boundary. The positivity of the mean water depth is ensured via a time step restriction based on analysis of a maximum principle for the discretized continuity equation while using an HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudo density (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. The approach is hypothesized to extend to finite-volume discretizations with similar mean level and slope reconstruction.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2003

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1683
    ISSN (Print)0169-2690

    Keywords

    • MSC-65M60
    • IR-65868
    • EWI-3503
    • MSC-76M10

    Cite this

    Bokhove, O. (2003). Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension. Enschede: University of Twente, Department of Applied Mathematics.
    Bokhove, Onno. / Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension. Enschede : University of Twente, Department of Applied Mathematics, 2003.
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    title = "Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension",
    abstract = "Free boundaries in shallow-water equations demarcate the time-dependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous finite element discretization of the one-dimensional or symmetric shallow-water equations is presented. The algorithm uses fixed Eulerian flooded elements and one mixed Eulerian-Lagrangian element at each free boundary. The positivity of the mean water depth is ensured via a time step restriction based on analysis of a maximum principle for the discretized continuity equation while using an HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudo density (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. The approach is hypothesized to extend to finite-volume discretizations with similar mean level and slope reconstruction.",
    keywords = "MSC-65M60, IR-65868, EWI-3503, MSC-76M10",
    author = "Onno Bokhove",
    note = "Imported from MEMORANDA",
    year = "2003",
    language = "Undefined",
    publisher = "University of Twente, Department of Applied Mathematics",
    number = "1683",

    }

    Bokhove, O 2003, Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension. University of Twente, Department of Applied Mathematics, Enschede.

    Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension. / Bokhove, Onno.

    Enschede : University of Twente, Department of Applied Mathematics, 2003.

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension

    AU - Bokhove, Onno

    N1 - Imported from MEMORANDA

    PY - 2003

    Y1 - 2003

    N2 - Free boundaries in shallow-water equations demarcate the time-dependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous finite element discretization of the one-dimensional or symmetric shallow-water equations is presented. The algorithm uses fixed Eulerian flooded elements and one mixed Eulerian-Lagrangian element at each free boundary. The positivity of the mean water depth is ensured via a time step restriction based on analysis of a maximum principle for the discretized continuity equation while using an HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudo density (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. The approach is hypothesized to extend to finite-volume discretizations with similar mean level and slope reconstruction.

    AB - Free boundaries in shallow-water equations demarcate the time-dependent water line between ``flooded'' and ``dry'' topography. A novel numerical algorithm to treat flooding and drying in a formally second-order explicit space discontinuous finite element discretization of the one-dimensional or symmetric shallow-water equations is presented. The algorithm uses fixed Eulerian flooded elements and one mixed Eulerian-Lagrangian element at each free boundary. The positivity of the mean water depth is ensured via a time step restriction based on analysis of a maximum principle for the discretized continuity equation while using an HLLC flux. The algorithm and its implementation are tested in comparison with a large and relevant suite of known exact solutions. The essence of the flooding and drying algorithm pivots around the analysis of a continuity equation with a fluid velocity and a pseudo density (in the shallow water case the depth). It therefore also applies, for example, to space discontinuous finite-element discretizations of the compressible Euler equations in which vacuum regions emerge, in analogy of the above dry regions. The approach is hypothesized to extend to finite-volume discretizations with similar mean level and slope reconstruction.

    KW - MSC-65M60

    KW - IR-65868

    KW - EWI-3503

    KW - MSC-76M10

    M3 - Report

    BT - Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Bokhove O. Flooding and drying in finite-element discretizations of shallow-water equations. Part 1: One dimension. Enschede: University of Twente, Department of Applied Mathematics, 2003.