Space-time discontinuous Galerkin finite element method for shallow water flows

V.R. Ambati, Onno Bokhove

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    A space-time discontinuous Galerkin (DG) finite element method is presented for the shallow water equations over varying bottom topography. The method results in non-linear equations per element, which are solved locally by establishing the element communication with a numerical HLLC flux. To deal with spurious oscillations around discontinuities, we employ a dissipation operator only around discontinuities using Krivodonova's discontinuity detector. The numerical scheme is verified by comparing numerical and exact solutions, and validated against a laboratory experiment involving flow through a contraction. We conclude that the method is second order accurate in both space and time for linear polynomials.
    Original languageEnglish
    Article number10.1016/
    Pages (from-to)452-462
    Number of pages11
    JournalJournal of computational and applied mathematics
    Issue number2
    Publication statusPublished - Jul 2007


    • Shallow water equations
    • Numerical dissipation
    • Discontinuous Galerkin �nite element methods
    • Discontinuity detector
    • MSC-65M60


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