A Runge-Kutta discontinuous Galerkin method for linear free-surface gravity waves using high order velocity recovery

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    We present a higher order accurate discontinuous Galerkin finite element method for the simulation of linear free-surface gravity waves. The method uses the classical Runge–Kutta method for the time-discretization of the free-surface equations and the discontinuous Galerkin method for the space-discretization. In order to circumvent numerical instabilities arising from an asymmetric mesh a stabilization term is added to the free-surface equations. In combination with a higher order velocity recovery technique this stabilizes the numerical discretization with minimal effect on the accuracy of the wave computations. A stability analysis of the semi and fully-discrete scheme is presented, which suggests that for a suitable choice of the stabilization constant a relatively large time step can be chosen for accurate simulations over a long period of time. Numerical examples of a number of problems are also presented.
    Original languageUndefined
    Article number10.1016/j.cma.2006.11.007
    Pages (from-to)1984-1996
    Number of pages13
    JournalComputer methods in applied mechanics and engineering
    Issue number7/13-16
    Publication statusPublished - 1 Mar 2007


    • EWI-11811
    • IR-62140
    • METIS-245973

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