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

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Tomar, S.K. and Vegt, J.J.W. van der (2007) A Runge-Kutta discontinuous Galerkin method for linear free-surface gravity waves using high order velocity recovery. Computer Methods in Applied Mechanics and Engineering, 196 (13-16). pp. 1984-1996. ISSN 0045-7825

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Abstract: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.
Item Type:Article
Copyright:© 2007 Elsevier
Faculty:
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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Link to this item:http://purl.utwente.nl/publications/62140
Official URL:http://dx.doi.org/10.1016/j.cma.2006.11.007
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