A Runge–Kutta discontinuous Galerkin method for linear free-surface gravity waves using high order velocity recovery
✍ Scribed by S.K. Tomar; J.J.W. van der Vegt
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 395 KB
- Volume
- 196
- Category
- Article
- ISSN
- 0045-7825
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✦ Synopsis
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.