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Advisor(s)
Abstract(s)
An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.
Description
Keywords
Boussinesq Equations Surface Water Waves Differential Operators Asymptotic Analysis Continuous Discontinuous FEMs Predictor-Corrector and Runge-Kutta Schemes
Citation
LOPES, N. D.; PEREIRA, P. J. S., TRABUCHO, L. – A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM. International Journal for Numerical Methods in Fluids. ISSN: 0271-2091. Vol. 69, nr. 7 (2012), pp. 1186-1218
Publisher
Wiley-blackwell