Internal wave generation in an improved two-dimensional Boussinesq model

Skotner, C.; Apelt, C. J.

doi:10.1016/s0029-8018(97)10023-3

Cited by 7 publications

(2 citation statements)

References 30 publications

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“…They showed that this approach could be used on fairly general geometries, within the restrictions of the Cartesian ÿnite di erence grid. Skotner and Apelt [15] have described an alternative internal wave generation method for a two-dimensional ÿnite di erence model of Nwogu's extended Boussinesq equations. The method is relatively complex, involving a modiÿed stencil in the wave generation region and explicit removal of the wave in the region behind the wave generator to prevent re ection.…”

Section: Non-re Ecting In Ow Boundary Conditionsmentioning

confidence: 99%

“…Nwogu applied a ÿnite di erence method to his extended Boussinesq system and has used it to model multi-directional wave interactions in the nearshore zone [4]. Wei and Kirby [13] described a di erent ÿnite di erence model of Nwogu's equations and this method has subsequently been used by Zang et al [14] and Skotner and Apelt [15] for prototype harbour geometries. Schr oter et al [16] applied a ÿnite di erence method, similar in principle to that of Abbot et al, to a di erent set of extended Boussinesq equations and this model was used to simulate the wave disturbances in a real harbour geometry, reported in a separate publication [3].…”

Section: Introductionmentioning

confidence: 99%

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A finite element method for the two‐dimensional extended Boussinesq equations

Walkley

Berzins

2002

Numerical Methods in Fluids

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SUMMARYA new numerical method for Nwogu's (ASCE Journal of Waterway, Port, Coastal and Ocean Engineering 1993; 119:618) two-dimensional extended Boussinesq equations is presented using a linear triangular ÿnite element spatial discretization coupled with a sophisticated adaptive time integration package. The authors have previously presented a ÿnite element method for the one-dimensional form of these equations (M. Walkley and M. Berzins (International Journal for Numerical Methods in Fluids 1999; 29 (2):143)) and this paper describes the extension of these ideas to the two-dimensional equations and the application of the method to complex geometries using unstructured triangular grids. Computational results are presented for two standard test problems and a realistic harbour model. Copyright ?

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Section: Non-re Ecting In Ow Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A finite element method for the two‐dimensional extended Boussinesq equations

Walkley

Berzins

2002

Numerical Methods in Fluids

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DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations

Engsig-Karup

Hesthaven

Bingham

et al. 2008

Coastal Engineering

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Abstract. We present a high-order nodal Discontinuous Galerkin Finite Element Method (DG-FEM) solution based on a set of highly accurate Boussinesq-type equations for solving general water-wave problems in complex geometries. A nodal DG-FEM is used for the spatial discretization to solve the Boussinesq equations in complex and curvilinear geometries which amends the application range of previous numerical models that have been based on structured Cartesian grids. The Boussinesq method provides the basis for the accurate description of fully nonlinear and dispersive water waves in both shallow and deep waters within the breaking limit. To demonstrate the current applicability of the model both linear and nonlinear test cases are considered where the water waves interact with bottom-mounted fully reflecting structures. It is established that by simple symmetry considerations combined with a mirror principle it is possible to impose weak slip boundary conditions for both structured and general curvilinear wall boundaries while maintaining the accuracy of the scheme. As is standard for current high-order Boussinesq-type models, arbitrary waves can be generated and absorbed in the interior of the computational domain using a flexible relaxation technique applied on the free surface variables.

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