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

Publication: Research - peer-reviewJournal article – Annual report year: 2008

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DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations. / Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.; Warburton, T.

In: Coastal Engineering, Vol. 55, No. 3, 03.2008, p. 197-208.

Publication: Research - peer-reviewJournal article – Annual report year: 2008

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Author

Engsig-Karup, Allan Peter; Hesthaven, Jan; Bingham, Harry B.; Warburton, T. / DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations.

In: Coastal Engineering, Vol. 55, No. 3, 03.2008, p. 197-208.

Publication: Research - peer-reviewJournal article – Annual report year: 2008

Bibtex

@article{c4a1864947414809be12faac39c23cfc,
title = "DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations",
keywords = "Grid adaption, nonlinear and dispersive water waves, discontinuous Galerkin finite element method, high-order Boussinesq-type equations, unstructured and curvilinear grids, Wave-structure interaction",
publisher = "Elsevier BV",
author = "Engsig-Karup, {Allan Peter} and Jan Hesthaven and Bingham, {Harry B.} and T. Warburton",
year = "2008",
doi = "10.1016/j.coastaleng.2007.09.005",
volume = "55",
number = "3",
pages = "197--208",
journal = "Coastal Engineering",
issn = "0378-3839",

}

RIS

TY - JOUR

T1 - DG-FEM solution for nonlinear wave-structure interaction using Boussinesq-type equations

A1 - Engsig-Karup,Allan Peter

A1 - Hesthaven,Jan

A1 - Bingham,Harry B.

A1 - Warburton,T.

AU - Engsig-Karup,Allan Peter

AU - Hesthaven,Jan

AU - Bingham,Harry B.

AU - Warburton,T.

PB - Elsevier BV

PY - 2008/3

Y1 - 2008/3

N2 - 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 mildly nonlinear test cases are considered in two horizontal dimensions 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.

AB - 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 mildly nonlinear test cases are considered in two horizontal dimensions 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.

KW - Grid adaption

KW - nonlinear and dispersive water waves

KW - discontinuous Galerkin finite element method

KW - high-order Boussinesq-type equations

KW - unstructured and curvilinear grids

KW - Wave-structure interaction

U2 - 10.1016/j.coastaleng.2007.09.005

DO - 10.1016/j.coastaleng.2007.09.005

JO - Coastal Engineering

JF - Coastal Engineering

SN - 0378-3839

IS - 3

VL - 55

SP - 197

EP - 208

ER -