Localization in Spatial-Spectral Method for Water Wave Applications

Ruddy Kurnia; Embrecht W.C. van Groesen

doi:10.1007/978-3-319-19800-2_27

Localization in Spatial-Spectral Method for Water Wave Applications

Ruddy Kurnia, Embrecht W.C. van Groesen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

4 Citations (Scopus)

Abstract

In the description of water waves, dispersion is one of the most important physical properties; it specifies the propagation speed as function of the wavelength. Accurate modelling of dispersion is essential to obtain high-quality wave propagation results. The relation between speed and wavelength is given by a non-algebraic relation; for finite element/difference methods this relation has to be approximated and leads to restrictions for waves that are propagated correctly. By using a spectral implementation dispersion can be dealt with exactly above flat bottom using a pseudo-differential operator so that all wavelengths can be propagated correctly. However, spectral methods are most commonly applied for problems in simple domains, while most water wave applications need complex geometries such as (harbour) walls, varying bathymetry, etc.; also breaking of waves requires a local procedure at the unknown position of breaking. This paper deals with such inhomogeneities in space; the models are formulated using Fourier integral operators and include non-trivial localization methods. The efficiency and accuracy of a so-called spatial-spectral implementation is illustrated here for a few test cases: wave run-up on a coast, wave reflection at a wall and the breaking of a focussing wave. These methods are included in HAWASSI software (Hamiltonian Wave-Ship-Structure Interaction) that has been developed over the past years.

Original language	Undefined
Title of host publication	Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
Editors	Robert M. Kirby, Martin Berzins, Jan S. Hesthaven
Place of Publication	Switzerland
Publisher	Springer
Pages	305-313
Number of pages	9
ISBN (Print)	978-3-319-19799-9
DOIs	https://doi.org/10.1007/978-3-319-19800-2_27
Publication status	Published - 2015
Event	International Conference on Spectral and High Order Methods, ICOSAHOM 2014 - Salt Lake City, UT, USA Duration: 23 Jun 2014 → 27 Jun 2014

Publication series

Name	Lecture Notes in Computational Science and Engineering
Publisher	Springer International Publishing
Volume	106
ISSN (Print)	1439-7358

Conference

Conference	International Conference on Spectral and High Order Methods, ICOSAHOM 2014
Period	23/06/14 → 27/06/14
Other	23-27 June 2014

Keywords

EWI-26457
IR-98256
METIS-315032

Access to Document

10.1007/978-3-319-19800-2_27

http://eprints.eemcs.utwente.nl/secure2/26457/01/2015_icosahom_RK_EvG_pusblished.pdf

Cite this

Kurnia, R., & van Groesen, E. W. C. (2015). Localization in Spatial-Spectral Method for Water Wave Applications. In R. M. Kirby, M. Berzins, & J. S. Hesthaven (Eds.), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 (pp. 305-313). (Lecture Notes in Computational Science and Engineering; Vol. 106). Springer. https://doi.org/10.1007/978-3-319-19800-2_27

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abstract = "In the description of water waves, dispersion is one of the most important physical properties; it specifies the propagation speed as function of the wavelength. Accurate modelling of dispersion is essential to obtain high-quality wave propagation results. The relation between speed and wavelength is given by a non-algebraic relation; for finite element/difference methods this relation has to be approximated and leads to restrictions for waves that are propagated correctly. By using a spectral implementation dispersion can be dealt with exactly above flat bottom using a pseudo-differential operator so that all wavelengths can be propagated correctly. However, spectral methods are most commonly applied for problems in simple domains, while most water wave applications need complex geometries such as (harbour) walls, varying bathymetry, etc.; also breaking of waves requires a local procedure at the unknown position of breaking. This paper deals with such inhomogeneities in space; the models are formulated using Fourier integral operators and include non-trivial localization methods. The efficiency and accuracy of a so-called spatial-spectral implementation is illustrated here for a few test cases: wave run-up on a coast, wave reflection at a wall and the breaking of a focussing wave. These methods are included in HAWASSI software (Hamiltonian Wave-Ship-Structure Interaction) that has been developed over the past years.",

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Kurnia, R & van Groesen, EWC 2015, Localization in Spatial-Spectral Method for Water Wave Applications. in RM Kirby, M Berzins & JS Hesthaven (eds), Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol. 106, Springer, Switzerland, pp. 305-313, International Conference on Spectral and High Order Methods, ICOSAHOM 2014, 23/06/14. https://doi.org/10.1007/978-3-319-19800-2_27

Localization in Spatial-Spectral Method for Water Wave Applications. / Kurnia, Ruddy; van Groesen, Embrecht W.C.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. ed. / Robert M. Kirby; Martin Berzins; Jan S. Hesthaven. Switzerland : Springer, 2015. p. 305-313 (Lecture Notes in Computational Science and Engineering; Vol. 106).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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N2 - In the description of water waves, dispersion is one of the most important physical properties; it specifies the propagation speed as function of the wavelength. Accurate modelling of dispersion is essential to obtain high-quality wave propagation results. The relation between speed and wavelength is given by a non-algebraic relation; for finite element/difference methods this relation has to be approximated and leads to restrictions for waves that are propagated correctly. By using a spectral implementation dispersion can be dealt with exactly above flat bottom using a pseudo-differential operator so that all wavelengths can be propagated correctly. However, spectral methods are most commonly applied for problems in simple domains, while most water wave applications need complex geometries such as (harbour) walls, varying bathymetry, etc.; also breaking of waves requires a local procedure at the unknown position of breaking. This paper deals with such inhomogeneities in space; the models are formulated using Fourier integral operators and include non-trivial localization methods. The efficiency and accuracy of a so-called spatial-spectral implementation is illustrated here for a few test cases: wave run-up on a coast, wave reflection at a wall and the breaking of a focussing wave. These methods are included in HAWASSI software (Hamiltonian Wave-Ship-Structure Interaction) that has been developed over the past years.

AB - In the description of water waves, dispersion is one of the most important physical properties; it specifies the propagation speed as function of the wavelength. Accurate modelling of dispersion is essential to obtain high-quality wave propagation results. The relation between speed and wavelength is given by a non-algebraic relation; for finite element/difference methods this relation has to be approximated and leads to restrictions for waves that are propagated correctly. By using a spectral implementation dispersion can be dealt with exactly above flat bottom using a pseudo-differential operator so that all wavelengths can be propagated correctly. However, spectral methods are most commonly applied for problems in simple domains, while most water wave applications need complex geometries such as (harbour) walls, varying bathymetry, etc.; also breaking of waves requires a local procedure at the unknown position of breaking. This paper deals with such inhomogeneities in space; the models are formulated using Fourier integral operators and include non-trivial localization methods. The efficiency and accuracy of a so-called spatial-spectral implementation is illustrated here for a few test cases: wave run-up on a coast, wave reflection at a wall and the breaking of a focussing wave. These methods are included in HAWASSI software (Hamiltonian Wave-Ship-Structure Interaction) that has been developed over the past years.

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SN - 978-3-319-19799-9

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BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014

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A2 - Berzins, Martin

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