Abstract
| 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 | |
| Publication status | Published - 2015 |
Publication series
| Name | Lecture Notes in Computational Science and Engineering |
|---|---|
| Publisher | Springer International Publishing |
| Volume | 106 |
| ISSN (Print) | 1439-7358 |
Keywords
- EWI-26457
- IR-98256
- METIS-315032
Cite this
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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
TY - GEN
T1 - Localization in Spatial-Spectral Method for Water Wave Applications
AU - Kurnia, Ruddy
AU - van Groesen, Embrecht W.C.
N1 - 10.1007/978-3-319-19800-2_27
PY - 2015
Y1 - 2015
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.
KW - EWI-26457
KW - IR-98256
KW - METIS-315032
U2 - 10.1007/978-3-319-19800-2_27
DO - 10.1007/978-3-319-19800-2_27
M3 - Conference contribution
SN - 978-3-319-19799-9
T3 - Lecture Notes in Computational Science and Engineering
SP - 305
EP - 313
BT - Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
A2 - Kirby, Robert M.
A2 - Berzins, Martin
A2 - Hesthaven, Jan S.
PB - Springer
CY - Switzerland
ER -