Improved boussinesq equations for surface water waves

Nuno D. Lopes; Pedro J. S. Pereira; Luís Trabucho

doi:10.1007/978-3-642-23099-8_25

Improved boussinesq equations for surface water waves

Nuno D. Lopes, Pedro J. S. Pereira, Luís Trabucho

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

2 Citations (Scopus)

Abstract

The main motivation of this work is the implementation of a general finite element solver for some of the improved Boussinesq models. Here, we use an extension of the model proposed by Zhao et al. (2004) to investigate the behavior of surface water waves. The equations in this model do not contain spatial derivatives with an order higher than two. Some effects like energy dissipation and wave generation by natural phenomena or external physical mechanisms are also included. As a consequence, some modified dispersion relations are derived for this extended model. A matrixbased linear stability analysis of the proposed model is presented. It is shown that this model is robust with respect to instabilities related to steep bottom gradients.

Original language	English
Title of host publication	Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book
Editors	A. Logg, K. A. Mardal, G. Wells
Place of Publication	Berlin, Heidelberg
Publisher	Springer
Pages	471-504
Number of pages	34
ISBN (Electronic)	978-3-642-23099-8
ISBN (Print)	978-3-642-23098-1
DOIs	https://doi.org/10.1007/978-3-642-23099-8_25
Publication status	Published - 2012

Publication series

Name	Lecture Notes in Computational Science and Engineering
Publisher	Springer
Volume	84
ISSN (Print)	1439-7358
ISSN (Electronic)	2197-7100

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10.1007/978-3-642-23099-8_25

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Lopes, N. D., Pereira, P. J. S., & Trabucho, L. (2012). Improved boussinesq equations for surface water waves. In A. Logg, K. A. Mardal, & G. Wells (Eds.), Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (pp. 471-504). (Lecture Notes in Computational Science and Engineering; Vol. 84). Springer. https://doi.org/10.1007/978-3-642-23099-8_25

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title = "Improved boussinesq equations for surface water waves",

abstract = "The main motivation of this work is the implementation of a general finite element solver for some of the improved Boussinesq models. Here, we use an extension of the model proposed by Zhao et al. (2004) to investigate the behavior of surface water waves. The equations in this model do not contain spatial derivatives with an order higher than two. Some effects like energy dissipation and wave generation by natural phenomena or external physical mechanisms are also included. As a consequence, some modified dispersion relations are derived for this extended model. A matrixbased linear stability analysis of the proposed model is presented. It is shown that this model is robust with respect to instabilities related to steep bottom gradients.",

author = "Lopes, \{Nuno D.\} and Pereira, \{Pedro J. S.\} and Lu{\'i}s Trabucho",

note = "Funding Information: This work is partially supported by Funda??o para a Ci?ncia e Tecnologia, Financiamento Base 2008-ISFL-1-209. ",

year = "2012",

doi = "10.1007/978-3-642-23099-8\_25",

language = "English",

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series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer",

pages = "471--504",

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booktitle = "Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book",

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Lopes, ND , Pereira, PJS & Trabucho, L 2012, Improved boussinesq equations for surface water waves. in A Logg, KA Mardal & G Wells (eds), Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. Lecture Notes in Computational Science and Engineering, vol. 84, Springer, Berlin, Heidelberg, pp. 471-504. https://doi.org/10.1007/978-3-642-23099-8_25

Improved boussinesq equations for surface water waves. / Lopes, Nuno D.; Pereira, Pedro J. S.; Trabucho, Luís.
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. ed. / A. Logg; K. A. Mardal; G. Wells . Berlin, Heidelberg: Springer, 2012. p. 471-504 (Lecture Notes in Computational Science and Engineering; Vol. 84).

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

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T1 - Improved boussinesq equations for surface water waves

AU - Lopes, Nuno D.

AU - Pereira, Pedro J. S.

AU - Trabucho, Luís

N1 - Funding Information: This work is partially supported by Funda??o para a Ci?ncia e Tecnologia, Financiamento Base 2008-ISFL-1-209.

PY - 2012

Y1 - 2012

N2 - The main motivation of this work is the implementation of a general finite element solver for some of the improved Boussinesq models. Here, we use an extension of the model proposed by Zhao et al. (2004) to investigate the behavior of surface water waves. The equations in this model do not contain spatial derivatives with an order higher than two. Some effects like energy dissipation and wave generation by natural phenomena or external physical mechanisms are also included. As a consequence, some modified dispersion relations are derived for this extended model. A matrixbased linear stability analysis of the proposed model is presented. It is shown that this model is robust with respect to instabilities related to steep bottom gradients.

AB - The main motivation of this work is the implementation of a general finite element solver for some of the improved Boussinesq models. Here, we use an extension of the model proposed by Zhao et al. (2004) to investigate the behavior of surface water waves. The equations in this model do not contain spatial derivatives with an order higher than two. Some effects like energy dissipation and wave generation by natural phenomena or external physical mechanisms are also included. As a consequence, some modified dispersion relations are derived for this extended model. A matrixbased linear stability analysis of the proposed model is presented. It is shown that this model is robust with respect to instabilities related to steep bottom gradients.

UR - https://www.scopus.com/pages/publications/84943366463

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SN - 978-3-642-23098-1

T3 - Lecture Notes in Computational Science and Engineering

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EP - 504

BT - Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book

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A2 - Mardal, K. A.

A2 - Wells , G.

PB - Springer

CY - Berlin, Heidelberg

ER -

Improved boussinesq equations for surface water waves

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