Volume 49, Issue 3
Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking

Magnar Bjørkavåg, Henrik Kalisch, Zahra Khorsand & Dimitrios Mitsotakis

J. Math. Study, 49 (2016), pp. 221-237.

Published online: 2016-09

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  • Abstract

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy. The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.

  • Keywords

Boussinesq system Legendre projection undular bore wave breaking boundary conditions spectral accuracy

  • AMS Subject Headings

35Q53, 65M70, 76B15, 76B25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

magnar.bjorkavag@math.uib.no (Magnar Bjørkavåg)

henrik.kalisch@uib.no (Henrik Kalisch)

zahra.khorsand@math.uib.no (Zahra Khorsand)

dimitrios.mitsotakis@vuw.ac.nz (Dimitrios Mitsotakis)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-221, author = {Bjørkavåg , Magnar and Kalisch , Henrik and Khorsand , Zahra and Mitsotakis , Dimitrios}, title = {Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking}, journal = {Journal of Mathematical Study}, year = {2016}, volume = {49}, number = {3}, pages = {221--237}, abstract = {

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy. The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n3.16.02}, url = {http://global-sci.org/intro/article_detail/jms/1000.html} }
TY - JOUR T1 - Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking AU - Bjørkavåg , Magnar AU - Kalisch , Henrik AU - Khorsand , Zahra AU - Mitsotakis , Dimitrios JO - Journal of Mathematical Study VL - 3 SP - 221 EP - 237 PY - 2016 DA - 2016/09 SN - 49 DO - http://doi.org/10.4208/jms.v49n3.16.02 UR - https://global-sci.org/intro/article_detail/jms/1000.html KW - Boussinesq system KW - Legendre projection KW - undular bore KW - wave breaking KW - boundary conditions KW - spectral accuracy AB -

In this paper, we propose a spectral projection of a regularized Boussinesq system for wave propagation on the surface of a fluid. The spectral method is based on the use of Legendre polynomials, and is able to handle time-dependent Dirichlet boundary conditions with spectral accuracy. The algorithm is applied to the study of undular bores, and in particular to the onset of wave breaking connected with undular bores. As proposed in [2], an improved version of the breaking criterion recently introduced in [5] is used. This tightened breaking criterion together with a careful choice of the relaxation parameter yields rather accurate predictions of the onset of breaking in the leading wave of an undular bore.

Magnar Bjørkavåg, Henrik Kalisch, Zahra Khorsand & Dimitrios Mitsotakis. (2020). Legendre Pseudospectral Approximation of Boussinesq Systems and Applications to Wave Breaking. Journal of Mathematical Study. 49 (3). 221-237. doi:10.4208/jms.v49n3.16.02
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