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, Legendre projection, undular bore, wave breaking, boundary conditions, spectral accuracy.
AB - <p style="text-align: justify;">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.<br/>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.</p>