dc.contributor.author | Maxwell, Peter | |
dc.contributor.author | Ellingsen, Simen Andreas Ådnøy | |
dc.date.accessioned | 2021-04-09T08:24:34Z | |
dc.date.available | 2021-04-09T08:24:34Z | |
dc.date.created | 2020-08-03T15:39:57Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Water Waves. 2020, 2 381-414. | en_US |
dc.identifier.issn | 2523-367X | |
dc.identifier.uri | https://hdl.handle.net/11250/2737065 | |
dc.description.abstract | The path-following scheme in Loisel and Maxwell (SIAM J Matrix Anal Appl 39(4):1726–1749, 2018) is adapted to efficiently calculate the dispersion relation curve for linear surface waves on an arbitrary vertical shear current. This is equivalent to solving the Rayleigh stability equation with linearized free-surface boundary condition for each sought point on the curve. Taking advantage of the analyticity of the dispersion relation, a path-following or continuation approach is adopted. The problem is discretized using a collocation scheme, parametrized along either a radial or angular path in the wave vector plane, and differentiated to yield a system of ODEs. After an initial eigenproblem solve using QZ decomposition, numerical integration proceeds along the curve using linear solves as the Runge–Kutta F(⋅) function; thus, many QZ decompositions on a size 2N companion matrix are exchanged for one QZ decomposition and a small number of linear solves on a size N matrix. A piecewise interpolant provides dense output. The integration represents a nominal setup cost whereafter very many points can be computed at negligible cost whilst preserving high accuracy. Furthermore, a two-dimensional interpolant suitable for scattered data query points in the wave vector plane is described. Finally, a comparison is made with existing numerical methods for this problem, revealing that the path-following scheme is the most competitive algorithm for this problem whenever calculating more than circa 1,000 data points or relative normwise accuracy better than 10−4 is sought. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.rights | Navngivelse 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/deed.no | * |
dc.title | Path-Following Methods for Calculating Linear Surface Wave Dispersion Relations on Vertical Shear Flows | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | publishedVersion | en_US |
dc.source.pagenumber | 381-414 | en_US |
dc.source.volume | 2 | en_US |
dc.source.journal | Water Waves | en_US |
dc.identifier.doi | 10.1007/s42286-020-00030-0 | |
dc.identifier.cristin | 1821404 | |
cristin.ispublished | true | |
cristin.fulltext | preprint | |
cristin.fulltext | preprint | |
cristin.qualitycode | 1 | |