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Gravitational mode calculation of basins discretized by orthogonal curvilinear grids

TitleGravitational mode calculation of basins discretized by orthogonal curvilinear grids
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication2003
AuthorsBeltrami, G.M., Bargagli A., and Briganti R.
JournalOcean Engineering
Volume30
Pagination833-853
ISSN00298018
Keywordsboundary condition, Boundary conditions, Curvilinear grids, eigenvalue, Eigenvalues and eigenfunctions, Gravitational effects, Numerical methods, numerical model, Ocean engineering, shallow-water equation, Vectors
Abstract

This paper presents a simple and straightforward method for carrying out the direct numerical solution of the eigenvalue problem associated to the homogeneous linear shallow-water equations expressed using orthogonal curvilinear coordinates, when 'adiabatic' boundary conditions apply. These equations, together with the boundary conditions, define a self-adjoint problem in the continuum. The method presented here, which is thought for calculating the 2-D theoretical gravity modes of both natural and artificial basins, relies on a change of basis of the dependent variable vector. This preliminary transformation makes it, in fact, possible to formulate two different numerical approaches which guarantee the self-adjoint property of the discrete form of the system consisting of the governing equations and the boundary conditions. The method is tested using a square and a fully circular domain, both of which allow comparisons with well-known analytical and numerical solutions. Discretizing the physical domain of a fully circular basin by a cylindrical coordinate grid makes it possible to show the actual efficiency of the method in calculating the theoretical gravity modes of basins discretized by a boundary-following coordinate grid which allows laterally variable resolution. © 2002 Elsevier Science Ltd. All rights reserved.

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URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-0037408723&doi=10.1016%2fS0029-8018%2802%2900079-3&partnerID=40&md5=18dbd2ab866791d527982eecfdbfda42
DOI10.1016/S0029-8018(02)00079-3
Citation KeyBeltrami2003833