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An improved explicit finite element method for tidal flow
Author(s) -
Kikukawa H.,
Ichikawa H.
Publication year - 1984
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620200809
Subject(s) - mass matrix , finite element method , weighting , conservation of mass , residual , mathematics , mathematical analysis , matrix (chemical analysis) , function (biology) , diagonal , mathematical optimization , geometry , mechanics , physics , engineering , structural engineering , algorithm , chemistry , acoustics , neutrino , biology , chromatography , evolutionary biology , nuclear physics
A weighting function by which the mass matrix is made to be diagonal is deduced on the two‐dimensional simplex element. Adopting the weighted residual method with the deduced weighting function for spatial domain and the two‐step Lax–Wendroff method for time differentiation, the two‐dimensinoal tidal flow in a model basin is calculated by means of the explicit finite element method. The water mass transport integrated over one tidal period at some cross‐sections of the basin is also estimated, in order to verify the water mass conservation. It is found that the water mass is nearly conserved in the present method, although the usual lumped mass matrix technique fails to conserve. The present explicit finite element method with the conservative form of governing equations is also investigated and the water mass conservation is found to be a little more improved in this case than in the case of non‐conservative forms. Application to a real bay indicates that the method with the conservative form of equations could be used for the estimation of tidal residual flow.