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An efficient three‐dimensional semi‐implicit finite element scheme for simulation of free surface flows
Author(s) -
Li Y. S.,
Zhan J. M.
Publication year - 1993
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650160303
Subject(s) - discretization , mathematics , quadratic equation , finite element method , scheme (mathematics) , momentum (technical analysis) , test case , stability (learning theory) , free surface , mathematical analysis , geometry , computer science , mechanics , engineering , regression analysis , structural engineering , physics , machine learning , finance , economics , statistics
An efficient semi‐implicit finite element model is proposed for the simulation of three‐dimensional flows in stratified seas. The body of water is divided into a number of layers and the two horizontal momentum equations for each layer of water are first integrated vertically. Nine‐node Lagrangian quadratic isoparametric elements are employed for spatial discretization in the horizontal domain. The time derivatives are approximated using a second‐order‐accurate semi‐implicit time‐stepping scheme. The distinguishing feature of the proposed numerical scheme is that only nodal values on the same vertical line are coupled. Two test cases for which analytic solutions are available are employed to test the proposed scheme. The test results show that the scheme is efficient and stable. A numerical experiment is also included to compare the proposed scheme with a finite difference scheme.