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The application of a variational finite element method to problems in fluid dynamics
Author(s) -
Usuki S.
Publication year - 1977
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.1620110313
Subject(s) - finite element method , mathematics , lift (data mining) , drag , reynolds number , computational fluid dynamics , boundary value problem , flow (mathematics) , mechanics , extended finite element method , mathematical analysis , geometry , structural engineering , physics , engineering , computer science , turbulence , data mining
The finite element method is applied to the analysis of a two‐dimensional steady flow around a box girder in uniform flow. The local potential principle for an incompressible viscous fluid flow is introduced as a basis for establishing finite element models and a determination is made as to whether or not approximate solutions obtained by the use of the principle give upper or lower bounds of the solution. The boundaries are set so as to be appropriately far from the girder and the velocities are specified at the upstream, upper boundary and the lower boundary and the total stresses are specified at the downstream boundary. The system of non‐linear equations is solved by the standard Newton–Raphson method. Integrating the pressures and viscous stresses acting on the surface of the girder, the coefficients of drag, lift and pitching moment are numerically obtained for some Reynolds numbers. The wind tunnel test has been the only means to determine these coefficients for a body with irregular shape. The finite element method presents a new powerful procedure to determine these coefficients.