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Transient finite element method for calculating steady state three‐dimensional free surfaces
Author(s) -
Wambersie O.,
Crochet M. J.
Publication year - 1992
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.1650140307
Subject(s) - free surface , decoupling (probability) , conjugate gradient method , solver , finite element method , kinematics , inertia , mathematics , mechanics , transient (computer programming) , mathematical analysis , geometry , surface (topology) , computational fluid dynamics , multiphysics , physics , algorithm , classical mechanics , mathematical optimization , structural engineering , computer science , engineering , control engineering , operating system
Abstract In order to reduce the cost of large three‐dimensional calculations of steady state free surfaces, we have combined a time‐dependent approach, a decoupling algorithm and a conjugate gradient solver along the lines introduced earlier by Gresho and Chan. The free surface is calculated separately by applying the kinematic condition to a number of faces defined on the undeformed surface. For the pseudo‐time‐marching technique we show that it is economical to adopt different time steps for the free surface calculation and the other fields. The accuracy of the method is tested on the well‐known circular die problem; the method is then used to reveal the effects of inertia and shear thinning on square and rectangular dies.