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Finite element technique to solve the elastic strain for Leonov fluid flow
Author(s) -
Lin GwoGeng,
Tseng HsiengCheng,
Ju YiShi
Publication year - 1989
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.1650090902
Subject(s) - finite element method , mathematics , linearization , galerkin method , mathematical analysis , flow (mathematics) , nonlinear system , geometry , engineering , physics , structural engineering , quantum mechanics
Abstract The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi‐linear coupled first‐order hyperbolic differential equations together with a non‐linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed.