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A new general‐purpose least‐squares finite element model for steady incompressible low‐viscosity laminar flow using isoparametric C 1 ‐continuous Hermite elements
Author(s) -
Nassehi V.,
Petera J.
Publication year - 1994
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.1650180205
Subject(s) - laminar flow , mathematics , finite element method , flow (mathematics) , incompressible flow , least squares function approximation , mathematical analysis , geometry , mechanics , physics , estimator , thermodynamics , statistics
Abstract This paper deals with a critical evaluation of various finite element models for low‐viscosity laminar incompressible flow in geometrically complex domains. These models use Galerkin weighted residuals UVP, continuous penalty, discrete penalty and least‐squares procedures. The model evaluations are based on the use of appropriate tensor product Lagrange and simplex quadratic triangular elements and a newly developed isoparametric Hermite element. All of the described models produce very accurate results for horizontal flows. In vertical flow domains, however, two different cases can be recognized. Downward flows, i.e. when the gravitational force is in the direction of the flow, usually do not present any special problem. In contrast, laminar flow of low‐viscosity Newtonian fluids where the gravitational force is acting in the direction opposite to the flow presents a difficult case. We show that only by using the least‐squares method in conjunction with C 1 ‐continuous Hermite elements can this type of laminar flow be modelled accurately. The problem of smooth isoparametric mapping of C 1 Hermite elements, which is necessary in dealing with geometrically complicated domains, is tackled by means of an auxiliary optimization procedure. We conclude that the least‐squares method in combination with isoparmetric Hermite elements offers a new general‐purpose modelling technique which can accurately simulate all types of low‐viscosity incompressible laminar flow in complex domains.