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A spectral/ hp least‐squares finite element analysis of the Carreau–Yasuda fluids
Author(s) -
Kim Namhee,
Reddy J. N.
Publication year - 2016
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.4230
Subject(s) - finite element method , mathematics , spectral element method , compressibility , least squares function approximation , mathematical analysis , mixed finite element method , incompressible flow , flow (mathematics) , constitutive equation , mechanics , geometry , physics , thermodynamics , statistics , estimator
Summary A least‐squares finite element model with spectral/ hp approximations was developed for steady, two‐dimensional flows of non‐Newtonian fluids obeying the Carreau–Yasuda constitutive model. The finite element model consists of velocity, pressure, and stress fields as independent variables (hence, called a mixed model). Least‐squares models offer an alternative variational setting to the conventional weak‐form Galerkin models for the Navier–Stokes equations, and no compatibility conditions on the approximation spaces used for the velocity, pressure, and stress fields are necessary when the polynomial order ( p ) used is sufficiently high (say, p > 3, as determined numerically). Also, the use of the spectral/ hp elements in conjunction with the least‐squares formulation with high p alleviates various forms of locking, which often appear in low‐order least‐squares finite element models for incompressible viscous fluids, and accurate results can be obtained with exponential convergence. To verify and validate, benchmark problems of Kovasznay flow, backward‐facing step flow, and lid‐driven square cavity flow are used. Then the effect of different parameters of the Carreau–Yasuda constitutive model on the flow characteristics is studied parametrically. Copyright © 2016 John Wiley & Sons, Ltd.