Symmetric factorization of the conformation tensor in viscoelastic fluid models

The positive-definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformati...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2011-06, Vol.166 (11), p.546-553
Main Authors: Balci, Nusret, Thomases, Becca, Renardy, Michael, Doering, Charles R.
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Direct numerical simulations
Equations of motion
Evolution
Exact sciences and technology
FENE-P
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Non-newtonian fluid flows
Norms
Numerical methods
Oldroyd-B
Physics
Roots
Tensors
Viscoelastic fluid models
Viscoelastic fluids
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Summary:The positive-definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models’ equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability.
ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2011.02.008