Symmetric factorization of the conformation tensor in viscoelastic fluid\n models

2010/06/17 by Nusret Balci, Balci, Nusret, Becca Thomases +5 · 1 citation
Chemical Engineering · Engineering · #76A10 #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Vibration Analysis #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.1006.3488

openalex publication_date 2010/06/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

The positive definite symmetric polymer conformation tensor possesses a\nunique symmetric square root that satisfies a closed evolution equation in the\nOldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms\nof the velocity field and the symmetric square root of the conformation tensor,\nthese models' equations of motion formally constitute an evolution in a Hilbert\nspace with a total energy functional that defines a norm. Moreover, this\nformulation is easily implemented in direct numerical simulations resulting in\nsignificant practical advantages in terms of both accuracy and stability.\n

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• Linear, decoupled, positivity preserving, positive-definiteness preserving and energy stable schemes for the diffusive Oldroyd-B coupled with PNP model

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