Fully-implicit log-conformation formulation of constitutive laws
| Autor: | Knechtges, Philipp, Behr, Marek, Elgeti, Stefanie |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of Non-Newtonian Fluid Mechanics 214 (2014) 78-87 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jnnfm.2014.09.018 |
| Popis: | Subject of this paper is the derivation of a new constitutive law in terms of the logarithm of the conformation tensor that can be used as a full substitute for the 2D governing equations of the Oldroyd-B, Giesekus and other models. One of the key features of these new equations is that - in contrast to the original log-conf equations given by Fattal and Kupferman (2004) - these constitutive equations combined with the Navier-Stokes equations constitute a self-contained, non-iterative system of partial differential equations. In addition to its potential as a fruitful source for understanding the mathematical subtleties of the models from a new perspective, this analytical description also allows us to fully utilize the Newton-Raphson algorithm in numerical simulations, which by design should lead to reduced computational effort. By means of the confined cylinder benchmark we will show that a finite element discretization of these new equations delivers results of comparable accuracy to known methods. Comment: 21 pages, 5 figures |
| Databáze: | arXiv |
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