Volume 55, Number 5, September-October 2021
|Page(s)||1699 - 1740|
|Published online||17 September 2021|
Numerical analysis of a Reynolds Stress Model for turbulent mixing: the one-dimensional case
Université de Paris, Sorbonne Université, CNRS, Laboratoire Jacques Louis Lions, F-75013 Paris, France
2 CEA, DAM, DIF, F-91297 Arpajon, France
* Corresponding authour: firstname.lastname@example.org
Accepted: 13 July 2021
A mixed hyperbolic-parabolic, non conservative, Reynolds Stress Model (RSM), is studied. It is based on an underlying set of Langevin equations, and allows to describe turbulent mixing, including transient demixing effects as well as incomplete mixing. Its mathematical structure is analysed, and specific regimes, related to acoustic-like, Riemann-type, or self-similar solutions, are identified. A second-order accurate numerical scheme is proposed in arbitrary curvilinear geometry. Its accuracy and convergence behaviour are tested by comparison with analytical solutions in the different regimes. The numerical scheme can be generalized to multi-dimensional configurations, with potentially cylindrical symmetry, on unstructured meshes.
Mathematics Subject Classification: 65M12 / 65M22 / 76F25
Key words: Turbulence / Reynolds Stress Model / incomplete mixing / demixing / hyperbolic system
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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