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.
Keywords: Turbulence, Reynolds Stress Model, incomplete mixing, demixing, hyperbolic system
@article{M2AN_2021__55_5_1699_0,
author = {Blanc, Xavier and Colavolpe, Charles and Duclous, Roland and Griffond, J\'er\^ome and Soulard, Olivier},
title = {Numerical analysis of a {Reynolds} {Stress} {Model} for turbulent mixing: the one-dimensional case},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1699--1740},
year = {2021},
publisher = {EDP-Sciences},
volume = {55},
number = {5},
doi = {10.1051/m2an/2021035},
mrnumber = {4313372},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2021035/}
}
TY - JOUR AU - Blanc, Xavier AU - Colavolpe, Charles AU - Duclous, Roland AU - Griffond, Jérôme AU - Soulard, Olivier TI - Numerical analysis of a Reynolds Stress Model for turbulent mixing: the one-dimensional case JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2021 SP - 1699 EP - 1740 VL - 55 IS - 5 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2021035/ DO - 10.1051/m2an/2021035 LA - en ID - M2AN_2021__55_5_1699_0 ER -
%0 Journal Article %A Blanc, Xavier %A Colavolpe, Charles %A Duclous, Roland %A Griffond, Jérôme %A Soulard, Olivier %T Numerical analysis of a Reynolds Stress Model for turbulent mixing: the one-dimensional case %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2021 %P 1699-1740 %V 55 %N 5 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/m2an/2021035/ %R 10.1051/m2an/2021035 %G en %F M2AN_2021__55_5_1699_0
Blanc, Xavier; Colavolpe, Charles; Duclous, Roland; Griffond, Jérôme; Soulard, Olivier. Numerical analysis of a Reynolds Stress Model for turbulent mixing: the one-dimensional case. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 55 (2021) no. 5, pp. 1699-1740. doi: 10.1051/m2an/2021035
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