Numerical analysis of a Reynolds Stress Model for turbulent mixing: the one-dimensional case

Xavier Blanc (1) , Charles Colavolpe (2) , Roland Duclous (2) , Jérôme Griffond (2) , Olivier Soulard (2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 DAM/DIF - DAM Île-de-France

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.

Mots clés: Turbulence; Reynolds Stress Model; incomplete mixing; demixing; hyperbolic system

Domaines: Mathématiques [math]

Xavier Blanc, Charles Colavolpe, Roland Duclous, Jérôme Griffond, Olivier Soulard. Numerical analysis of a Reynolds Stress Model for turbulent mixing: the one-dimensional case. ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55 (5), pp.1699-1740. ⟨10.1051/m2an/2021035⟩. ⟨hal-03348215⟩