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New explicit algebraic stress model for three‐dimensional turbulent flows
Author(s) -
Vigdorovich Igor,
Foysi Holger
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610282
Subject(s) - reynolds stress , tensor (intrinsic definition) , mathematics , algebraic number , turbulence , cauchy stress tensor , algebraic equation , strain rate tensor , rotation (mathematics) , mathematical analysis , anisotropy , pure mathematics , physics , geometry , mechanics , nonlinear system , quantum mechanics
An explicit algebraic turbulent‐stress model is built in the framework of so‐called Rodi's weak‐equilibrium approximation, which, taking into account the known model representations for the pressure‐strain‐rate correlation and turbulence‐dissipation rate, reduces the differential equations for the Reynolds‐tensor components to a system of quasi‐linear algebraic equations for the five independent components of the anisotropy tensor B. We propose an original method for solving this quasi‐linear system. The tensor in question B is sought in the form of an expansion in a tensorial basis formed from the mean strain and rotation rate tensors which contains only five elements. The expansion's coefficients are functions of five simultaneous invariants of these tensors. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)