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A stable algorithm for Reynolds stress turbulence modelling with applications to rectilinear and circular tidal flows
Author(s) -
Sajjadi S. G.,
Waywell M. N.
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19980215)26:3<251::aid-fld621>3.0.co;2-9
Subject(s) - turbulence , reynolds stress , reynolds number , reynolds stress equation model , computational fluid dynamics , mechanics , turbulence modeling , physics , k epsilon turbulence model , reynolds decomposition , reynolds averaged navier–stokes equations , k omega turbulence model , mathematics , computer science
This paper employs one‐point, linear eddy viscosity and differential second‐moment (DSM) turbulence closures to predict the turbulent characteristics of both rectilinear and circular tidal flows. The numerical scheme is based on a finite volume approach applied to a non‐staggered grid such that all flow variables are stored at one and the same set of nodes. Numerical stability is maintained through the implementation of apparent viscosities and source term linearization, which are essential if eddy viscosity terms are absent. A stable algorithm is devised for the Reynolds stresses which includes a non‐linear velocity smoothing in order to stabilise the numerical scheme during flow reversal and relaminarization. Favourable agreement with the experimental rectilinear tidal data of Schröder ( Tech. Rep. GK55 87/E/16 , GKSS‐Forshungszentrum Geesthacht, 1983) and McClean ( Turbulence and Sediment Transport Measurements in a North Sea Tidal Inlet (the Jade) , Springer, New York, 1987, p. 436) is reported. Numerical calculations of circular tidal flows are also presented which were motivated by the preliminary investigations of Davies and Jones ( Int. j. numer. meth. fluids , 12 , 17 (1991)) and Davies ( Continental Shelf. Res. , 11 , 1313 (1991)), who employed the one‐equation, k – l , eddy viscosity turbulence model to simulate rectilinear and circular tidal flows. © 1998 John Wiley & Sons, Ltd.