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ON THE CONSTRUCTION OF A THIRD‐ORDER ACCURATE MONOTONE CONVECTION SCHEME WITH APPLICATION TO TURBULENT FLOWS IN GENERAL DOMAINS
Author(s) -
ZIJLEMA M.
Publication year - 1996
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(19960415)22:7<619::aid-fld370>3.0.co;2-l
Subject(s) - upwind scheme , turbulence , monotone polygon , mathematics , finite volume method , flux limiter , convection–diffusion equation , monotonic function , k epsilon turbulence model , variable (mathematics) , mathematical analysis , mathematical optimization , geometry , mechanics , physics , discretization
A formally third‐order accurate finite volume upwind scheme which preserves monotonicity is constructed. It is based on a third‐order polynomial interpolant in Leonard's normalized variable space. A flux limiter is derived using the fact that there exists a one‐to‐one map between normalized variable and TVD spaces. This scheme, which is relatively simple and quite compact, is implemented in a staggered general co‐ordinates finite volume algorithm including the standard k –ϵ model and applied to the turbulence transport equations. A number of test problems demonstrate the utility of the proposed scheme. It is shown that in cases where turbulence convection is dominant, the application of a higher‐order monotone convection scheme to the turbulence equations leads to results which are more accurate than those obtained using the first‐order upwind scheme.