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Performance of very‐high‐order upwind schemes for DNS of compressible wall‐turbulence
Author(s) -
Gerolymos G. A.,
Sénéchal D.,
Vallet I.
Publication year - 2009
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/fld.2096
Subject(s) - upwind scheme , turbulence , direct numerical simulation , discretization , mathematics , compressible flow , compressibility , computational fluid dynamics , reynolds number , physics , mechanics , mathematical analysis
The purpose of the present paper is to evaluate very‐high‐order upwind schemes for the direct numerical simulation ( DNS ) of compressible wall‐turbulence. We study upwind‐biased ( UW ) and weighted essentially nonoscillatory ( WENO ) schemes of increasingly higher order‐of‐accuracy ( J. Comp. Phys. 2000; 160 :405–452), extended up to WENO 17 ( AIAA Paper 2009‐1612 , 2009). Analysis of the advection–diffusion equation, both as Δ x →0 (consistency), and for fixed finite cell‐Reynolds‐number Re Δ x (grid‐resolution), indicates that the very‐high‐order upwind schemes have satisfactory resolution in terms of points‐per‐wavelength ( PPW ). Computational results for compressible channel flow ( Re τ w∈[180, 230]; M̄ CL ∈[0.35, 1.5]) are examined to assess the influence of the spatial order of accuracy and the computational grid‐resolution on predicted turbulence statistics, by comparison with existing compressible and incompressible DNS databases. Despite the use of baseline O (Δ t 2 ) time‐integration and O (Δ x 2 ) discretization of the viscous terms, comparative studies of various orders‐of‐accuracy for the convective terms demonstrate that very‐high‐order upwind schemes can reproduce all the DNS details obtained by pseudospectral schemes, on computational grids of only slightly higher density. Copyright © 2009 John Wiley & Sons, Ltd.