Performance of very-high-order upwind schemes for DNS of compressible wall-turbulence
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 (WEND) schemes of increasingly higher order-of-accuracy (J. Comp. Phys. 2000; 160:405-452), extended up to WENO17 (AIAA Paper 2009-1612, 2009). Analysis of the advection-diffusion equation, both as Delta x --> 0 (consistency), and for fixed finite cell-Reynolds-number Re(Delta 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(tau w) is an element of [180,2301; (M) over bar (CL) is an element of [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(Delta t(2)) time-integration and O(Delta 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 (C) 2009 John Wiley & Sons, Ltd.
upwind schemes dns compressible wall-turbulence weno reconstruction high-order schemes reynolds-stresses