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Performance of very-high-order upwind schemes for DNS of compressible wall-turbulence. (English) Zbl 1407.76044
Summary: 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 [D. S. Balsara and C.-W. Shu, J. Comput. Phys. 160, No. 2, 405–452 (2000; Zbl 0961.65078)], extended up to WENO17 [the authors, Very-high-order WENO schemes. AIAA Paper 2009-1612, 47. Aerospace Sciences Meeting, Orlando, FL, U.S.A., 5–8 January 2009]. Analysis of the advection-diffusion equation, both as $$\Delta x \longrightarrow 0$$ (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 ($$Re_{\tau_w}\in [180,230];\bar M _{\text{CL}}\in [0.35,1.5]$$) 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.

##### MSC:
 76F65 Direct numerical and large eddy simulation of turbulence 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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