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SUMMARYThe 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.

The purpose of the present paper is to study the influence of wall-echo on pressure fluctuations p , and on statistical correlations containing p , viz redistribution φ ij , pressure diffusion d (p) ij , and velocity/pressure-gradient Π ij . We extend the usual analysis of turbulent correlations containing pressure fluctuations in wall-bounded dns computations [Kim J.: J. Fluid Mech. 205 (1989) ) and surface (wall-echo; p (r;w) and p (s;w) ) terms. An algorithm, based on a Green's function approach, is developed to compute the above splittings for various correlations containing pressure fluctuations (redistribution, pressure diffusion, velocity/pressure-gradient), in fully developed turbulent plane channel flow. This exact analysis confirms previous results based on a method-of-images approximation [Manceau R., Wang M., Laurence D.: J. Fluid Mech. 438 (2001) 307-338] showing that, at the wall, p (V) and p (w) are usually of the same sign and approximately equal. The above results are then used to study the contribution of each mechanism on the pressure correlations in low Reynolds-number plane channel flow, and to discuss standard second-moment-closure modelling practices.