Natural grid stretching for DNS of wall-bounded flows

Abstract

We propose a natural stretching function for DNS of wall-bounded flows, which blends uniform near-wall spacing with uniform resolution in terms of Kolmogorov units in the outer wall layer. Numerical simulations of pipe flow are used to educe optimal value of the blending parameter and of the wall grid spacing which guarantee accuracy and computational efficiency as a result of maximization of the allowed time step. Conclusions are supported by DNS carried out at sufficiently high Reynolds number that a near logarithmic layer in the mean velocity profile is present. Given a target Reynolds number, we provide a definite prescription for the number of grid points and grid clustering needed to achieve accurate results with optimal exploitation of resources.