Natural grid stretching for DNS of wall-bounded flows

TL;DR

This paper introduces a natural grid stretching method for DNS of wall-bounded flows, optimizing accuracy and efficiency by blending near-wall and outer-layer resolutions, supported by high-Reynolds-number simulations.

Contribution

It presents a novel grid stretching function that combines uniform near-wall spacing with Kolmogorov-scale resolution in the outer layer, providing a practical prescription for grid design.

Findings

Optimal blending parameter identified for pipe flow

Maximized time step for computational efficiency

Guidelines for grid points and clustering at target Reynolds numbers

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 results of maximization of the allowed time step. Conclusions are supported by DNS carried out at sufficiently high Reynolds number that a near logarithmic layer is 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.