Full Turbulence Simulation of Channel Flow at $Re_{\tau} \approx 1000$

TL;DR

This study performs a high-fidelity turbulence simulation of channel flow at Re_tau approximately 1000, establishing resolution criteria and demonstrating the efficiency of spectral methods for accurate turbulence statistics.

Contribution

It introduces practical resolution guidelines for high-Reynolds-number DNS and compares spectral and finite-difference methods in turbulence simulation accuracy.

Findings

Spectral methods achieve 1% accuracy with fewer grid points.

Wall-normal resolution confirms no adverse numerical effects.

Guidelines for Re_tau = O(10^4) simulations are provided.

Abstract

A Full Turbulence Simulation (FTS) of turbulent channel flow at friction Reynolds number (Re_tau) approx 1000 was performed by resolving the Kolmogorov wavenumber in all spatial directions. At this Reynolds number, the intermediate layer attains a physically meaningful width and is fully resolved in the present computation, providing the reference dataset that captures its turbulence and dissipation characteristics with high fidelity. The wall-normal grid spacing of the FTS also confirms that, when the Kolmogorov length scale is sufficiently resolved, the second-order central-difference scheme introduces no adverse numerical effects in the wall-normal direction. In the wall-parallel directions, two resolution criteria were identified based on the present FTS: a first-approximation DNS resolution that resolves more than 99 percent of the turbulent kinetic energy and dissipation rate (Delta x+ approx 19, Delta y+ approx 8, where Delta x+ and Delta y+ denote the streamwise and spanwise spatial resolutions in wall units) and a full dissipation-resolution criterion (Delta x+ approx 7.5, Delta y+ approx 5.0). The first-approximation resolution by means of a spectral method reproduces the essential turbulence statistics within 1 percent accuracy while requiring only one-eighth of the grid points used in the FTS, demonstrating its practical efficiency. In contrast, even the highest-resolution second-order central-difference case (Delta x+ approx 5.0, Delta y+ approx 4.5) fails to match the accuracy of the first-approximation spectral resolution. These findings provide important resolution guidelines for high-Reynolds-number DNS, particularly for simulations at Re_tau = O(10^4).