A spectral-Galerkin turbulent channel flow solver for large-scale simulations

TL;DR

This paper introduces a spectral-Galerkin solver for large-scale turbulent channel flow simulations, utilizing Chebyshev functions and advanced algorithms to achieve stability and accuracy at high Reynolds numbers.

Contribution

The paper presents a novel, stable spectral-Galerkin solver with efficient algorithms for large-scale turbulent flow simulations, validated at high Reynolds numbers.

Findings

Successfully reproduces first-order statistics at Re_tau=2000

Provides open-source spectralDNS implementation

Achieves stability and robustness at large scales

Abstract

A fully (pseudo-)spectral solver for direct numerical simulations of large-scale turbulent channel flows is described. The solver utilizes the Chebyshev base functions suggested by J. Shen [SIAM J. Sci. Comput., 16, 1, 1995], that lead to stable and robust numerical schemes, even at very large scale. New and fast algorithms for the direct solution of the linear systems are devised, and algorithms and matrices for all required scalar products and transforms are provided. We validate the solver for very high Reynolds numbers. Specifically, the solver is shown to reproduce the first order statistics of Hoyas and Jim\'{e}nez [Phys. Fluids, 18(1), 2006], for a channel flow at $Re_{\tau}=2000$. The solver is available through the open source project spectralDNS [https://github.com/spectralDNS].