An efficient numerical method for the generalised Kolmogorov equation. Issue 8 (3rd August 2019)

• Record Type: Journal Article
• Authors: Gatti, Davide; Remigi, Alberto; Chiarini, Alessandro; Cimarelli, Andrea; Quadrio, Maurizio
• Is Part Of: Journal of turbulence. Volume 20:Issue 8(2019)
• Page Start: 457
• Page End: 480
• Publication Date: 2019-08-03
• Subjects: Turbulence -- channel flow -- generalised Kolmogorov equation -- GKE -- scale energy -- direct numerical simulation; Turbulence -- Periodicals; Turbulence -- Périodiques; 532.0527
• DOI: 10.1080/14685248.2019.1664746
• Languages: English
• ISSNs: 1468-5248

Abstract

ABSTRACT: An efficient algorithm for computing the terms appearing in the Generalised Kolmogorov Equation (GKE) written for the indefinite plane channel flow is presented. The algorithm, which features three distinct strategies for parallel computing, is designed such that CPU and memory requirements are kept to a minimum, so that high- Re wall-bounded flows can be afforded. Computational efficiency is mainly achieved by leveraging the Parseval's theorem for the two homogeneous directions available in the plane channel geometry. A speedup of 3-4 orders of magnitude, depending on the problem size, is reported in comparison to a key implementation used in the literature. Validation of the code is demonstrated by computing the residual of the GKE, and example results are presented for channel flows at R e τ = 200 and R e τ = 1000, where for the first time they are observed in the whole four-dimensional domain. It is shown that the space and scale properties of the scale-energy fluxes change for increasing values of the Reynolds number. Among all scale-energy fluxes, the wall-normal flux is found to show the richest behaviour for increasing streamwise scales.