[Paper Review] A second-order consistent, low-storage method for time-resolved channel flow simulations up to $Re_ au=5300$

Alberto Vela-Martín, Miguel P. Encinar+2 more|arXiv (Cornell University)|Aug 20, 2018

Fluid Dynamics and Turbulent FlowsEngineering20 references3 citations

TL;DR

This paper presents a low-storage, second-order consistent numerical method for time-resolved direct numerical simulations of turbulent channel flow up to $Re_\tau = 5300$. By retaining only large and intermediate scales while preserving full reconstructibility of instantaneous filtered fields and second-order statistics, the method enables long-duration simulations on large domains with minimal storage, implemented via a high-performance CUDA-MPI hybrid code.

ABSTRACT

Wall-bounded flows play an important role in numerous common applications, and have been intensively studied for over a century. However, the dynamics and structure of the logarithmic and outer regions remain controversial to this date, and understanding their mechanics is essential for the development of effective control strategies and for the construction of a complete theory of wall-bounded flows. Recently, the use of time-resolved direct numerical simulations of turbulent flows at high Reynolds numbers has proved useful to study the physics of wall-bounded turbulence, but a proper analysis of the logarithmic and outer layers requires simulations at high Reynolds numbers in large domains, making the storage of complete time series impractical. In this paper a novel low-storage method for time-resolved simulations is presented. This approach reduces the cost of storing time-resolved data by retaining only the required large and intermediate scales, taking care to keep all the variables needed to fully reconstruct the flow at the level of instantaneous filtered fields and second-order statistics. This new methodology is efficiently implemented as a new high-resolution hybrid CUDA-MPI code, which exploits the advantages of GPU co-processors on distributed memory systems, and allows running for physically meaningful times. The resulting temporally-resolved database of channel flow at up to $Re_ au=5300$, in large boxes for long times, is briefly introduced. The code is available at { t this https URL\_GPU}.

Motivation & Objective

• To enable time-resolved direct numerical simulations of turbulent wall-bounded flows at high Reynolds numbers with practical data storage requirements.
• To resolve the logarithmic and outer layer dynamics in wall-bounded turbulence, which remain controversial despite over a century of study.
• To develop a storage-efficient simulation framework that retains sufficient data to reconstruct instantaneous filtered fields and second-order statistics.
• To facilitate long-duration simulations in large computational domains necessary for studying the statistical and dynamical properties of the outer layer.
• To provide a publicly available, high-performance simulation code for the research community to study high-Reynolds-number turbulence.

Proposed method

• A low-storage algorithm is developed that retains only large and intermediate flow scales, discarding fine-scale resolved data to reduce storage demands.
• The method ensures second-order consistency in time and space, preserving accuracy for statistical and instantaneous field reconstruction.
• The approach maintains all variables required to fully reconstruct the instantaneous filtered velocity fields and second-order statistics from the stored data.
• A hybrid CUDA-MPI implementation is used, leveraging GPU acceleration on distributed-memory systems to achieve high performance and scalability.
• The simulation framework supports long-time integration in large domains, enabling physically meaningful statistical analysis of turbulent channel flow.
• The code is designed to be efficient and scalable, with data output optimized for post-processing of turbulence statistics and coherent structures.

Experimental results

Research questions

• RQ1 How can time-resolved direct numerical simulations of high-Reynolds-number wall-bounded turbulence be performed with minimal data storage overhead?
• RQ2 What is the role of the logarithmic and outer regions in the dynamics of turbulent channel flow at $Re_\tau = 5300$?
• RQ3 Can a low-storage method preserve the necessary information for reconstructing instantaneous filtered fields and second-order statistics?
• RQ4 What are the statistical and structural characteristics of the outer layer in high-Reynolds-number channel flow?
• RQ5 How does the performance and scalability of a GPU-accelerated, hybrid CUDA-MPI code enable long-duration simulations of turbulent flows?

Key findings

• The proposed low-storage method enables time-resolved simulations of turbulent channel flow up to $Re_\tau = 5300$ with significantly reduced data storage requirements.
• The method preserves all necessary variables to reconstruct both instantaneous filtered velocity fields and second-order statistics from the stored data.
• The hybrid CUDA-MPI implementation achieves high performance and scalability, allowing long-duration simulations on large domains.
• A temporally resolved database of channel flow at $Re_\tau = 5300$ is generated, enabling detailed analysis of logarithmic and outer layer dynamics.
• The simulation framework is made publicly available at {t this https URL_GPU}, supporting reproducibility and further research in high-Reynolds-number turbulence.