[Paper Review] A Parallel Integrated Computational-Statistical Platform for Turbulent Transport Phenomena

Ali Akhavan-Safaei, Mohsen Zayernouri|arXiv (Cornell University)|Dec 9, 2020

Fluid Dynamics and Turbulent Flows32 references6 citations

TL;DR

This paper presents an open-source, parallel, high-fidelity computational-statistical platform for direct numerical simulation (DNS) of homogeneous isotropic turbulence and passive scalar transport using a pseudo-spectral method on distributed-memory supercomputers. It enables automated tracking of statistical quantities, achieving fully developed turbulent states verified by equilibrium in energy, enstrophy, and scalar variance production/dissipation rates, with results validated over 25 large-eddy turnover times.

ABSTRACT

In this paper, we present an open-source, automated, and multi-faceted computational-statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport. A parallel implementation of the well-known pseudo-spectral method in addition to the comprehensive record of the statistical and small-scale quantities of the turbulent transport are offered for executing on distributed memory CPU-based supercomputers. The user-friendly workflow and easy-to-run design of the developed package is disclosed through an extensive and step-by-step example. The resulting low- and high-order statistical records vividly verify well-established and fully-developed turbulent state as well as the seamless statistical balance of conservation laws. Post-processing tools provided in this platform would let the user to readily construct multiple important transport quantities from the primitive turbulent fields.

Motivation & Objective

• To develop a sustainable, open-source, and user-friendly computational-statistical platform for high-fidelity DNS of homogeneous isotropic turbulence.
• To enable automated, parallel, and high-order accurate simulation of incompressible Navier-Stokes and advection-diffusion equations on distributed-memory architectures.
• To provide comprehensive statistical monitoring of turbulent fields, including low- and high-order moments, to verify fully developed and statistically stationary turbulent states.
• To support the generation of high-fidelity data for training and validating data-driven turbulence models and subgrid-scale closures.
• To bridge the educational gap in fluid mechanics, CFD, and turbulent transport by offering an integrated, accessible tool for researchers and students.

Proposed method

• The platform implements a pseudo-spectral method using Fourier collocation for spatial discretization of the incompressible Navier-Stokes and advection-diffusion equations on a triply periodic cubic domain.
• Time integration is performed using a fourth-order Runge-Kutta (RK4) scheme with dynamic artificial forcing to maintain statistical stationarity in the turbulent flow.
• The software uses MPI and Python with dependencies on NumPy, SciPy, and MPI4Py to enable scalable parallel execution across CPU-based supercomputers.
• Initial conditions are generated via spectral decomposition of a prescribed energy spectrum to produce divergence-free, homogeneous, and isotropic velocity fields.
• Statistical quantities—including velocity and scalar gradient moments, variance production, and dissipation rates—are computed and recorded at each time step in time-series format.
• Post-processing tools allow users to compute derived transport quantities and verify convergence to fully developed turbulent states through statistical equilibrium.

Experimental results

Research questions

• RQ1 How can a scalable, open-source platform be designed to automate high-fidelity DNS of homogeneous isotropic turbulence with integrated statistical monitoring?
• RQ2 What statistical indicators reliably confirm the onset of a fully developed and statistically stationary turbulent state in DNS?
• RQ3 How can passive scalar transport be accurately resolved in a fully developed turbulent velocity field with proper resolution of scalar gradient statistics?
• RQ4 To what extent does the platform’s statistical monitoring confirm the balance of conservation laws and established turbulence scaling laws?
• RQ5 Can the platform generate high-fidelity data suitable for training and validating data-driven turbulence models and subgrid-scale closures?

Key findings

• The platform successfully achieves a statistically stationary and fully developed turbulent state after approximately 25 large-eddy turnover times, as confirmed by equilibrium in energy and enstrophy spectra.
• The scalar variance production-to-dissipation ratio stabilizes at approximately 1.0 after two large-eddy turnover times, indicating the onset of equilibrium in passive scalar transport.
• High-order statistical moments of the scalar gradient, such as flatness factor (Kφ,2) and skewness (Sφ,2), reach stationary values of ~20.8 and ~1.4, respectively, for t/Te ≥ 5.
• The spatial resolution is sufficient for Sc ≥ 1, with the Batchelor scale ηB resolved via the velocity field resolution, ensuring well-resolved passive scalar dynamics.
• The platform’s statistical records confirm the seamless balance of conservation laws and validate the turbulent state using multiple independent metrics.
• The open-source, modular design enables reproducible, scalable, and extensible simulations suitable for advanced turbulence research and model development.