Kudge Dataset for Turbulence Modeling

• The Kudge Dataset is an open-source curated collection designed for machine learning-augmented turbulence closure modeling, integrating extensive RANS simulations with DNS/LES benchmarks.
• It encompasses four canonical turbulence closures with diverse configurations, providing approximately 3.58 million unique data samples across varied Reynolds numbers and geometries.
• The dataset offers a comprehensive suite of base variables and derived flow-gradient features, enabling direct application in tensor-basis and random forest closure models for improved predictive accuracy.

The Kudge Dataset is an open-source, curated collection designed for immediate application in machine learning-augmented turbulence closure modeling. Developed to systematically address the limitations of traditional Reynolds-averaged Navier-Stokes (RANS) models, it integrates a broad range of RANS simulations matched to reference Direct Numerical Simulation (DNS) and Large-Eddy Simulation (LES) data. The dataset targets standard two-equation turbulence closures and presents, for each configuration, a comprehensive suite of flow variables and derived invariants, facilitating data-driven model development and benchmarking under a unified numerical and meshing approach (McConkey et al., 2021).

1. Dataset Composition and Flow Configurations

The Kudge Dataset comprises RANS data for four canonical closures—$k$-$\varepsilon$, $k$-$\varepsilon$-$\phi_t$-$f$, $k$-$\omega$, and $k$-$\omega$ SST—with 29 cases per turbulence model. Each case corresponds to a specific flow configuration, ensuring diversity across geometry and Reynolds number:

Configuration	Parametric Variation	Number of Cases Per Model
Periodic Hills	Steepness ratio $\varepsilon$0	5
Square Duct	$\varepsilon$1 to $\varepsilon$2 (16 values)	16
Parametric Bumps	Bump heights $\varepsilon$3 mm	5
Converging–Diverging Channel	$\varepsilon$4	2
Curved Backward-Facing Step	$\varepsilon$5	1

For each turbulence model, RANS simulations are performed on meshes with $\varepsilon$6, and reference DNS/LES truth is interpolated onto these grids. After excluding extrapolated or non-realizable points (approximately 50 per model), each turbulence model contributes around 895,640 data points, resulting in roughly 3.58 million unique samples across all models, each with $\varepsilon$7 features and $\varepsilon$8 supervised labels.

2. Turbulence Closures and Governing Equations

The dataset utilizes the incompressible RANS equations, featuring several standard two-equation closures:

2.1 Continuity and Momentum Equations

$\varepsilon$9

$k$0

where $k$1 is the mean velocity, $k$2 is the kinematic pressure, $k$3 is the density (set to unity in all cases), $k$4 is the molecular viscosity, and $k$5 is the eddy viscosity.

2.2 Two-Equation Closures

$k$6–$k$7 Family

$k$8

$k$9

$\varepsilon$0

$\varepsilon$1–$\varepsilon$2 Family

$\varepsilon$3

$\varepsilon$4

$\varepsilon$5

$\varepsilon$6–f (v$\varepsilon$7–f) Model

Solves additional transport equations for wall-normal stress anisotropy $\varepsilon$8 and the elliptic-relaxation scalar $\varepsilon$9 (see Laurence et al. 2005 for explicit forms). This inclusion enables improved wall-normal stress redistribution.

3. Feature Suite and Derived Quantities

Each cell center in the RANS mesh records a comprehensive set of base variables and flow-gradient features, structured for direct use in modern machine-learning closure frameworks.

3.1 Base RANS Variables

• Spatial coordinates: $\phi_t$0, $\phi_t$1, $\phi_t$2
• Mean velocity components: $\phi_t$3, $\phi_t$4, $\phi_t$5
• Pressure: $\phi_t$6
• Turbulent kinetic energy: $\phi_t$7
• Dissipation rate: $\phi_t$8
• Specific dissipation: $\phi_t$9
• Anisotropy measure: $f$0
• v$f$1–f model scalar: $f$2

3.2 Derived Flow-Gradient Features

Derived features include quantities such as the strain-rate ($f$3) and rotation-rate ($f$4) tensors, their non-dimensionalized forms $f$5 and $f$6 using the turbulent time-scale $f$7, pressure and $f$8-gradients, time scales ($f$9, $k$0), antisymmetric tensors, and invariants. Forty-seven invariants and ten basis tensors (Pope 1975), five classical invariants (e.g., $k$1, $k$2; Ling et al. 2016), and four Galilean-invariant scalars ($k$3–$k$4 following Kaandorp & Dwight 2020) are included. All derived features are provided "ready to use," enabling reproduction of TBNN, TBRF, and related approaches without additional preprocessing.

4. DNS/LES Reference Labels

Each data point is annotated with linearly interpolated DNS/LES quantities, facilitating supervised learning and direct RANS–DNS/LES comparison.

Label Type	Included Quantities
Mean velocity	$k$5, $k$6, $k$7
Reynolds stress components	$k$8, $k$9, etc. ($\omega$0 total)
Derived tensor quantities	$\omega$1 (3×3)
DNS/LES $\omega$2
Reynolds stress anisotropy tensor $\omega$3	$\omega$4

Raw DNS/LES velocity and stress fields are also provided for reference and validation.

5. Data Organization and Access

The dataset is distributed in a compressed archive (∼1 GB), which unpacks into subdirectories for each turbulence model:

Subdirectory	Contents
/kepsilon/ (and analogues)	features.npz, labels.npz, base_fields.csv, derived_features.npz, derived_labels.npz
/dns_labels/	Raw DNS/LES velocity and stress tables

• features.npz contains both base fields and invariants.
• labels.npz includes targets such as Reynolds stresses.
• base_fields.csv and derived_features.npz store essential quantities and precomputed tensors/invariants.
• All arrays are compatible with NumPy; standard column naming follows the schema in the associated paper's "base_fields" and "fields_derived" tables.

Python access is supported via: $\omega$9 A Kaggle-API download workflow is also provided for reliability and ease of access.

6. Usage Recommendations and Benchmarking Protocols

Recommended practice involves train/test splits by flow case (e.g., leave-one-geometry-out), which robustly assesses generalization across both geometry and Reynolds number variation. Prior to model development, standardize each input feature to zero mean and unit variance (except for physically bounded variables, such as the wall-distance $\omega$5). Explicit outlier removal (values outside $\omega$6) or clipping is advised.

For tensor-basis models, invariant sets constructed from $\omega$7 may be accessed directly. Benchmark suggestions include reproducing the five-invariant TBNN of Ling et al. (2016), comparing predictions of eddy viscosity versus random-forest closure approaches, and evaluating the transferability of models trained on attached flows (duct, bump) to separated flows (hills, step).

Boundary conditions are treated precisely: RANS inlet profiles are derived from short "feeder" runs, and pressures in cyclic/periodic cases represent deviations from the imposed gradient. Minor differences in inlet profiles between turbulence models can produce Reynolds number shifts at the $\omega$8 level.

The dataset is structured to minimize the effort typically required for assembling consistent RANS-DNS/LES datasets, unifying numerical, meshing, and feature-calculation standards (McConkey et al., 2021). Its scope and comprehensiveness render it a foundational benchmark for contemporary and future data-driven turbulence closure strategies.