arXiv subjects

Paola Cinnella

Publications and source records attributed to Paola Cinnella.

At least 19 recordsLinked to original sources

arXiv2026

A high-fidelity numerical database for free-stream transition

The accurate prediction of laminar-to-turbulent transition is critical for the design of aerodynamic and turbomachinery systems, yet widely used experimental benchmarks, such as the ERCOFTAC T3 series, lack the full-field, three-dimensional, and time-resolved data required for modern model development. To address these limitations, this study presents a high-fidelity numerical database of bypass transition in boundary layers, generated using wall-resolved implicit Large Eddy Simulations (iLES) to rigorously mimic the ERCOFTAC T3 flat-plate experiments. Computations are performed using a high-order compressible Navier-Stokes solver across multiple configurations, encompassing a range of freestream turbulence intensities and both zero and varying pressure gradients. The numerical results demonstrate satisfactory agreement with legacy experimental data for skin friction, mean velocity, and fluctuation profiles. Finally, the resulting database is utilized to evaluate the predictive capabilities of standard Reynolds-Averaged Navier-Stokes (RANS) transition models (SA-BCM and $k-ω-γ$), revealing systemic flaws in predicting transition onset and length. This highlights the dataset's value as a foundational resource for the calibration, assessment, and development of next-generation, physics-informed machine learning transition closures.

physics.flu-dyn↗

arXiv2026

End-to-end optimization of subgrid scale models for discontinuous spectral element schemes based on the discrete adjoint method

In computational fluid dynamics, Large Eddy Simulation (LES) offers a compelling balance between accuracy and computational cost by resolving large-scale flow structures while modeling unresolved subgrid scales. However, its predictive capacity is critically dependent on the choice and calibration of subgrid-scale (SGS) models, which often involve problem-dependent parameters and exhibit intricate interactions with the numerical discretization. In this work, we propose a discrete-adjoint framework to optimize SGS model parameters in the loop, leveraging automatic differentiation within a high-order Spectral Difference (SD) solver. Coarse-grained simulations of Forced Homogeneous Isotropic Turbulence (FHIT), together with filtered Direct Numerical Simulation (DNS) data, are used to optimize a limited set of parameters for classical SGS models, including the Smagorinsky model and non-linear tensor-basis formulations. For chaotic systems such as LES, the choice of objective function plays a crucial role in the stability and accuracy of the optimization. Here, we consider the spatio-temporally averaged decay of the Legendre modal coefficients as the quantity of interest for the SD scheme. The optimization is performed across different grid resolutions and polynomial orders, highlighting the impact of numerical discretization on model performance. The methodology is applied to both one-dimensional Burgers turbulence and fully three-dimensional turbulence. The trained models are subsequently assessed on out-of-sample configurations, including Decaying Homogeneous Isotropic Turbulence (DHIT) and the Taylor-Green vortex. Variations in polynomial order, grid resolution, and Reynolds number are considered to evaluate robustness and generalization. In all test cases, the optimized models demonstrate significant improvements over baseline SGS closures.

physics.flu-dyn↗

arXiv2026

The Closure Challenge: a benchmark task for machine learning in turbulence modelling

We introduce a field-wide benchmark challenge for machine learning in Reynolds-averaged Navier-Stokes (RANS) turbulence modelling. Though open-source datasets exist for training data-driven turbulence closure models, the field has been notably lacking a standard benchmark metric and test dataset. The Closure Challenge is a curated collection of open-source datasets and evaluation code that remedies this problem. We provide a variety of high-fidelity training data in a standardized format, including mean velocity gradients. The test cases (periodic hills, square duct, and NASA wall-mounted hump) evaluate Reynolds number and geometry generalization, two key issues in the field. We present results from three early submissions to the challenge. This is an ongoing challenge, intended to continuously spur innovation in machine learning for turbulence modelling. Our goal is for this benchmark to become the standard evaluation for new machine learning frameworks in RANS. The Closure Challenge is available at https://github.com/rmcconke/closure-challenge-benchmark.

physics.flu-dyn↗

arXiv2025

Bayesian and non-Bayesian multi-fidelity surrogate models for multi-objective aerodynamic optimization under extreme cost imbalance

Aerodynamic shape optimization in industry still faces challenges related to robustness and scalability. This aspect becomes crucial for advanced optimizations that rely on expensive high-fidelity flow solvers, where computational budget constraints only allow a very limited number of simulations within the optimization loop. To address these challenges, we investigate strategies based on multi-fidelity surrogate models. In particular, we focus on the case of extreme computational cost imbalance between the high- and low-fidelity models, which severely limits the maximum allowable number of high-fidelity function calls. To maximize the information extracted from the high-fidelity samples, we generate a reduced representation of the design space and use an adaptive infill strategy to smartly place the high-fidelity samples where they can best guide the optimization. Bayesian co-kriging and non-Bayesian multi-fidelity neural networks are trained by combining low- and high-fidelity models for a use-case consisting of a low Reynolds linear outlet guide vane at subsonic and transitional flow conditions. Coarse-mesh RANS simulations are used as low-fidelity model while RANS simulations with a transition model and automatically (feature-based) adapted meshes are chosen as the high-fidelity one. Each surrogate model is then associated to an infill strategy of its kind and a proper orthogonal decomposition of the shape parametrization is used to reduce by half the dimension of the problem. Based on inverted distance and hypervolume metrics, we find that the simpler co-kriging representation in conjunction with Bayesian infill yields better performance than the multi-fidelity neural network and the considered non-Bayesian method.

physics.flu-dyn↗

arXiv2025

Recent developments and research needs in turbulence modeling of hypersonic flows

Hypersonic flow conditions pose exceptional challenges for Reynolds-Averaged Navier-Stokes (RANS) turbulence modeling. Critical phenomena include compressibility effects, shock/turbulent boundary layer interactions, turbulence-chemistry interaction in thermo-chemical non-equilibrium, and ablation-induced surface roughness and blowing effects. This comprehensive review synthesizes recent developments in adapting turbulence models to hypersonic applications, examining approaches ranging from empirical modifications to physics-based reformulations and novel data-driven methodologies. We provide a systematic evaluation of current RANS-based turbulence modeling capabilities, comparing eddy viscosity and Reynolds stress transport formulations in their ability to predict engineering quantities of interest such as separation characteristics and wall heat transfer. Our analysis encompasses the latest experimental and direct numerical simulation datasets for validation, specifically addressing two- and three-dimensional equilibrium turbulent boundary layers and shock/turbulent boundary layer interactions across both smooth and rough surfaces. Key multi-physics considerations including catalysis and ablation phenomena along with the integration of conjugate heat transfer into a RANS solver for efficient design of a thermal protection system are also discussed. We conclude by identifying the critical gaps in the available validation databases and limitations of the existing turbulence models and suggest potential areas for future research to improve the fidelity of turbulence modeling in the hypersonic regime.

physics.flu-dyn↗

arXiv2025

Decoding complexity: how machine learning is redefining scientific discovery

As modern scientific instruments generate vast amounts of data and the volume of information in the scientific literature continues to grow, machine learning (ML) has become an essential tool for organising, analysing, and interpreting these complex datasets. This paper explores the transformative role of ML in accelerating breakthroughs across a range of scientific disciplines. By presenting key examples -- such as brain mapping and exoplanet detection -- we demonstrate how ML is reshaping scientific research. We also explore different scenarios where different levels of knowledge of the underlying phenomenon are available, identifying strategies to overcome limitations and unlock the full potential of ML. Despite its advances, the growing reliance on ML poses challenges for research applications and rigorous validation of discoveries. We argue that even with these challenges, ML is poised to disrupt traditional methodologies and advance the boundaries of knowledge by enabling researchers to tackle increasingly complex problems. Thus, the scientific community can move beyond the necessary traditional oversimplifications to embrace the full complexity of natural systems, ultimately paving the way for interdisciplinary breakthroughs and innovative solutions to humanity's most pressing challenges.

cs.LG↗

arXiv2025

Cost-effective multi-fidelity strategy for the optimization of high-Reynolds number turbine flows guided by LES

A cost-effective multi-objective shape optimization strategy is proposed for high-Reynolds number flows involving complex phenomena such as boundary layer transition, shock-wave interactions, and turbulent wakes. These processes are poorly captured by Reynolds-Averaged Navier--Stokes (RANS) models, necessitating higher-fidelity approaches like Large Eddy Simulation (LES). However, LES is computationally prohibitive at high Reynolds numbers, making its direct use in optimization impractical. To address this, we introduce a low-dimensional design space representation using Singular Value Decomposition (SVD) and construct a multi-fidelity co-Kriging (MFK) surrogate model combining wall-resolved LES (WRLES) and RANS. Adaptive infill criteria are employed to strategically enrich the surrogate model within a limited computational budget (fewer than 10 LES samples). The methodology is applied to optimize a supersonic turbine vane for Organic Rankine Cycles (ORC), operating at Reynolds numbers of $\sim 10^6$. While RANS-LES correlation weakens near the optimal region, the MFK model outperforms single-fidelity Kriging (SFK) trained on the same LES data, effectively leveraging both abundant low-fidelity and scarce high-fidelity data. RANS accurately predicts global objective function trends but fails to resolve key flow features, whereas the MFK model captures fine-detail geometry trends from LES. Loss analysis reveals that LES is essential for identifying performance-detrimental mechanisms, while RANS-only optimization yields sub-optimal designs.

physics.flu-dyn↗

arXiv2025

Machine-learning-assisted Blending of Data-Driven Turbulence Models

We present a machine learning-based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier-Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models (hereafter referred to as experts) are trained via sparse Bayesian learning and symbolic regression for distinct flow classes, including turbulent channel flows, separated flows, and a near-sonic axisymmetric jet. These experts are then combined intrusively within the RANS equations using weighting functions, initially derived via a Gaussian kernel on a dataset spanning equilibrium shear conditions to separated flows. Finally, a Random Forest Regressor is trained to map local physical features to these weighting functions, enabling deployment in previously unseen scenarios. We evaluate the resulting blended model on three representative test cases: a turbulent zero-pressure-gradient flat plate, a wall-mounted hump, and a NACA0012 airfoil at various angles of attack, ranging from fully attached to near-stall conditions. Results for these 2D flows show that the proposed strategy adapts to local flow characteristics, effectively leveraging the strengths of individual models and consistently selecting the most suitable expert in each region. Notably, the blended model also demonstrates robustness for flow configurations not included in the training set, underscoring its potential as a practical and generalizable framework for RANS turbulence modeling.

physics.flu-dyn↗

arXiv2024

NeurIPS 2024 ML4CFD Competition: Harnessing Machine Learning for Computational Fluid Dynamics in Airfoil Design

The integration of machine learning (ML) techniques for addressing intricate physics problems is increasingly recognized as a promising avenue for expediting simulations. However, assessing ML-derived physical models poses a significant challenge for their adoption within industrial contexts. This competition is designed to promote the development of innovative ML approaches for tackling physical challenges, leveraging our recently introduced unified evaluation framework known as Learning Industrial Physical Simulations (LIPS). Building upon the preliminary edition held from November 2023 to March 2024, this iteration centers on a task fundamental to a well-established physical application: airfoil design simulation, utilizing our proposed AirfRANS dataset. The competition evaluates solutions based on various criteria encompassing ML accuracy, computational efficiency, Out-Of-Distribution performance, and adherence to physical principles. Notably, this competition represents a pioneering effort in exploring ML-driven surrogate methods aimed at optimizing the trade-off between computational efficiency and accuracy in physical simulations. Hosted on the Codabench platform, the competition offers online training and evaluation for all participating solutions.

physics.flu-dyn↗

arXiv2024

Space-dependent Aggregation of Stochastic Data-driven Turbulence Models

A stochastic Machine-Learning approach is developed for data-driven Reynolds-Averaged Navier-Stokes (RANS) predictions of turbulent flows, with quantified model uncertainty. This is done by combining a Bayesian symbolic identification methodology for learning stochastic RANS model corrections for selected classes of flows (expert models), and a Mixture-of-Experts methodology that aggregates their predictions. The expert models are learned using the recently proposed SBL-SpaRTA algorithm, which generates sparse analytical expressions of the corrective terms with model parameters described by probability distributions. They outperform the baseline RANS model for flows similar to those used for training, but their generalization to different flows is not warranted. With the aim of quantifying the predictive uncertainty associated with the data-driven models while improving predictive accuracy and generalization capabilities, a space-dependent model aggregation technique (XMA) is then adopted. A gating function, which assigns each model a performance score (weight) based on a vector of local flow features, is trained alongside the expert models. The weights can be interpreted as the probability that a candidate model will outperform its competitors given the flow behavior at a given location. Predictions of unseen flows are formulated as a locally weighted average of the stochastic solutions of the expert models. A prediction uncertainty estimate is obtained by propagating the models' posterior parameter distributions and by evaluating the inter-model prediction variance. The expectancy of the XMA prediction is significantly more accurate than the baseline deterministic solution and the individual solutions of the experts for well-documented benchmark flows not included in the training set, while providing consistent estimates of the predictive variance.

physics.flu-dyn↗

arXiv2024

Data-driven turbulence modeling

This chapter provides an introduction to data-driven techniques for the development and calibration of closure models for the Reynolds-Averaged Navier--Stokes (RANS) equations. RANS models are the workhorse for engineering applications of computational fluid dynamics (CFD) and are expected to play an important role for decades to come. However, RANS model inadequacies for complex, non-equilibrium flows and uncertainties in modeling assumptions and calibration data are still a major obstacle to the predictive capability of RANS simulations. In the following, we briefly recall the origin and limitations of RANS models, and then review their shortcomings and uncertainties. Then, we provide an introduction to data-driven approaches to RANS turbulence modeling. The latter can range from simple model parameter inference to sophisticated machine learning techniques. We conclude with some perspectives on current and future research trends.

physics.flu-dyn↗

arXiv2024

Enhancing non-intrusive Reduced Order Models with space-dependent aggregation methods

In this manuscript, we combine non-intrusive reduced order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM. The prediction of the mixed formulation is given by a convex linear combination of the predictions of some previously-trained ROMs, where we assign to each model a space-dependent weight. The ROMs taken into account to build the mixed model exploit different reduction techniques, such as Proper Orthogonal Decomposition (POD) and AutoEncoders (AE), and/or different approximation techniques, namely a Radial Basis Function Interpolation (RBF), a Gaussian Process Regression (GPR) or a feed-forward Artificial Neural Network (ANN). The contribution of each model is retained with higher weights in the regions where the model performs best, and, vice versa, with smaller weights where the model has a lower accuracy with respect to the other models. Finally, a regression technique, namely a Random Forest, is exploited to evaluate the weights for unseen conditions. The performance of the aggregated model is evaluated on two different test cases: the 2D flow past a NACA 4412 airfoil, with an angle of attack of 5 degrees, having as parameter the Reynolds number varying between 1e5 and 1e6 and a transonic flow over a NACA 0012 airfoil, considering as parameter the angle of attack. In both cases, the mixed-ROM has provided improved accuracy with respect to each individual ROM technique.

math.NA↗

arXiv2023

AirfRANS: High Fidelity Computational Fluid Dynamics Dataset for Approximating Reynolds-Averaged Navier-Stokes Solutions

Surrogate models are necessary to optimize meaningful quantities in physical dynamics as their recursive numerical resolutions are often prohibitively expensive. It is mainly the case for fluid dynamics and the resolution of Navier-Stokes equations. However, despite the fast-growing field of data-driven models for physical systems, reference datasets representing real-world phenomena are lacking. In this work, we develop AirfRANS, a dataset for studying the two-dimensional incompressible steady-state Reynolds-Averaged Navier-Stokes equations over airfoils at a subsonic regime and for different angles of attacks. We also introduce metrics on the stress forces at the surface of geometries and visualization of boundary layers to assess the capabilities of models to accurately predict the meaningful information of the problem. Finally, we propose deep learning baselines on four machine learning tasks to study AirfRANS under different constraints for generalization considerations: big and scarce data regime, Reynolds number, and angle of attack extrapolation.

cs.LG↗

arXiv2023

Space-dependent turbulence model aggregation using machine learning

In this article, we propose a data-driven methodology for combining the solutions of a set of competing turbulence models. The individual model predictions are linearly combined for providing an ensemble solution accompanied by estimates of predictive uncertainty due to the turbulence model choice. First, for a set of training flow configurations we assign to component models high weights in the regions where they best perform, and vice versa, by introducing a measure of distance between high-fidelity data and individual model predictions. The model weights are then mapped into a space of features, representative of local flow physics, and regressed by a Random Forests (RF) algorithm. The RF regressor is finally employed to infer spatial distributions of the model weights for unseen configurations. Predictions of new cases are constructed as a convex linear combination of the underlying models solutions, while the between model variance provides information about regions of high model uncertainty. The method is demonstrated for a class of flows through the compressor cascade NACA65 V103 at Re~3e5. The results show that the aggregated solution outperforms the accuracy of individual models for the quantity used to inform the RF regressor, and performs well for other quantities well-correlated to the preceding one. The estimated uncertainty intervals are generally consistent with the target high-fidelity data. The present approach then represents a viable methodology for a more objective selection and combination of alternative turbulence models in configurations of interest for engineering practice

physics.flu-dyn↗

arXiv2022

Shock impingement on a transitional hypersonic high-enthalpy boundary layer

The dynamics of a shock wave impinging on a transitional high-enthalpy boundary layer out of thermochemical equilibrium is investigated for the first time by means of a direct numerical simulation. The freestream Mach number is equal to 9 and the oblique shock impinges with a cooled flat-plate boundary layer with an angle of 10°, generating a reversal flow region. In conjunction with freestream disturbances, the shock impingement triggers a transition to a fully turbulent regime shortly downstream of the interaction region. Accordingly, wall properties emphasize the presence of a laminar region, a recirculation bubble, a transitional zone and fully turbulent region. The breakdown to turbulence is characterized by an anomalous increase of skin friction and wall heat flux, due to the particular shock pattern. At the considered thermodynamic conditions the flow is found to be in a state of thermal non-equilibrium throughout, with non-equilibrium effects enhanced and sustained by the shock-induced laminar/turbulent transition, while chemical activity is almost negligible due to wall cooling. In the interaction region, relaxation towards thermal equilibrium is delayed and the fluctuating values of the rototranslational and the vibrational temperatures strongly differ, despite the strong wall-cooling. The fully turbulent portion exhibits evolutions of streamwise velocity, Reynolds stresses and turbulent Mach number in good accordance with previous results for highly-compressible cooled-wall boundary layers in thermal nonequilibrium, with turbulent motions sustaining thermal nonequilibrium. Nevertheless, the vibrational energy is found to contribute little to the total wall heat flux.

physics.flu-dyn↗

arXiv2021

Assessment of a high-order shock-capturing central-difference scheme for hypersonic turbulent flow simulations

High-speed turbulent flows are encountered in most space-related applications (including exploration, tourism and defense fields) and represent a subject of growing interest in the last decades. A major challenge in performing high-fidelity simulations of such flows resides in the stringent requirements for the numerical schemes to be used. These must be robust enough to handle strong, unsteady discontinuities, while ensuring low amounts of intrinsic dissipation in smooth flow regions. Furthermore, the wide range of temporal and spatial active scales leads to concurrent needs for numerical stabilization and accurate representation of the smallest resolved flow scales in cases of under-resolved configurations. In this paper, we present a finite-difference high-order shock-capturing technique based on Jameson's artificial diffusivity methodology. The resulting scheme is ninth-order-accurate far from discontinuities and relies on the addition of artificial dissipation close to large gradients. The shock detector is slightly revised to enhance its selectivity and avoid spurious activations of the shock-capturing term. A suite of test cases ranging from 1D to 3D configurations (namely, shock tubes, Shu-Osher problem, isentropic vortex advection, under-expanded jet, compressible Taylor-Green Vortex, supersonic and hypersonic turbulent boundary layers) is analysed in order to test the capability of the proposed numerical strategy to handle a large variety of problems, ranging from calorically-perfect air to multi-species reactive flows. Results obtained on under-resolved grids are also considered to test the applicability of the proposed strategy in the context of implicit Large-Eddy Simulations.

physics.flu-dyn↗

arXiv2021

Finite-rate chemistry effects in turbulent hypersonic boundary layers: a direct numerical simulation study

The influence of high-enthalpy effects on hypersonic turbulent boundary layers is investigated by means of direct numerical simulations (DNS). A quasi-adiabatic flat-plate air flow at free-stream Mach number equal to 10 is simulated up to fully-developed turbulent conditions using a five-species, chemically-reacting model. A companion DNS based on a frozen-chemistry assumption is also carried out, in order to isolate the effect of finite-rate chemical reactions and assess their influence on turbulent quantities. In order to reduce uncertainties associated with turbulence generation at the inlet of the computational domain, both simulations are initiated in the laminar flow region and the flow is let to evolve up to the fully turbulent regime. Modal forcing by means of localized suction and blowing is used to trigger laminar-to-turbulent transition. The high temperatures reached in the near wall region including the viscous and buffer sublayers activate significant dissociation of both oxygen and nitrogen. This modifies in turn the thermodynamic and transport properties of the reacting mixture, affecting the first-order statistics of thermodynamic quantities. Due to the endothermic nature of the chemical reactions in the forward direction, temperature and density fluctuations in the reacting layer are smaller than in the frozen-chemistry flow. However, the first- and second-order statistics of the velocity field are found to be little affected by the chemical reactions under a scaling that accounts for the modified fluid properties. We also observed that the Strong Reynolds Analogy (SRA) remains well respected despite the severe hypersonic conditions and that the computed skin friction coefficient distributions match well the results of the Renard-Deck decomposition extended to compressible flows.

physics.flu-dyn↗

arXiv2020

Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression

** This article is published (open-access). ** A novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills ($Re$=10595), converging-diverging channel ($Re$=12600) and curved backward-facing step ($Re$=13700). The predictions of the discovered models are significantly improved over the $k$-$ω$ SST also for a true prediction of the flow over periodic hills at $Re$=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.

physics.comp-ph↗