arXiv subjects

Richard P. Dwight

Publications and source records attributed to Richard P. Dwight.

14 recordsLinked to original sources

arXiv2026

Bayesian neural network correction of RANS turbulence models with uncertainty quantification in separated flows

Data-driven correction of turbulence models offers a promising route for improving Reynolds-averaged Navier-Stokes (RANS) predictions, but quantifying uncertainty in such corrections and ensuring generalization across flows remain key challenges. This work presents a Bayesian neural network (BNN) framework for uncertainty-aware correction of RANS models. The BNN represents both epistemic and input-dependent aleatoric uncertainty, interpreted here as irreducible scatter in the feature-to-correction relationship, with the latter propagated as spatially correlated fields through the RANS solver. The framework is trained exclusively on a periodic-hill configuration and evaluated without retraining on five unseen separated-flow configurations. The learned corrections improve the training-flow prediction, but the strong momentum-field benefit obtained from the anisotropy correction does not transfer consistently to the unseen flows. Out-of-distribution under-coverage is already present at the correction-field level, indicating that the loss of calibration is already present in transfer of the learned correction rather than being introduced primarily by CFD propagation. Overall, the framework enables joint propagation of epistemic and aleatoric uncertainty while exposing the present limitations of uncertainty calibration under distribution shift.

physics.flu-dyn↗

arXiv2026

Uncertainty analysis of URANS simulations coupled with an anisotropic pressure fluctuation model

Accurate prediction of pressure and velocity fluctuations in turbulent flows is essential for understanding flow-induced vibration and structural fatigue. This study investigates the role of turbulence model parameter uncertainty in such predictions using a combination of global sensitivity analysis, surrogate modeling, and Bayesian inference. The methodology is applied to two fluid-only flow cases: turbulent channel flow and turbulent annular flow. In the channel flow case, calibrated parameter distributions lead to improved agreement with reference data. In the annular case, limited parameter identifiability is observed, though predictions remain consistent with high-fidelity trends. The results demonstrate both the potential and limitations of model calibration strategies in wall-bounded turbulent flows.

physics.flu-dyn↗

arXiv2026

Physics-guided Bayesian neural networks for zonal corrections and uncertainty quantification in separated flows

Data-driven techniques have improved the accuracy of Reynolds-averaged Navier-Stokes (RANS) models in fluid dynamics. However, modeling separated flows remains challenging due to their complex physics and sensitivity to local conditions. Existing approaches often struggle with generalization beyond training cases and lack robust uncertainty quantification frameworks, limiting their utility in complex flow regimes. We propose a Bayesian neural network (BNN)-based framework specifically designed for two-dimensional separated flows. By focusing on flow zones near separated regions, we ensure targeted training and enhance predictive reliability. The BNN framework incorporates physics-guided, invariant inputs to maintain consistency with turbulence physics. Correction terms predicted by the BNN are selectively applied to specific regions of the flow domain using a novel classifier, improving accuracy. A key feature of this approach is propagating BNN-derived corrections to flow solutions, enabling uncertainty quantification in unseen test cases. This probabilistic characterization of modeling errors offers insights into the reliability of RANS predictions across geometries with similar topologies. Preliminary results demonstrate that this method accurately predicts correction terms for Reynolds stress anisotropy and turbulent kinetic energy production in separated flow regions, effectively addressing dominant modeling errors and advancing turbulence modeling through uncertainty quantification.

physics.flu-dyn↗

arXiv2025

Discovery of a Physically Interpretable Data-Driven Wind-Turbine Wake Model

This study presents a compact data-driven Reynolds-averaged Navier-Stokes (RANS) model for wind turbine wake prediction, built as an enhancement of the standard $k$-$\varepsilon$ formulation. Several candidate models were discovered using the symbolic regression framework Sparse Regression of Turbulent Stress Anisotropy (SpaRTA), trained on a single Large Eddy Simulation (LES) dataset of a standalone wind turbine. The leading model was selected by prioritizing simplicity while maintaining reasonable accuracy, resulting in a novel linear eddy viscosity model. This selected leading model reduces eddy viscosity in high-shear regions, particularly in the wake, to limit turbulence mixing and delay wake recovery. This addresses a common shortcoming of the standard $k$-$\varepsilon$ model, which tends to overpredict mixing, leading to unrealistically fast wake recovery. Moreover, the formulation of the leading model closely resembles that of the established $k$-$\varepsilon$-$f_P$ model. Consistent with this resemblance, the leading and $k$-$\varepsilon$-$f_P$ models show nearly identical performance in predicting velocity fields and power output, but they differ in their predictions of turbulent kinetic energy. In addition, the generalization capability of the leading model was assessed using three unseen six-turbine configurations with varying spacing and alignment. Despite being trained solely on a standalone turbine case, the model produced results comparable to LES data. These findings demonstrate that data-driven methods can yield interpretable, physically consistent RANS models that are competitive with traditional modeling approaches while maintaining simplicity and achieving generalizability.

physics.flu-dyn↗

arXiv2025

Data-Driven RANS Closures Using a Relative Importance Term Analysis Based Classifier for 2D and 3D Separated Flows

This study presents a novel approach for enhancing Reynolds-averaged Navier-Stokes (RANS) turbulence modeling through the application of a Relative Importance Term Analysis (RITA) methodology to develop a new zonally-augmented $k-ω$ SST model. Traditional Linear Eddy Viscosity Models often struggle with separated flows. Our approach introduces a physics-based binary classifier that systematically identifies separated shear layers requiring correction by analyzing the relative magnitudes of terms in the turbulence kinetic energy equation. Using symbolic regression, we develop compact correction terms for Reynolds stress anisotropy and turbulent kinetic energy production. Trained on two-dimensional configurations, our model demonstrates significant improvements in predicting separation dynamics while maintaining baseline performance and fully attached flows. Generalization tests on Ahmed body and Faith Hill three-dimensional configurations confirm robust transferability, establishing an effective methodology for targeted enhancement of RANS predictions in separated flows.

physics.flu-dyn↗

arXiv2025

Data-driven turbulence modelling for magnetohydrodynamic flows in annular pipes

We present a data-driven approach to Reynolds-averaged Navier-Stokes turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the $k$-$ω$ SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.

physics.flu-dyn↗

arXiv2022

Probabilistic surrogate modeling of offshore wind-turbine loads with chained Gaussian processes

Heteroscedastic Gaussian process regression, based on the concept of chained Gaussian processes, is used to build surrogates to predict site-specific loads on an offshore wind turbine. Stochasticity in the inflow turbulence and irregular waves results in load responses that are best represented as random variables rather than deterministic values. Moreover, the effect of these stochastic sources on the loads depends strongly on the mean environmental conditions -- for instance, at low mean wind speeds, inflow turbulence produces much less variability in loads than at high wind speeds. Statistically, this is known as heteroscedasticity. Deterministic and most stochastic surrogates do not account for the heteroscedastic noise, giving an incomplete and potentially misleading picture of the structural response. In this paper, we draw on the recent advancements in statistical inference to train a heteroscedastic surrogate model on a noisy database to predict the conditional pdf of the response. The model is informed via 10-minute load statistics of the IEA-10MW-RWT subject to both aero- and hydrodynamic loads, simulated with OpenFAST. Its performance is assessed against the standard Gaussian process regression. The predicted mean is similar in both models, but the heteroscedastic surrogate approximates the large-scale variance of the responses significantly better.

stat.AP↗

arXiv2022

A PDE-free, neural network-based eddy viscosity model coupled with RANS equations

Most turbulence models used in Reynolds-averaged Navier-Stokes (RANS) simulations are partial differential equations (PDE) that describe the transport of turbulent quantities. Such quantities include turbulent kinetic energy for eddy viscosity models and the Reynolds stress tensor (or its anisotropy) in differential stress models. However, such models all have limitations in their robustness and accuracy. Inspired by the successes of machine learning in other scientific fields, researchers have developed data-driven turbulence models. Recently, a nonlocal vector-cloud neural network with embedded invariance was proposed, with its capability demonstrated in emulating passive tracer transport in laminar flows. Building upon this success, we use nonlocal neural network mapping to model the transport physics in the k-epsilon model and couple it to RANS solvers, leading to a PDE-free eddy-viscosity model. We demonstrate the robustness and stability of the RANS solver with a neural network-based turbulence model on flows over periodic hills of parameterized geometries. Our work serves as a proof of concept for using a vector-cloud neural network as an alternative to traditional turbulence models in coupled RANS simulations. The success of the coupling paves the way for neural network-based emulation of Reynolds stress transport models.

physics.flu-dyn↗

arXiv2020

Data-driven RANS closures for three-dimensional flows around bluff bodies

In this short note we apply the recently proposed data-driven RANS closure modelling framework of Schmelzer et al. (2020) to fully three-dimensional, high Reynolds number flows: namely wall-mounted cubes and cuboids at Re=40,000, and a cylinder at Re=140,000. For each flow, a new RANS closure is generated using sparse symbolic regression based on LES or DES reference data. This new model is implemented in a CFD solver, and subsequently applied to prediction of the other flows. We see consistent improvements compared to the baseline $k-ω$ SST model in predictions of mean-velocity in the complete flow domain.

physics.flu-dyn↗

arXiv2020

Data-driven RANS closures for wind turbine wakes under neutral conditions

The state-of-the-art in wind-farm flow-physics modeling is Large Eddy Simulation (LES) which makes accurate predictions of most relevant physics, but requires extensive computational resources. The next-fidelity model types are Reynolds-Averaged Navier-Stokes (RANS) which are two orders of magnitude cheaper, but resolve only mean quantities and model the effect of turbulence. They often fail to accurately predict key effects, such as the wake recovery rate. Custom RANS closures designed for wind-farm wakes exist, but so far do not generalize well: there is substantial room for improvement. In this article we present the first steps towards a systematic data-driven approach to deriving new RANS models in the wind-energy setting. Time-averaged LES data is used as ground-truth, and we first derive optimal corrective fields for the turbulence anisotropy tensor and turbulence kinetic energy (t.k.e.) production. These fields, when injected into the RANS equations (with a baseline $k-ε$ model) reproduce the LES mean-quantities. Next we build a custom RANS closure from these corrective fields, using a deterministic symbolic regression method to infer algebraic correction as a function of the (resolved) mean-flow. The result is a new RANS closure, customized to the training data. The potential of the approach is demonstrated under neutral atmospheric conditions for multi-turbine constellations at wind-tunnel scale. The results show significantly improved predictions compared to the baseline closure, for both mean velocity and the t.k.e. fields.

physics.flu-dyn↗

arXiv2020

Customized data-driven RANS closures for bi-fidelity LES-RANS optimization

Multi-fidelity optimization methods promise a high-fidelity optimum at a cost only slightly greater than a low-fidelity optimization. This promise is seldom achieved in practice, due to the requirement that low- and high-fidelity models correlate well. In this article, we propose an efficient bi-fidelity shape optimization method for turbulent fluid-flow applications with Large-Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) as the high- and low-fidelity models within a hierarchical-Kriging surrogate modelling framework. Since the LES-RANS correlation is often poor, we use the full LES flow-field at a single point in the design space to derive a custom-tailored RANS closure model that reproduces the LES at that point. This is achieved with machine-learning techniques, specifically sparse regression to obtain high corrections of the turbulence anisotropy tensor and the production of turbulence kinetic energy as functions of the RANS mean-flow. The LES-RANS correlation is dramatically improved throughout the design-space. We demonstrate the effectiveness and efficiency of our method in a proof-of-concept shape optimization of the well-known periodic-hill case. Standard RANS models perform poorly in this case, whereas our method converges to the LES-optimum with only two LES samples.

physics.comp-ph↗

arXiv2020

Data-Driven Modelling of the Reynolds Stress Tensor using Random Forests with Invariance

A novel machine learning algorithm is presented, serving as a data-driven turbulence modeling tool for Reynolds Averaged Navier-Stokes (RANS) simulations. This machine learning algorithm, called the Tensor Basis Random Forest (TBRF), is used to predict the Reynolds-stress anisotropy tensor, while guaranteeing Galilean invariance by making use of a tensor basis. By modifying a random forest algorithm to accept such a tensor basis, a robust, easy to implement, and easy to train algorithm is created. The algorithm is trained on several flow cases using DNS/LES data, and used to predict the Reynolds stress anisotropy tensor for new, unseen flows. The resulting predictions of turbulence anisotropy are used as a turbulence model within a custom RANS solver. Stabilization of this solver is necessary, and is achieved by a continuation method and a modified $k$-equation. Results are compared to the neural network approach of Ling et al. [J. Fluid Mech, 807(2016):155-166, (2016)]. Results show that the TBRF algorithm is able to accurately predict the anisotropy tensor for various flow cases, with realizable predictions close to the DNS/LES reference data. Corresponding mean flows for a square duct flow case and a backward facing step flow case show good agreement with DNS and experimental data-sets. Overall, these results are seen as a next step towards improved data-driven modelling of turbulence. This creates an opportunity to generate custom turbulence closures for specific classes of flows, limited only by the availability of LES/DNS data.

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↗

arXiv2018

Stochastic turbulence modeling in RANS simulations via Multilevel Monte Carlo

A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are considered to demonstrate the applicability of the MLMC method. The first approach is based on global perturbation of the baseline eddy viscosity field using a lognormal random field. A more general second extension is considered based on the work of [Xiao et al.(2017)], where the entire Reynolds Stress Tensor (RST) is perturbed while maintaining realizability. For two fundamental flows, we show that the MLMC method based on a hierarchy of meshes is asymptotically faster than plain Monte Carlo. Additionally, we demonstrate that for some flows an optimal multilevel estimator can be obtained for which the cost scales with the same order as a single CFD solve on the finest grid level.

physics.comp-ph↗