Fluid Dynamics

arXiv:physics.flu-dyn

Turbulence, instabilities, control of fluid flows, computational fluid dynamics.

Fluid Dynamics

arXiv:physics.flu-dyn

Turbulence, instabilities, control of fluid flows, computational fluid dynamics.

Trending in Fluid Dynamics

Ensemble of Fixed Points in Multi-branch Shell Models of Turbulent Cascades

Stationary solutions of a shell model of turbulence defined on a dyadic tree topology are studied. Each node's amplitude is expressed as the product of amplitude multipliers associated with its ancestors, providing a recursive representation of the cascade process. A geometrical rule governs the tree growth, and we prove the existence of a continuum of fixed points, including the Kolmogorov solution, that sustain a strictly forward energy cascade. Sampling along randomly chosen branches defines a homogeneous Markov chain, enabling a stochastic characterization of extended self-similarity and intermittency through the spectral properties of the associated Feynman-Kac operators. Numerical simulations confirm the theoretical predictions, showing that multi-branch shell models offer a minimal yet physically rich framework for exploring the complexity of nonlinear energy transfer across scales.

2601.04788

Jan 2026Fluid Dynamics

Related categories:

Accelerator Physics Atmospheric and Oceanic Physics Applied Physics Atomic and Molecular Clusters Atomic Physics

1,896 papers

Bifurcations in Stokes Flow Sedimentation

Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can be understood. We use experimental measurements of helical ribbons, with controlled center of mass offsets, to identify the key bifurcation from complex dynamics to a single attracting state as the magnitude of the offset increases. The sedimentation dynamics are very sensitive to small center of mass offsets, with the bifurcation occurring for offsets less than one percent of the particle length. Using mobility tensors obtained from immersed boundary method simulations, we simulate helical particle sedimentation and identify an alignment bifurcation surface, defined in the three dimensional space of center of mass offsets, that separates simple from complex sedimentation dynamics. Inside this surface we find limit cycles which emerge through Hopf and homoclinic bifurcations. Cocentered particles with coincident centers of force and mobility provide a reference case at the center of the bifurcation surface. We show how the geometric and dynamical symmetries of sedimenting cocentered particles are broken as the center of force offset moves away from the cocentered case. Three parity time-reversal (PT) symmetries exist for all cocentered particles under reflections normal to the eigenvectors of its translation-rotation coupling tensor. When a center of force offset preserves at least one of these PT symmetries, then there are closed orbits for particles inside the alignment bifurcation surface.

2604.03193Apr 2026

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How pore-scale disorder controls fluid stretching in porous media

Fluid stretching in porous media governs the mixing of reactants, contaminants, and nutrients, yet how the solid microstructure controls the stretching statistics remains poorly understood. We investigate how porous-medium heterogeneity controls stretching using (i) particle-tracking velocimetry experiments in 3D-printed millifluidic cells, (ii) numerical simulations of solute-plume deformation in the measured flow fields, and (iii) analytical calculations of fluid stretching. The cells contain arrays of cylindrical rods with systematically-varying disorder levels, from ordered to random. Velocity and shear-rate measurements reveal that fluid deformation is strongly localized near solid boundaries for all disorder levels, suggesting that near-wall flow is the main driver of stretching. The mean stretching grows linearly in time for ordered media and quadratically for disordered media, while the stretching distributions are approximately log-normal. We analytically describe the stretching produced by flow around an isolated cylinder and embed this description in a random-walk model that reproduces the observed stretching statistics in random media. These results provide the first quantitative connection between porous-medium structure and fluid-stretching statistics, revealing the extent to which disordered media accelerate mixing relative to ordered media and enabling progress beyond the common mean-field description of stretching in two-dimensional media as a simple shear flow.

2604.02981Apr 2026

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A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems

Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling framework for prediction of fluid flows, and demonstrate it for high-pressure gas injection phenomena relevant to reciprocating engines. The approach employs a hierarchical Vision Transformer (SwinV2-UNet) architecture that processes multimodal flow datasets from multi-fidelity simulations. The model architecture is conditioned on auxiliary tokens explicitly encoding the data modality and time increment. Model performance is assessed on two different tasks: (1) spatiotemporal rollouts, where the model autoregressively predicts the flow state at future times; and (2) feature transformation, where the model infers unobserved fields/views from observed fields/views. We train separate models on multimodal datasets generated from in-house CFD simulations of argon jet injection into a nitrogen environment, encompassing multiple grid resolutions, turbulence models, and equations of state. The resulting data-driven models learn to generalize across resolutions and modalities, accurately forecasting the flow evolution and reconstructing missing flow-field information from limited views. This work demonstrates how large vision transformer-based models can be adapted to advance predictive modeling of complex fluid flow systems.

2604.02483Apr 2026

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Parametric Reduced-Order modeling and Closed-Loop Control of Tandem-Cylinder Wakes

The flow around two circular cylinders arranged in a tandem exhibits complex wake interactions that lead to amplified unsteady loads, particularly in the co-shedding regime where a fully developed wake forms in the gap between the cylinders. Although various control strategies have been proposed to mitigate these effects, most prior studies have focused primarily on load alleviation. Complete suppression of vortex shedding, both in the gap region and in the wake of the second cylinder, has so far only been achieved using open-loop approaches. In this work, we propose a closed-loop control framework for suppressing vortex shedding in tandem cylinder flows in the co-shedding regime. Focusing on low Reynolds numbers and sufficiently large spacings, we derive a parametric reduced-order model using a global weakly nonlinear analysis of the incompressible Navier-Stokes equations. The model is generalized to account for time dependent forcing and facilitates the real time prediction of the flow evolution. Using this model, we design a model predictive controller and apply it to the full-order system via velocity measurements and volumetric forcing. The approach is demonstrated for a cylinder spacing of eight diameters. Vortex shedding is fully suppressed in both the gap region and the downstream wake for Reynolds numbers $Re=50$, $60$, and $70$, while a significant reduction in flow unsteadiness is achieved at $Re=80$. We further show that effective control is possible with limited sensing: suppression is achieved using a single measurement point for $Re=50$ and two-point measurements for $Re=60$ and $70$.

2604.02440Apr 2026

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Revisiting Conservativeness in Fluid Dynamics: Failure of Non-Conservative PINNs and a Path-Integral Remedy

The choice between conservative and non-conservative formulations is a fundamental dilemma in CFD. While non-conservative forms offer intuitive modeling in primitive variables, they typically produce erroneous shock speeds. This paper critically analyzes these formulations, contrasting classical failures against the capabilities of Physics-Informed Neural Networks (PINNs). Using the Adaptive Weight and Viscosity (PINNs-AWV) architecture, we evaluate cases ranging from shallow water equations to unsteady 1D and 2D Euler equations. Results reveal a significant dichotomy: while PINNs-AWV restores physical fidelity in scalar and steady systems, standard non-conservative PINNs fail in unsteady systems like the Sod shock tube. We demonstrate this failure stems from non-vanishing source terms introduced by viscous regularization, which violate the Rankine--Hugoniot jump conditions. To resolve this, we implement a path-integral framework based on Dal Maso--LeFloch--Murat (DLM) theory. By incorporating path-consistent losses in PINNs (PI-PINN) and using path-conservative numerical schemes, we successfully recover correct shock speeds within non-conservative frameworks. Our results prove the path-integral approach provides a rigorous mathematical bridge for physical accuracy in both classical and machine learning solvers, enabling primitive-variable formulations in transient, high-speed simulations.

2604.01968Apr 2026

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Deep learning accelerated solutions of incompressible Navier-Stokes equations on non-uniform Cartesian grids

The pressure Poisson equation (PPE) represents the primary computational bottleneck in fractional step methods for incompressible flow simulations, requiring iterative solutions of large-scale linear systems. We previously introduced HyDEA, a hybrid approach to accelerate the PPE solution process. However, its current implementation is limited to uniform Cartesian grids. Accurately resolving complex flow dynamics near solid boundaries requires local grid refinement, yet extending the original HyDEA to non-uniform Cartesian grids is fundamentally challenging, as its standard convolution operators are inherently ill-suited for processing data with spatially varying resolutions. To address this limitation, we adopt the Mesh-Conv (MConv) operator, which explicitly incorporates grid spacing information into convolution operations. Specifically, MConv operator replaces a subset of the standard convolution operators within the U-Net-based branch network of the deep operator network, with the necessary grid spacing information computed via a novel multi-level distance vector map construction strategy. Building upon this enhanced architecture, the framework seamlessly extends to simulate flows interacting with solid structures using a decoupled immersed boundary projection method. Furthermore, by training exclusively on fabricated linear systems rather than conventional flow-dependent datasets, the model generalizes effortlessly across diverse immersed obstacle geometries with fixed neural network weights. Benchmark results demonstrate that the MConv-based HyDEA significantly outperforms both standalone preconditioned conjugate gradient methods and the standard convolution-based HyDEA in convergence performance on strongly non-uniform Cartesian grids. The robustness and generalizability of the MConv-based HyDEA underscore its potential for real-world computational fluid dynamics applications.

2604.01800Apr 2026

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Small-Scale Dynamo for Full Spectrum of Hydrodynamic Turbulence in Kazantsev Model

A method is proposed for computing coefficients in the Kazantsev equation of small-scale dynamo for the full spectrum of hydromagnetic turbulence comprising the inertial range together with the range of viscous dissipation. The dynamo equation with so-defined coefficients is solved numerically for magnetic (Rm) and hydrodynamic (Re) Reynolds numbers from $10^2$ to $10^8$. The threshold value ${\rm Rm}_c$ for onset of dynamo increases initially with Re but then saturates at a constant value of ${\rm Rm}_c \simeq 300$ for ${\rm Re}\geq 10^5$. In the case of small Prandtl number Pm = Rm/Re << 1, the field growth rate is also small and depends logarithmically on Rm. In this case, the magnetic energy spectrum peaks around the scale of Ohmic dissipation, which decreases with increasing Pm. The decrease stops at the scale of viscous dissipation while the growth rate increases sharply when Pm approaches the value of one. The increase in the growth rate proceeds to ${\rm Pm} > 1$ but slows down and then saturates at a value somewhat below the inverse lifetime of most short-living eddies. An explanation of the results is proposed.

2604.01718Apr 2026

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Rapidly rotating internally heated convection: bounds on long-time averages

Convection on geophysical and astrophysical scales is subject to rapid rotation and strong heating from within the domain. In studying the long-time behaviour of the solutions for such a system, energy identities fail to capture the effects of rotation because the Coriolis force does no work, and rapid rotation can be prohibitive for direct numerical simulations. Instead, we derive an asymptotically reduced model for rapidly rotating convection driven by uniform internal heating between isothermal stress-free boundaries in a plane periodic layer. The main contribution is the proof of bounds on the mean temperature, and the mean vertical convective heat transport, in terms of the Rayleigh and Ekman numbers, in the limit of infinite Prandtl number. The first quantity represents the mixing of the flow, and the second the asymmetry in heat leaving the bottom and top boundaries due to convection, and unlike Rayleigh-Bénard convection, the two are not a priori related. We employ alternative estimation techniques to those used in previous studies (Grooms \& Whitehead, 2014 \textit{Nonlinearity}, 28, 29) and identify two distinct scaling behaviours for both quantities. Finally, our bounds are optimised, within the methodology, and provide a rigorous constraint for future studies of rotation-dominated internally heated convection.

2604.01380Apr 2026

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A Shakhov-based Bhatnagar-Gross-Krook model for polyatomic molecules and for atomic as well as polyatomic mixtures

The implementation of the Shakhov Bhatnagar-Gross-Krook (SBGK) method in the open-source particle code PICLas is extended for modeling of polyatomic molecules, as well as mixtures including atoms and molecules, while accounting for non-equilibrium in the internal degrees of freedom. The conservation properties of the model are shown and the model parameter for the Prandtl number is derived. In order to determine the viscosity and thermal conductivity of gas mixtures, the first approximation of the transport properties using collision integrals is employed. The model is verified with simulation test cases of a supersonic Couette flow and a hypersonic flow around a 70° blunted cone with different flow parameters and gas compositions. The results are compared to the Direct Simulation Monte Carlo (DSMC) method as well as the Ellipsoidal Statistical BGK (ESBGK) method to assess the accuracy of the model, where overall good agreement is achieved. In particular, the proposed SBGK model captures the shock in front of the 70° blunted cone more precisely than the ESBGK model.

2604.01377Apr 2026

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Branching Paths Statistics for confined Flows : Adressing Navier-Stokes Nonlinear Transport

Recent advances have allowed to tackle exact path-space probabilistic representations of macroscopic advection-diffusion models involving advection nonlinearities by step forward approaches in terms of continuous branching stochastic processes. Yet, the need of such paradigm shift is huge for the broad flied of fluid flows. In deed, wherever for climate dynamics, engeenering, geophysical and planetary formations, or biomedical applications, complex transport phenomena involving diffusion and advection in confined domains set the physics. In this work, we advance this framework by casting such branching representations within the class of Navier-Stokes strongly nonlinear transport. This yields novel propagator representations for fluid dynamics and opens new routes for efficient simulations of fluids in confined domains by use of new Backward Monte Carlo algorithms.

2604.01292Apr 2026

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Two-stage dispersion mechanism of clean spherical bubbles rising in a chain

Wake-induced lift is a key mechanism governing the initial destabilization of bubbles rising in a chain (Atasi et al., 2023). Moore's wake model predicts limited interfacial vorticity and a relatively slender, spatially confined wake for clean spherical bubbles, suggesting that wake-mediated interactions weaken as the inter-bubble spacing increases. However, we observed pronounced large-scale lateral dispersion and strong bubble frequency dependence in controlled experiments where bubble diameter and generation frequency were independently varied, even when the inter-bubble separation exceed the characteristic wake length. A reduced-order model incorporating pairwise wake-induced interactions captured the onset of bubble chain destabilization but systematically underpredicted the subsequent emergence of large-scale dispersion. We demonstrate that bubbles rising in a chain collectively generate a mean upward liquid flow that modifies the local shear field, enhancing the lateral migration through shear-induced lift. Incorporating this self-induced weak flow into the model quantitatively reproduced both the dispersion magnitude and its frequency dependence. These results suggest that the dispersion of bubbles rising in a chain involves a two-stage mechanism, with initial chain destabilization mediated by wake interactions, followed by flow modification arising from two-way coupling between bubbles and the liquid. This collective mechanism highlights the importance of self-induced mean flow effects in continuum descriptions of bubble flows.

2604.00612Apr 2026

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Numerical Bow Shock Instabilities in Inert Polyatomic Gases

We investigate inviscid numerical instabilities that arise in simulations of axisymmetric flow over a hypersonic sphere in an inert, calorically perfect gas at low specific heat ratio ($γ\approx 1.1$--$1.2$). We show that when the density ratio across the bow shock is high and the computational mesh is relatively coarse, numerically induced traveling-wave instabilities of the carbuncle type can develop in the shock layer near stagnation for inert gases. These instabilities, not previously documented in the literature, are noteworthy because bow shock oscillations are also observed experimentally in polyatomic gases exhibiting post-shock thermochemical relaxation. When such gases are modeled as inert with an effectively low $γ$, our results emphasize the need for caution to avoid conflating genuine physical instabilities with numerical artifacts in simulations.

2604.00577Apr 2026

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Turbulent heat transfer enhancement by compliant walls

This study investigates the effect of compliant walls on the turbulent heat transfer in channel flows over viscous-hyperelastic walls. We perform Direct Numerical Simulations, fully resolving the mutual fluid-structure interactions between the turbulent flow and the compliant walls, varying the wall elasticity and the thermal diffusivity in a fully turbulent condition. We show that the compliant wall leads to an increase not only of the momentum transfer but also of the heat transfer. Since the compliant wall can dynamically move, in the near-wall region heat flux is mostly transferred via turbulent convection rather than diffusion, as typically found with rigid walls. Thus, the heat flux can be controlled not only by varying the thermal diffusivity, but also by changing the transverse modulus of elasticity which governs the wall-normal velocity fluctuations and consequently the temperature ones. Finally, we show that the physical mechanism controlling these modifications are the sweep and ejection events.

2604.00484Apr 2026

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Predictor-Driven Diffusion for Spatiotemporal Generation

Multiscale spatial structure complicates temporal prediction because small-scale spatial fluctuations influence large-scale evolution, yet resolving all scales is often intractable. Standard diffusion models do not address this problem effectively since they apply uniform decay across all Fourier modes. We propose Predictor-Driven Diffusion, a framework that combines renormalization-group-based spatial coarse-graining with a path-integral formulation of temporal dynamics. The forward process applies scale-dependent Laplacian damping together with additive noise, producing a hierarchy of coarse-grained fields indexed by diffusion scale $λ$. Training minimizes the Kullback-Leibler divergence between data-induced and predictor-induced path densities, leading to a simple regression loss on temporal derivatives. The resulting predictor captures how eliminated small-scale components statistically influence large-scale evolution. A key insight is that the same predictor provides a path score for reverse-$λ$ sampling, unifying simulation, unconditional generation, and super-resolution in a single framework. Our unified approach is validated through experiments on two multiscale turbulent systems.

2604.00327Mar 2026

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Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures

High-curvature observables in incompressible flows, including $k^4$-weighted spectra, can arise from explicit internal rotation, elimination of a fast spin variable, or polynomial higher-gradient closure. Building on a retained-spin micropolar closure derived separately from the Boltzmann--Curtiss equation, we show that these mechanisms are dynamically distinguishable in transverse linear response. In a fast-spin regime the retained-spin theory reduces to a one-field model with a rational $k$-dependent kernel whose low-$k$ expansion generates $k^4$ and $k^6$ terms, while preserving the large-$k$ roll-off of the eliminated degree of freedom. We compare four closures: incompressible Navier--Stokes, a polynomial Burnett-type surrogate, the explicit-spin micropolar theory, and the eliminated-spin rational-kernel theory. The explicit-spin theory has two poles, the eliminated-spin theory retains only the slow pole, and finite polynomial truncations fail qualitatively: a strict $k^4$ truncation becomes over-damped, while a matched $k^6$ truncation develops near-critical amplification and finite-$k$ instability. Many-particle event-driven simulations of perfectly rough spheres show that these observables are measurable and, in targeted campaigns, discriminating at the microscopic level: fixed-$k$ and multi-$k$ harmonic forcing resolve a finite spin-to-vorticity phase lag that strongly favors retained-spin dynamics over instantaneous adiabatic elimination, while the stronger-drive multi-$k$ vorticity response rejects a pure $k^2$ closure and favors the rational eliminated-spin kernel over a polynomial surrogate. Transverse response thus provides a practical diagnostic for separating retained rotational microphysics, eliminated-spin effective dynamics, and ordinary polynomial higher-gradient closures.

2604.00177Mar 2026

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Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence

Recent advances in data-driven turbulence modeling have established tensor basis neural networks (TBNN) as a physically grounded framework for Reynolds-stress closure in Reynolds-averaged Navier-Stokes (RANS) simulations. However, their robustness in wall-bounded turbulent flows remains limited across Reynolds numbers and geometries due to the lack of an intrinsic scaling mechanism. In this work, we propose a self-scaling tensor basis neural network (STBNN) for Reynolds-stress modeling of wall-bounded turbulence. The model incorporates an invariant velocity-gradient normalization derived from the first two invariants of the velocity-gradient tensor, providing an intrinsic and geometry-independent scale that balances strain and rotation effects without relying on empirical coefficients or wall-distance inputs. Owing to its frame-indifferent formulation, the approach preserves Galilean and rotational invariance while maintaining a physically interpretable representation of Reynolds-stress anisotropy. STBNN is evaluated through a priori and a posteriori studies using direct numerical simulation (DNS) data of canonical wall-bounded flows, including plane channel and periodic hill flows. In a priori tests, the model accurately reproduces Reynolds-stress anisotropy, with correlation coefficients exceeding 99% and relative errors below 10%, while capturing near-wall scaling and logarithmic-layer behavior. In a posteriori RANS simulations, STBNN predicts mean velocity profiles in close agreement with DNS and improves prediction of separation and reattachment compared with linear and quadratic eddy-viscosity models and the baseline TBNN. Notably, a model trained at low Reynolds numbers generalizes to higher Reynolds numbers and unseen geometries. These results demonstrate the effectiveness of the proposed framework for data-driven Reynolds-stress modeling in wall-bounded turbulent flows.

2603.29659Mar 2026

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A framework for diagnosing inertial lift generation in wall-bounded flows: application to eccentric rotating cylinders in Newtonian and shear-thinning fluids

A body moving in a wall-bounded flow often experiences a hydrodynamic lift force normal to the wall, which plays an important role in many fluid systems. In this study, we develop a framework for diagnosing steady inertial lift from the internal structure of the flow field. Based on the generalised reciprocal theorem for finite-Reynolds-number flows, the lift is expressed as a volume integral that identifies both the dominant contributions and the regions from which they arise. We apply this framework to numerically obtained steady flows of Newtonian and shear-thinning fluids between eccentric rotating cylinders, and analyse the lift acting on the inner cylinder undergoing rotation and orbital motion. In particular, we focus on lift reversal induced by increasing eccentricity in a Newtonian fluid and on lift reversal induced by stronger shear-thinning behaviour at high eccentricity. The volume-integral expression decomposes the lift into a vortex-force contribution associated with inertia and a viscous stress contribution associated with the non-uniform viscosity field, and shows that the former dominates over the parameter range considered here. As the eccentricity increases, negative relative vorticity, and in some cases tangential velocity, become stronger in the narrow-gap region, thereby enhancing the negative local vortex-force contribution and inducing lift reversal. Stronger shear-thinning behaviour, on the other hand, amplifies negative relative vorticity near the inner cylinder, thereby increasing the positive local vortex-force contribution and inducing lift reversal. These results demonstrate that the proposed framework is useful for diagnosing and interpreting steady inertial lift in wall-bounded flows.

2603.29605Mar 2026

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Piezoelectric tiles for passive flow rate monitoring across a surface

We introduce a method for measuring the velocity of turbulent fluid flow passing through a pipe using piezoelectric tiles without penetrating the pipe, and without having previously designed the pipe to easily allow monitoring. To measure the flow, the vibrations induced on the pipe by the fluctuating pressure loading induced by the turbulent flow are measured and compared across flow speeds to establish effective invertible relationships from vibration to velocity. Measurements are reported for instrumented pipes transporting, in separate experiments, water and air. The water experiment was able to resolve linear velocity differences on the order of 1~cm/second, while the air experiment was able to resolve on the order of 15~cm/sec. Turned inside out, a similar system might be used to assess external flow velocity, determine differential velocities on opposite sides of a body traveling through air and water, and thus provide navigational data in the form of speed and attitude/angle of attack information. Although this approach is prototyped for a single sensor, it is likely to benefit substantially from the noise suppression possible when employing an array of sensors.

2603.29081Mar 2026

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Data-informed lifting line theory

We present a data-driven framework that extends the predictive capability of classical lifting-line theory (LLT) to a wider aerodynamic regime by incorporating higher-fidelity aerodynamic data from panel method simulations. A neural network architecture with a convolutional layer followed by fully connected layers is developed, comprising two parallel subnetworks to separately process spanwise collocation points and global geometric/aerodynamic inputs such as angle of attack, chord, twist, airfoil distribution, and sweep. Among several configurations tested, this architecture is most effective in learning corrections to LLT outputs. The trained model captures higher-order three-dimensional effects in spanwise lift and drag distributions in regimes where LLT is inaccurate, such as low aspect ratios and high sweep, and generalizes well to wing configurations outside both the LLT regime and the training data range. The method retains LLT's computational efficiency, enabling integration into aerodynamic optimization loops and early-stage aircraft design studies. This approach offers a practical path for embedding high-fidelity corrections into low-order methods and may be extended to other aerodynamic prediction tasks, such as propeller performance.

2603.29051Mar 2026

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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.

2603.28884Mar 2026

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Fluid Dynamics Papers (physics.flu-dyn) - ScienceStack

1,896 papers

Bifurcations in Stokes Flow Sedimentation

2604.03193Apr 2026

View

How pore-scale disorder controls fluid stretching in porous media

2604.02981Apr 2026

View

A Multimodal Vision Transformer-based Modeling Framework for Prediction of Fluid Flows in Energy Systems

2604.02483Apr 2026

View

Parametric Reduced-Order modeling and Closed-Loop Control of Tandem-Cylinder Wakes

2604.02440Apr 2026

View

Revisiting Conservativeness in Fluid Dynamics: Failure of Non-Conservative PINNs and a Path-Integral Remedy

2604.01968Apr 2026

View

Deep learning accelerated solutions of incompressible Navier-Stokes equations on non-uniform Cartesian grids

2604.01800Apr 2026

View

Small-Scale Dynamo for Full Spectrum of Hydrodynamic Turbulence in Kazantsev Model

2604.01718Apr 2026

View

Rapidly rotating internally heated convection: bounds on long-time averages

2604.01380Apr 2026

View

A Shakhov-based Bhatnagar-Gross-Krook model for polyatomic molecules and for atomic as well as polyatomic mixtures

2604.01377Apr 2026

View

Branching Paths Statistics for confined Flows : Adressing Navier-Stokes Nonlinear Transport

2604.01292Apr 2026

View

Two-stage dispersion mechanism of clean spherical bubbles rising in a chain

2604.00612Apr 2026

View

Numerical Bow Shock Instabilities in Inert Polyatomic Gases

2604.00577Apr 2026

View

Turbulent heat transfer enhancement by compliant walls

2604.00484Apr 2026

View

Predictor-Driven Diffusion for Spatiotemporal Generation

2604.00327Mar 2026

View

Distinct transverse-response signatures of retained-spin, eliminated-spin, and polynomial Burnett-type surrogate closures

2604.00177Mar 2026

View

Self-scaling tensor basis neural network for Reynolds stress modeling of wall-bounded turbulence

2603.29659Mar 2026

View

A framework for diagnosing inertial lift generation in wall-bounded flows: application to eccentric rotating cylinders in Newtonian and shear-thinning fluids

2603.29605Mar 2026

View

Piezoelectric tiles for passive flow rate monitoring across a surface

2603.29081Mar 2026

View

Data-informed lifting line theory

2603.29051Mar 2026

View

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

2603.28884Mar 2026

View

Page 1 of 95