High-fidelity fluid simulations are central to understanding transport phenomena, yet resolving large or geometrically complex systems remains computationally prohibitive with existing methods. Here we introduce a tensor-network formulation of the lattice Boltzmann method based on matrix product states (MPS), commonly known as a quantum-inspired approach, enabling compressed representations of structured flow fields with inherent error control. We demonstrate the generality of the method on flows through structured media and complex vascular geometries, establishing for the first time that tensor-network techniques can efficiently resolve fluid dynamics in complex, irregular domains. We show that in the presence of translational or approximate symmetries of the geometry, fluid states exhibit low effective complexity in MPS form, yielding compression ratios exceeding two orders of magnitude while preserving physical structure and dynamical fidelity. This reduction enables systematic numerical exploration of regimes that were previously intractable. Our results position tensor networks as a scalable paradigm for continuum mechanics.

Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting framework, we show that standard DDPMs induce a fundamental \emph{spectral collapse}: a Fourier-space analysis of the forward SDE reveals a closed-form, mode-wise signal-to-noise ratio (SNR) that decays monotonically in wavenumber, $|k|$ for spectra $S(k)\!\propto\!|k|^{-\lambda}$, rendering high-wavenumber modes indistinguishable from noise and producing an intrinsic spectral bias. We reinterpret the noise schedule as a spectral regularizer and introduce power-law schedules $\beta(\tau)\!\propto\!\tau^\gamma$ that preserve fine-scale structure deeper into diffusion time, along with \emph{Lazy Diffusion}, a one-step distillation method that leverages the learned score geometry to bypass long reverse-time trajectories and prevent high-$k$ degradation. Applied to high-Reynolds-number 2D Kolmogorov turbulence and $1/12^\circ$ Gulf of Mexico ocean reanalysis, these methods resolve spectral collapse, stabilize long-horizon autoregression, and restore physically realistic inertial-range scaling. Together, they show that naïve Gaussian scheduling is structurally incompatible with power-law physics and that physics-aware diffusion processes can yield accurate, efficient, and fully probabilistic surrogates for multiscale dynamical systems.

Configuring computational fluid dynamics (CFD) simulations requires significant expertise in physics modeling and numerical methods, posing a barrier to non-specialists. Although automating scientific tasks with large language models (LLMs) has attracted attention, applying them to the complete, end-to-end CFD workflow remains a challenge due to its stringent domain-specific requirements. We introduce CFD-copilot, a domain-specialized LLM framework designed to facilitate natural language-driven CFD simulation from setup to post-processing. The framework employs a fine-tuned LLM to directly translate user descriptions into executable CFD setups. A multi-agent system integrates the LLM with simulation execution, automatic error correction, and result analysis. For post-processing, the framework utilizes the model context protocol (MCP), an open standard that decouples LLM reasoning from external tool execution. This modular design allows the LLM to interact with numerous specialized post-processing functions through a unified and scalable interface, improving the automation of data extraction and analysis. The framework was evaluated on benchmarks including the NACA~0012 airfoil and the three-element 30P-30N airfoil. The results indicate that domain-specific adaptation and the incorporation of the MCP jointly enhance the reliability and efficiency of LLM-driven engineering workflows.

We analyse the stability of viscoelastic Dean flow (flow of an elastic fluid through a curved two-dimensional channel, driven by an azimuthal pressure gradient) in the absence of fluid inertia. This configuration is well known to exhibit a hoop-stress-driven `purely elastic' instability (referred to henceforth as the hoop-stress mode -- `HSM') on account of the base-flow streamline curvature. The objective of this study is to demonstrate the existence and importance of a distinct elastic instability in this flow configuration, which is not driven by hoop-stresses, but instead is a continuation of a novel `centre-mode' (CM) instability recently identified in rectilinear shear flows. We use both the Oldroyd-B and FENE-P models to map out parameter regimes in the $W\!i$--$\epsilon$--$\beta$ space where the aforementioned instabilities are present. Here, $W\!i$ is a suitably defined Weissenberg number that characterizes fluid elasticity, $\beta$ is the ratio of solvent to total solution viscosity, and $\epsilon$ is the ratio of the gap (channel) width to the radius of curvature. For FENE-P model, decreasing the finite extensibility parameter $L$ has opposing effects on the HSM and CM instabilities -- stabilising the former, but destabilising the latter. In the dilute solution regime ($\beta > 0.95$), and for realistic values of $L \sim O(100)$, corresponding to polymer molecular weights of $O(10^{5-6})$g/mol, the CM remains the most unstable mode for $\epsilon \leq 0.25$, rendering it potentially relevant to the onset of elastic turbulence in the flow of such polymer solutions through curved channels.

The linear and non-linear dynamics of centrifugal instability in Taylor-Couette flow are investigated when fluids are stably stratified and highly diffusive. One-dimensional local linear stability analysis (LSA) on cylindrical Couette flow confirms that the stabilising role of stratification on centrifugal instability is suppressed by strong thermal diffusion (i.e. low Prandtl number $Pr$). For $Pr\ll1$, it is verified that the instability dependence on thermal diffusion and stratification with the non-dimensional Brunt-Väisälä frequency $N$ can be prescribed by a single rescaled parameter $P_{N}=N^{2}Pr$. From direct numerical simulation (DNS), various non-linear features such as axisymmetric Taylor vortices at saturation, secondary instability leading to non-axisymmetric patterns or transition to chaotic states are investigated for various values of $Pr\leq1$ and the Reynolds number $Re_{i}$. Two-dimensional bi-global LSA on axisymmetric Taylor vortices, which appear as primary centrifugal instability saturates nonlinearly, is also performed to find the secondary critical Reynolds number $Re_{i,2}$ at which the Taylor vortices become unstable by non-axisymmetric perturbation. The bi-global LSA reveals that $Re_{i,2}$ increases (i.e. the onset of secondary instability is delayed) in the range $10^{-3}

The paper presents a two-phase hydrodynamic model for the numerical simulation of collective motion in a thin layer of active colloids containing spherical microswimmers. The model accounts for three fundamental mechanisms governing the dynamics of the active colloid: the random motion of the microswimmers, their mutual collisions, and their interaction with the surrounding fluid phase. The accurate resolution of the characteristic time scales associated with each mechanism is crucial for reproducing the different dynamic modes. The model reproduces two primary modes of motion: Brownian and collective, as well as the transition between them. It is demonstrated that hydrodynamic interactions begin to play a significant role when the microswimmer velocity exceeds a critical threshold. At this point, the kinetic energy transferred to the fluid phase is sufficient to generate a noticeable feedback effect on the swimmers' motion. Conversely, a further increase in microswimmers' velocity enhances the role of collisions, causing the system to revert from a collective mode back to a Brownian-like state. A similar transition occurs at higher volume fractions of microswimmers within the colloid.

Zermelo's navigation problem seeks the trajectory of minimal travel time between two points in a fluid flow. We address this problem for an agent -- such as a micro-robot or active particle -- that is advected by a two-dimensional flow, self-propels at a fixed speed smaller than or comparable to the characteristic flow velocity, and can steer its direction. The flows considered span increasing levels of complexity, from steady solid-body rotation to the Taylor-Green flow and fully developed turbulence in the inverse cascade regime. Although optimal control theory provides time-minimizing trajectories, these solutions become unstable in chaotic regimes realized for complex background flows. To design robust navigation strategies under such conditions, we apply reinforcement learning. Both action-value (Q-learning) and policy-gradient (one-step actor-critic) methods achieve successful navigation with comparable performance. Crucially, we show that agents trained on coarse-grained flows -- retaining only large-scale features -- generalize effectively to the full turbulent field. This robustness to incomplete flow information is essential for practical navigation in real-world oceanic and atmospheric environments.

The variability of X-rays observed from accreting black hole systems, including quasi-periodic oscillations (QPOs), suggests a complex nonlinear dynamics in the corona. Here, we propose a new theoretical framework for this problem, based on non-equilibrium thermodynamics. In this model, coronal variability arises from feedback between a macroscopic oscillation of the plasma and the rate at which it is cooled by the inverse Compton scattering of soft photons from the disc. The "pair thermostat'' mechanism then allows the corona to act as a heat engine that extracts work cyclically from the underlying thermal disequilibrium between the low-entropy heating and the high-entropy cooling by the soft photons, in close analogy to the well-known $\kappa$-mechanism for pulsating stars. This coronal self-oscillation may explain QPOs without the need to invoke an external resonant driving. Moreover, we argue that this mechanism can provide the power to generate turbulence and jets in the corona.

Compressibility transformations are used to relate hypersonic zero-pressure-gradient (ZPG) turbulent boundary layers (TBLs) to incompressible reference states, but their assessment has largely focused on the collapse of transformed mean velocity profiles, without enforcing a unique, Mach-independent representation of the mean shear. In this work, a stricter consistency condition is proposed, requiring that a single incompressible inner-outer model for the mean velocity gradient reproduce all transformed compressible profiles when expressed in terms of a transformed wall-normal coordinate. This implies collapse not only of the transformed mean velocity but also of semilocal eddy viscosity and TKE production. Existing compressibility transformations are shown, using hypersonic DNS, to incur velocity errors of 1-25% relative to the incompressible inner-outer model, particularly for strongly cooled cases. A new forward compressible-to-incompressible transformation is developed that constructs the transformed coordinate as a convex combination of semilocal and integral-type basis functions with coefficients modeled as functions of friction Mach number and wall heat transfer rate. Casewise optimization yields consistency errors of 1-4% across the available hypersonic DNS set, and this performance is retained using multi-linear and multi-quadratic regressions. The forward transformation is embedded in an inverse incompressible-to-compressible transformation framework, which reconstructs the compressible state from freestream and wall conditions at a prescribed BL thickness. The inverse solver recovers key BL parameters, velocity profiles, and skin friction distributions with good accuracy, and generally improves upon existing models for cold-wall hypersonic TBLs, thereby providing a physically constrained basis for near-wall modeling in hypersonic TBLs with strong wall cooling.

The integration of artificial intelligence into experimental fluid mechanics promises to accelerate discovery, yet most AI applications remain narrowly focused on numerical studies. This work proposes an AI Fluid Scientist framework that autonomously executes the complete experimental workflow: hypothesis generation, experimental design, robotic execution, data analysis, and manuscript preparation. We validate this through investigation of vortex-induced vibration (VIV) and wake-induced vibration (WIV) in tandem cylinders. Our work has four key contributions: (1) A computer-controlled circulating water tunnel (CWT) with programmatic control of flow velocity, cylinder position, and forcing parameters (vibration frequency and amplitude) with data acquisition (displacement, force, and torque). (2) Automated experiments reproduce literature benchmarks (Khalak and Williamson [1999] and Assi et al. [2013, 2010]) with frequency lock-in within 4% and matching critical spacing trends. (3) The framework with Human-in-the-Loop (HIL) discovers more WIV amplitude response phenomena, and uses a neural network to fit physical laws from data, which is 31% higher than that of polynomial fitting. (4) The framework with multi-agent with virtual-real interaction system executes hundreds of experiments end-to-end, which automatically completes the entire process of scientific research from hypothesis generation, experimental design, experimental execution, data analysis, and manuscript preparation. It greatly liberates human researchers and improves study efficiency, providing new paradigm for the development and research of experimental fluid mechanics.

Fast, geometry-generalizing surrogates for unsteady flow remain challenging. We present a time-dependent, geometry-aware Deep Operator Network that predicts velocity fields for moderate-Re flows around parametric and non-parametric shapes. The model encodes geometry via a signed distance field (SDF) trunk and flow history via a CNN branch, trained on 841 high-fidelity simulations. On held-out shapes, it attains $\sim 5\%$ relative L2 single-step error and up to 1000X speedups over CFD. We provide physics-centric rollout diagnostics, including phase error at probes and divergence norms, to quantify long-horizon fidelity. These reveal accurate near-term transients but error accumulation in fine-scale wakes, most pronounced for sharp-cornered geometries. We analyze failure modes and outline practical mitigations. Code, splits, and scripts are openly released at: this https URL to support reproducibility and benchmarking.

Quantum algorithms have been identified as a potential means to accelerate computational fluid dynamics (CFD) simulations, with the lattice Boltzmann method (LBM) being a promising candidate for realizing quantum speedups. Here, we extend the recent quantum algorithm for the incompressible LBM to account for realistic fluid dynamics setups by incorporating walls, inlets, outlets, and external forcing. We analyze the associated complexity cost and show that these modifications preserve the asymptotic scaling, and potential quantum advantage, of the original algorithm. Moreover, to support our theoretical analysis, we provide a classical numerical study illustrating the accuracy, complexity, and convergence of the algorithm for representative incompressible-flow cases, including the driven Taylor-Green vortex, the lid-driven cavity flow, and the flow past a cylinder. Our results provide a pathway to accurate quantum simulation of nonlinear fluid dynamics, and a framework for extending quantum LBM to more challenging flow configurations.

Driven by the advancement of GPUs and AI, the field of Computational Fluid Dynamics (CFD) is undergoing significant transformations. This paper bridges the gap between the machine learning and CFD communities by deconstructing industrial-scale CFD simulations into their core components. Our main contribution is to propose the first scaling law that incorporates CFD inputs for both data generation and model training to outline the unique challenges of developing and deploying these next-generation AI models for complex fluid dynamics problems. Using our new scaling law, we establish quantitative estimates for the large-scale limit, distinguishing between regimes where the cost of data generation is the dominant factor in total compute versus where the cost of model training prevails. We conclude that the incorporation of high-fidelity transient data provides the optimum route to a foundation model. We constrain our theory with concrete numbers, providing the first public estimates on the computational cost and time to build a foundation model for CFD.

A key aspect of learned partial differential equation (PDE) solvers is that the main cost often comes from generating training data with classical solvers rather than learning the model itself. Another is that there are clear axes of difficulty--e.g., more complex geometries and higher Reynolds numbers--along which problems become (1) harder for classical solvers and thus (2) more likely to benefit from neural speedups. Towards addressing this chicken-and-egg challenge, we study difficulty transfer on 2D incompressible Navier-Stokes, systematically varying task complexity along geometry (number and placement of obstacles), physics (Reynolds number), and their combination. Similar to how it is possible to spend compute to pre-train foundation models and improve their performance on downstream tasks, we find that by classically solving (analogously pre-generating) many low and medium difficulty examples and including them in the training set, it is possible to learn high-difficulty physics from far fewer samples. Furthermore, we show that by combining low and high difficulty data, we can spend 8.9x less compute on pre-generating a dataset to achieve the same error as using only high difficulty examples. Our results highlight that how we allocate classical-solver compute across difficulty levels is as important as how much we allocate overall, and suggest substantial gains from principled curation of pre-generated PDE data for neural solvers. Our code is available at this https URL

We present a comprehensive validation, performance characterization, and scalability analysis of a hardware-accelerated phase-averaged multiscale solver designed to simulate acoustically driven dilute bubbly suspensions. The carrier fluid is modeled using the compressible Navier-Stokes equations. The dispersed phase is represented through two distinct subgrid formulations: a volume-averaged model that explicitly treats discrete bubbles within a Lagrangian framework, and an ensemble-averaged model that statistically represents the bubble population through a discretized distribution of bubble sizes. For both models, the bubble dynamics are modeled via the Keller--Miksis equation. For the GPU cases, we use OpenACC directives to offload computation to the GPUs. The volume-averaged model is validated against the analytical Keller-Miksis solution and experimental measurements, showing excellent agreement with root-mean-squared errors of less than 8% for both single-bubble oscillation and collapse scenarios. The ensemble-averaged model is validated by comparing it to volume-averaged simulations. On an NCSA Delta node with 4 NVIDIA A100 GPUs, we observe a speedup 16-fold compared to a 64-core AMD Milan CPU. The ensemble-averaged model offers additional reductions in computational cost by solving a single set of averaged equations, rather than multiple stochastic realizations. However, the volume-averaged model enables the interrogation of individual bubble dynamics, rather than the averaged statistics of the bubble dynamics. Weak and strong scaling tests demonstrate good scalability across both CPU and GPU platforms. These results show the proposed method is robust, accurate, and efficient for the multiscale simulation of acoustically driven dilute bubbly flows.

While experiencing atmospheric turbulence on a commercial flight can be uncomfortable, it rarely compromises the stability of the aircraft. The situation is quite different for small air vehicles that operate in urban canyons, around mountainous terrains, and in the wakes of marine vessels, where they could encounter highly unsteady atmospheric conditions with relatively strong gusts. The spatiotemporal scales of such disturbances can be larger than the characteristic aerodynamic scales of the small vehicles, making the relative effect of disturbance significantly stronger than what a large commercial aircraft would experience. The gust ratio can exceed 1 in these extreme flight environments, making stable flight difficult, if not currently impossible. We refer to the study of aerodynamics for gust ratios over 1, extreme aerodynamics, and identify major challenges that require breakthroughs, particularly with data-driven approaches. Extreme aerodynamics present unique opportunities for innovative analysis techniques to study rich flow physics problems with strong nonlinearity, transient dynamics, and low-dimensional modeling over a large parameter space. Some of the approaches discussed herein should apply to a wider range of fluid dynamics problems with similar challenges.

Particle-like chiral magnetic skyrmions can flow in nanotracks and behave like chiral fluids. Using interacting flows to perform logical operations is an important topic in microfluidics and nanofluidics. Here, we report a basic nanofluidic logic computing system based on chiral magnetic skyrmions flowing in parallel pipelines connected by an H-shaped junction. The flow behaviors could be manipulated by adjusting the spin polarization angle, which controls the intrinsic skyrmion Hall angle. We demonstrate that within certain range of the spin polarization angle, fully developed skyrmion flows could lead to fluidic logical operations, which significantly reduce the complexity of skyrmion logic as there is no need for deterministic creation, precise control, and detection of a single isolated skyrmion. Our results suggest that the chiral flow behaviors of magnetic quasiparticles may offer possibilities for spintronic and nanofluidic functions.

The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity in solving this problem due to their ability to learn complex patterns from data and generalize across diverse conditions. Among these, diffusion models have emerged as particularly powerful in generative tasks, producing high-quality samples by iteratively refining noisy inputs. In contrast to other methods, these generative models are capable of reconstructing the smallest scales of the fluid spectrum. In this work, we introduce a novel sampling method for diffusion models that enables the reconstruction of high-fidelity samples by guiding the reverse process using the available sparse data. Moreover, we enhance the reconstructions with available physics knowledge using a conflict-free update method during training. To evaluate the effectiveness of our method, we conduct experiments on 2 and 3-dimensional turbulent flow data. Our method consistently outperforms other diffusion-based methods in predicting the fluid's structure and in pixel-wise accuracy. This study underscores the remarkable potential of diffusion models in reconstructing flow field data, paving the way for their application in Computational Fluid Dynamics research.

We present an efficient neural-based approach to estimate the instantaneous flow field around an airfoil from limited surface pressure measurements. The model, denoted SNN-POD, relies on two independent shallow neural networks to predict the instantaneous flow over a wide range of angles of attack [10{\textdegree},20{\textdegree}]. At all angles the global model correctly recovers the average characteristics of the flow from single-time sensor data, thus allowing combination with local, angle-dependent models. The method is applied to 2D URANS simulations of a thick airfoil at a Reynolds number of Re=4.5e6. The training set consists of snapshots obtained from a coarse sampling (1-2{\textdegree}) of the angle of attack range. A variance-based criterion is used to determine the number and positions of sensors. Tests are carried out for unseen snapshots at angles of attack within the set (sampled angles) as well as outside the set (interpolated angles). The maximum MSE error of attack for sampled and interpolated angles is respectively 2.9% and 6.6%. This makes it possible to develop adaptive strategies to improve the estimation if necessary.