Optical images of transparent three-dimensional objects can be different from a replica of the object's cross section in the image plane due to refraction at the surface or in the body of the object. Simulations of the object's image are thus needed for the visualization and validation of physical models. We report ray-tracing image simulations that achieved high physical fidelity, reproducing optical behaviors and image features not rendered in previous studies. We replicated brightfield microscopy images of drops with complex shapes and images of pressure and shock waves traveling inside them. For high physical fidelity, the simulations must replicate the spatial and angular distribution of illumination rays, and both the experiment and the simulation must be designed for accurate optical modeling. The simulations are highly sensitive to the properties of the drops and can be used to diagnose and refine fluid dynamics models. The simulated images can also be optimized to extract multiple 3D properties from experimental images. Compared to specialized single-shot 3D imaging methods, this approach has the advantage that it preserves the experimental simplicity, the high resolution, and the visual interpretability characteristic to basic optical imaging. The techniques introduced here are directly applicable to optical microscopy, so they can be used in other fields, such as microfluidics and biology, to expand the type and the accuracy of three-dimensional information that can be extracted from basic optical images.

The present work proposes a general framework that combines the good numerical stability of the lattice Boltzmann model for incompressible flows (LBM-IF) and the flexibility of finite difference/ volume methods in using nonuniform meshes and removing higher-order deviation terms. By adopting the second-order non-equilibrium moment as fundamental variables and neglecting higher-order non-equilibrium moments, to approximately increase entropy in the collision process, the non-equilibrium-moment-based macroscopic equations of LBM-IF are derived. Numerical investigations demonstrate that discretized equations can achieve even better numerical stability than the single-relaxation-time LBM-IF. It is concluded that the good numerical stability of LBM-IF can be roughly interpreted as the entropy increase of the collision step and the diffusion process of the streaming step. However, the discretized non-equilibrium-moments-based macroscopic equations are found to have significant numerical errors at a fixed Reynolds number and very small kinematic viscosities. By combining the non-equilibrium-moments-based and equilibrium-moments-based macroscopic equations, the paper proposes a hybrid model that achieves good numerical stability and accuracy for both small and large kinematic viscosities, even for inviscid flow. The deviation term in the recovered momentum equation of LBM-IF can be easily removed in the hybrid model. Compared with LBM-IF, finite difference/volume solvers based on the hybrid model exhibit better numerical stability and accuracy, as well as superior efficiency in simulations using nonuniform meshes.

Effective control of fluid flows is critical across transportation, energy and medicine, where it can increase lift, reduce drag, enhance mixing and attenuate noise1-3. Yet fluids are notoriously difficult to control because they involve high-dimensional, nonlinear and multiscale dynamics that resist conventional approaches4-6. Reinforcement learning has driven remarkable progress in fields such as protein folding and complex games, which have shared benchmarks and standardized environments7-10. Fluid dynamics has lacked such infrastructure, so each controller is typically tuned to a single geometry and operating condition, making progress difficult to accumulate, transfer and compare11-13. Here we introduce HydroGym, a solver-independent reinforcement learning platform providing more than 60 validated, openly available flow control environments spanning from canonical laminar flows to complex turbulent flows, with systematic progression in the Reynolds number up to Re = 4 × 105, and Mach number variations in two and three dimensions. Across these environments, agents repeatedly discover robust control principles, including boundary layer manipulation, disruption of acoustic feedback and reorganization of turbulent wakes. Critically, we demonstrate a proof of concept for zero-shot transfer, in which agents that are trained exclusively in inexpensive surrogate environments are deployed to challenging real-world scenarios such as a three-dimensional wing section. We achieve a 38% reduction in local skin friction while reducing exploration costs by four orders of magnitude compared with direct on-wing optimization. As this transfer exploits shared near-wall physics, the breadth of generalization remains open, suggesting a new pathway for research toward policy generalization across computationally prohibitive simulation environments. By offering a common, extensible foundation for reproducible research, HydroGym moves flow control from isolated case studies toward a cohesive community effort.

We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly accelerates LBM in reaching steady-states of porous media flows across all macroscopic fields, achieving up to 70

Velocity and temperature distributions are both crucial for modeling compressible wall-bounded turbulent flows. The compressible law of the wall for velocity has been extensively examined through velocity transformations. However, a well-established temperature transformation remains an open issue. We propose new Van Driest type (VD-type) and semi-local type (SL-type) temperature transformation for compressible turbulent channel flow. Our approach is based on an analysis of the momentum and energy balance equations in the overlap layer. It accounts for the influences of mixing length model, the work of the body force, and the turbulent kinetic energy (TKE) flux. The proposed transformations are evaluated using data from direct numerical simulations and wall-resolved large eddy simulations of compressible turbulent channel flow. The SL-type transformation provides better data collapse than the VD-type in the viscous sublayer and buffer layer. With a suitable mixing length model, the SL-type transformed temperature agrees well with the incompressible temperature profile or the extended law of the wall. For the isothermal wall, the integral mean error over the entire boundary layer remains below 2% for most cases, with root mean square value of about 1.7%. The results highlight the importance of mitigating the energy imbalance in the transformation. This work identifies the multi-layer structure of the turbulent TKE flux, which in turn enables approximate models and corresponding simplified yet effective temperature transformations. Applications of the proposed approach in near-wall modeling and inverse transformation, as well as its potential extension to more general configurations, are also discussed.

Supersonic gas-atomization nozzles generate complex compressible flow structures includingshocks, expansion fans, and shear layers that govern droplet breakup and ultimately determinepowder quality. Experimental diagnostics such as Schlieren imaging provide only path-integratedinformation, while high-fidelity computational fluid dynamics remains computationally expen-sive for rapid design exploration. In this work, we investigate denoising diffusion probabilisticmodels as structure-preserving surrogates for reconstructing full flow fields from partial observa-tions. We construct a dataset of approximately 5,000 two-dimensional axisymmetric simulationsacross a broad operating envelope and pair them with synthetic Schlieren inputs generated viaa forward Abel transform. We systematically analyze two key design dimensions: the condition-ing pathway through early and multi-scale fusion, and the training objective by comparing astandard noise-prediction loss with a hybrid loss that incorporates structural similarity. The re-sults show that augmenting the standard diffusion objective with a computationally inexpensivestructural similarity term leads to consistent and substantial improvements across all predictedvariables, including density, Mach number, and velocity magnitude. The hybrid objective re-duces the mean squared error by more than an order of magnitude, improves structural fidelity,stabilizes training, and yields uniform performance across the operating envelope. In contrast,the effectiveness of the conditioning pathway is strongly target-dependent. Multi-scale fusionsignificantly improves performance under pixel-based training, particularly for density fields thatare directly related to the Schlieren signal, but provides more limited gains for other target quan-tities. Once the hybrid loss is employed, the sensitivity to the conditioning strategy is largelymitigated, and both conditioning approaches achieve comparable performance. To assess ro-bustness under limited observational input, we evaluate a reduced-conditioning setting in whichSchlieren guidance is removed, and the model is conditioned only on operating parameters. Although the generation task is inherently more challenging, the hybrid objective retains a clearadvantage over the pixel-based baseline, demonstrating that structural regularization provides ameaningful inductive bias even in the absence of spatial measurements. Overall, these findingsshow that while conditioning strategies can enhance reconstruction in a task-dependent manner,the loss formulation is the dominant factor governing accuracy and physical consistency. Theproposed framework demonstrates the potential of diffusion-based generative models for recon-structing complex compressible flow fields from sparse or indirect measurements and provides afoundation for efficient surrogate modeling in nozzle analysis and design.

We introduce a hybrid approach utilising a quantum machine learning surrogate model to approximate the non-linear collision dynamics of the LBM. It effectively offloads the non-unitary operations that challenge pure quantum solvers. The expressivity of the surrogate is built on the ability of parameterised quantum circuits to implement partial Fourier series, with data re-uploading extending the spectrum of representable frequencies. Unlike previous approaches with a fixed relaxation parameter, the surrogate recovers the complete Bhatnagar-Gross-Krook (BGK) collision dynamics across the full physically admissible range of relaxation without retraining. We reassess the relevance of standard variational quantum circuit (VQC) metrics, including expressibility, entanglement, and effective dimension, by relating them directly to task-specific surrogate performance and identifying the key architectural parameters that determine approximation accuracy. The proposed surrogate is validated against the classical BGK collision operator using established benchmark problems, including the Taylor-Green vortex for evaluating energy dissipation and the double shear layer for assessing shear-driven instabilities and nonlinear flow evolution. Our results demonstrate that the hybrid model achieves high accuracy and generalisability while closely replicating classical solutions. These findings suggest that hybrid quantum-classical strategies offer a practical path toward realising the potential of quantum computing in fluid engineering.

Metal powder production via gas atomization of molten metals relies on inert gases, primarily nitrogen and argon, to meet the high-quality standards required in industries such as additive manufacturing, thermal spraying, or metal injection molding. Physicochemical interactions with the metal typically drive the selection of the atomizing gas. Additionally, the gas temperature T0 is a crucial parameter in the atomization process, as it directly affects the kinetic energy of the gas jet. The transition between open-and closed-wake flow, as a gas dynamic mechanism, is assumed to be a key contributor to process efficiency. This work provides a comprehensive experimental study of underlying mechanisms with Schlieren imaging and aspiration pressure measurement for argon and nitrogen as atomizing gas. Both gases are heated up to T0 approximate to 300 K, respectively approximate to 500 K. Experimental results show no significant differences in varied gas temperatures for nitrogen, in to the argon experiments. The temperature sensitivity of argon is caused by condensation that occurs low temperatures, resulting in non-ideal gas behavior. The transition between open-and closed-wake configurations occurs for one characteristic spatial jet expansion ratio provided ideal gas behavior assumed. The key conclusion is that for transition between open-and closed-wake flow to occur, a specific critical jet expansion ratio needs to be reached.

The collapse of vapour-bubble clusters near solid boundaries generates highly localised pressure loads that can damage propulsion and hydraulic systems but can also be exploited in therapeutic ultrasound applications. Predicting these loads with high-resolution compressible-flow simulations is computationally expensive, particularly when variability in the initial bubble configuration must be considered. This work develops a variational heteroscedastic multi-fidelity Gaussian-process surrogate for the peak area-averaged pressure recorded by a fixed sensor at the wall centre. The model combines numerous inexpensive coarse-grid simulations with a limited number of higher-resolution simulations through a nonlinear autoregressive architecture. At each fidelity level, separate latent processes represent the mean prediction and input-dependent aleatoric variance. The framework is first evaluated using controlled analytical benchmarks and a single-bubble-collapse case before being applied to randomly generated bubble clusters near a rigid wall.Assessed by negative log predictive density, continuous ranked probability score, and predictive-interval coverage, the surrogate is significantly more accurate and better calibrated than a single-fidelity model trained on the same resolved data at a fixed high-fidelity budget, and it captures the configuration-dependent scatter of the peak wall load. By reporting calibrated predictive intervals rather than an accurate mean alone, it enables uncertainty-aware assessment of cavitation loads and provides an inexpensive predictor of the extreme wall loading that governs erosion in engineering flows and therapeutic effect in focused-ultrasound applications.

This study numerically investigates the interaction of planar shock waves with cavity-embedded n-dodecane fuel cylinders under transcritical thermodynamic conditions. Fourteen cases with Mach numbers ranging from 1.2 to 2.1 are simulated using the finite-volume compressible multi-component solver CAvitation Technical University of Munich (CATUM), incorporating an optimized WENO3 reconstruction scheme and a modified Peng-Robinson equation of state. The numerical approach is validated against reference data, and mesh convergence is confirmed through four levels of grid refinement. The analysis highlights the influence of Mach number on wave dynamics, structural deformation, vorticity deposition, circulation growth, and enstrophy evolution. Compared with full-cylinder configurations, cavity-embedded cylinders undergo earlier deformation, faster downstream displacement, and stronger vorticity generation, leading to enhanced fuel-nitrogen mixing, with the effect becoming more pronounced at higher Mach numbers. Quantitative comparisons demonstrate that the proposed modified Zhang-Zou (M-ZZ) model reliably predicts circulation deposition across all examined Mach numbers, with errors of less than 10%. To assess cavity effects, a transcritical-enstrophy model (TEM) is developed, which predicts enstrophy evolution with errors below 12%. In particular, at Mach 2.0 the enstrophy of the cavity case is about 20% higher than that of the non-cavity case, representing the most significant enhancement among all examined conditions. Cavity-induced mechanisms substantially enhance mixing efficiency, which is evidenced by an increase in enstrophy of more than 10% under stronger shocks. These findings provide insights into instability-driven mixing processes in transcritical environments.

The present study introduces and validates a comprehensive numerical model for hydrogen-fueled high-velocity oxygen-fuel (HVOF) spraying of tungsten carbide-cobalt-chromium (WC-Co-Cr) powder. We conduct three-dimensional (3D), two-way coupled simulations of the reactive, particle-laden flow within the DJ2600 thermal spray gun and its supersonic exhaust jet. The model incorporates the real nozzle geometry, applies the eddy-dissipation concept (EDC) as a finite-rate chemistry approach for hydrogen combustion, and uses an explicit algebraic Reynolds stress model (EARSM) for turbulent scales. Consequently, our simulations enable a precise analysis of flame dynamics by revealing unprecedented levels of flow field detail in the nozzle’s convergent section. We find that the interaction of fuel, oxidizer, and cooling air streams produces diverse, three-dimensional flame shapes. Furthermore, we compare the standard particle modeling approach from literature with an enhanced approach that accounts for rarefied flow at the particle scale, viscous heating in the boundary layers around particles, and temperature-dependent particle heat capacities. Our results demonstrate that including these phenomena is critical for correctly predicting particle impact properties. Finally, we analyze particle states both in flight and upon impact on the target surface.

Resolving unsteady transport phenomena in geometrically complex domains is traditionally constrained by polynomial scaling of computational cost with spatial resolution. While methods based on tensor-network data representations or matrix-product states (MPS) data encodings have emerged as a technique to systematically reduce degrees of freedom, existing formulations do not extend to complex geometries and complex flow physics. Both capabilities are offered by lattice Boltzmann methods, for which we develop a generalized MPS formulation. This development marks a paradigm shift from classical methods that rely on explicit grid refinement for data reduction. Instead, our approach exploits non-local correlations in the MPS representation to systemically compress the global fluid state directly without modifying the underlying grid. We benchmark the proposed solver against classical LBM using three-dimensional flows through structured media and vascular geometries. The results confirm that the MPS formulation reproduces the reference solution with high fidelity while achieving compression ratios exceeding two orders of magnitude, positioning tensor networks or MPS encodings as a scalable paradigm for continuum mechanics on high-performance GPU hardware.

We present a general multi-rate (MR) time integration scheme for smoothed particle hydrodynamics (SPH) that enhances computational efficiency while preserving stability and accuracy. Unlike conventional single-rate methods, which enforce the most restrictive time step globally, the proposed approach splits the time advancement operator into substeps pertaining to advection, acoustic, viscous, and thermal effects, and advances each by considering its characteristic time scale. Validation against canonical benchmarks, including the Taylor–Green vortex, a three-dimensional dambreak, thermal Couette flow, and porous media flow, demonstrates that the scheme reproduces analytical solutions and experimental reference data with accuracy equal to that of single-rate integration. At the same time, it significantly reduces computational costs, with speed-ups up to 4 ×  depending on the degree of time-scale difference. The implementation is straightforward. We employ a modular, graphics processing unit (GPU)-accelerated framework. The approach is particularly advantageous for multi-physics problems, where time scales differ widely. This work establishes multi-rate time integration as a robust and efficient alternative to single-rate (SR) schemes for advancing the capabilities of SPH in engineering and scientific applications.

Inert gas atomization is the state-of-the-art production method for manufacturing high-quality metal powder particles (1 mu m to 150 mu m) required in industries such as metal additive manufacturing, metal injection molding, and thermal spraying. Previous research has highlighted the significance of pulsatile atomization mechanisms, which are linked to the efficiency and productivity of the gas atomization process. The melt pulsations are presumably connected to the transitions between open-to closed-wake flow. This work provides new insights into open-/closed-wake flow transition through experimental investigations at an industrial-scale atomization test bench, coupling high-frequency pressure measurements with high-speed Schlieren imaging. By triggering open-/closed-wake flow transition via time variations of the nozzle pressure dp0/dt, an aspiration pressure pAsp to nozzle pressure p0 hysteresis is observed, related to the presence of a dual solution at such operating conditions. Based on Schlieren imaging the internal shock is identified as a boundary manifold for information transport between the ambient atmosphere and the jets core. In open-wake configurations, the single recirculation zone is influenced by the ambient pressure pa, whereas in closed-wake flows, two separated zones exist, with the upstream zone unaffected by pa and the aspiration pressure pAsp for the closed-wake flow depends on the edge shock post-shock pressure.

Ultrasonic cleaning systems generate acoustic fields using high-frequency transducer vibrations. While transducer parameters can be tuned, a unified and efficient model for predicting field behavior across diverse cleaning conditions remains unavailable. In this work, we present Ultrasonic-Net, a Physics-Informed Neural Network (PINN) developed to predict ultrasonic fields, specifically targeting cleaning applications. The JAX-Fluids solver is used to generate ground truth for evaluation. The complex system, comprising the ultrasonic transducers (acoustic sources) and the target devices, is modeled using a sharp interface method. The design of Ultrasonic-Net is based on a synthesis of detailed physics and established knowledge. In the proposed architecture, Multi-scale Convolutional Neural Networks (Multi-Scale CNN) and Fast Kolmogorov-Arnold Networks (FastKAN) have been integrated into the Spline-based PINN. The Attention Fusion Layer integrates features from the multi-scale local and global branches by performing adaptive channel-wise recalibration on their concatenated representations. During training, the wave equation is employed as a physical constraint. The vibration frequency, along with the variations in transducers, and the configuration of the devices to be cleaned, is incorporated through initial and boundary condition (IBC) constraints. The decomposition method combined with vectorization is designed to facilitate the enforcement of these constraints. The combination is motivated by ultrasonic cleaning-specific physical requirements. Systematic ablation studies across seven PINN variants and multiple hyperparameter groups confirm that the proposed architecture and training configuration achieve the best accuracy-efficiency trade-off. Once trained, Ultrasonic-Net efficiently predicts the spatiotemporal evolution of acoustic waves under varying conditions, closely matching ground truth while significantly reducing computational cost. An extended experimental comparison is provided to further validate the model's performance. The model's practical utility is demonstrated through application to acoustically driven bubble dynamics. Finally, a systematic evaluation confirms its accuracy and generalization capacity across diverse conditions.

The ability to resolve complex physical phenomena with high fidelity and at low computational cost is central to addressing key challenges in modern engineering. A prime example lies in hypersonic flows, where the precise prediction of the full flowfield topology, in particular with respect to shock wave location and intensity, is critical. Yet supersonic and hypersonic flows continue to be a stumbling block for traditional reduced-order models and neural emulators that struggle to capture steep gradients in flow states with physical consistency in applications of industrial relevance. To that end, we introduce a fully GPU based workflow that integrates accelerated data generation with the training of neural emulators augmented by uncertainty quantification and physics-aware refinement. Our workflow is enabled by a differentiable high-fidelity solver (JAX-Fluids) which we employ for rapid dataset creation and residual-based improvement of the neural emulator to enhance physical consistency. Building on this framework, we first present a suite of model architectures and analyze their scaling behavior to expose their strengths and shortcomings. We then show that residual-based refinement enables training on cases where only mesh and input parameters are available, substantially reducing residuals and improving physical consistency. Together, differentiable simulation and residual-based refinement yield physics emulators that remain reliable beyond their training distribution, a key requirement for deploying surrogates in real-world engineering design loops.

Eulerian smoothed particle hydrodynamics (Eulerian SPH) is considered a potential meshless alternative to a traditional Eulerian mesh-based finite volume method (FVM) in computational fluid dynamics (CFD). While researchers have analyzed the differences between these two methods, a rigorous comparison of their performance and computational efficiency is hindered by the following two challenges: Firstly, the Eulerian SPH framework faces a constraint related to the normal direction of interfaces in pairwise particle interactions, which prevents achieving an equivalent algorithm of FVM; Secondly, there is no unified solver available that can be applied to both Eulerian SPH and FVM methods. To address the former constraint, this paper implements a certain form of Eulerian SPH method, where a kernel gradient correction is introduced to release the constraint. To address the latter constraint, the paper realizes the mesh-based FVM within an open-source SPH library using a shared solver, i.e. single algorithm for two methods, through developing a parser that extracts necessary information from the “.msh” format file exported from a commercial pre-processing tool, ICEM (Integrated Computer Engineering and Manufacturing). Several 2D and 3D numerical simulations using both methods within a unified codebase demonstrate that compared to the mesh-based FVM, the Eulerian SPH achieves smoother results and, when using a high-order kernel, a faster convergence rate, but at the cost of lower computational efficiency.

In this work, we present a data-driven high-order Godunov-type finite-volume scheme for machine-learned implicit large-eddy simulations (ML-ILES) of compressible homogeneous isotropic turbulence. For the simulation of compressible flows, many Godunov-type finite-volume schemes combine high-order shock-capturing schemes with approximate Riemann solvers. Here, we devise neural-network based reconstruction operators which are trained to best approximate turbulent subgrid-scales. In particular, we use separate reconstruction neural networks for each physical flow quantity and show that an optimal reconstruction for ILES may require different reconstruction strategies for different flow quantities. The neural networks used in the reconstruction operator are trained end-to-end, using the automatically differentiable JAX-Fluids CFD solver. The training data set comprises coarse-grained spatio-temporal trajectories of compressible temporally decaying homogeneous isotropic turbulence. Comparisons with established ILES discretizations show encouraging results.

The modeling and control of fluid flows remain a significant challenge with tremendous potential to advance fields including transportation, energy, and medicine. Effective fluid flow control can lead to drag reduction, enhanced mixing, and noise reduction, among other applications. While reinforcement learning (RL) has shown great success in complex domains, such as robotics and protein folding, its application to flow control is hindered by the lack of standardized platforms and the computational demands of fluid simulations. To address these challenges, we introduce HydroGym(1), a solver-independent RL platform for flow control research. HydroGym integrates sophisticated flow control benchmarks, a scalable runtime, and state-of-the-art RL algorithms. Our platform includes four validated non-differentiable fluid flow environments and one differentiable environment, all evaluated with a variety of modern RL algorithms. HydroGym's scalable design allows computations to run seamlessly from laptops to high-performance computing resources, providing a standardized interface for implementing new flow environments. HydroGym aims to bridge the gap in flow control research, providing a robust platform to support both non-differentiable and differentiable RL techniques, fostering advancements in scientific machine learning.

This paper proposes a diffusive wetting model for the weakly-compressible smoothed particle hydrodynamics (WCSPH) method to simulate individual water entry/exit as well as the complete process from water entry to exit. The model is composed of a physically consistent diffusive wetting equation to describe the wetting evolution at the fluid-solid interface, a wetting-coupled identification approach to determine the type of fluid particles by taking into account the wetting degree of the contacted solid, and a numerical regularization on the fluid particles at fully wetted fluid-solid interface. The accuracy, efficiency, and versatility of the present model are validated through qualitative and quantitative comparisons with experiments, including the 3-D water entry of a sphere, the 2-D water entry/exit of a cylinder, and the complete process from water entry to exit of a 2-D cylinder.