Papers

In aquatic environments, gradients in flow velocity and turbulence define a constantly shifting landscape that sets the physical constraints on propulsion and energy expenditure in fish. Successfully navigating these complex flows depends on the ability to sense and respond to subtle hydrodynamic cues in an energy-efficient manner. Revealing these mechanisms is central to understanding how fish identify and exploit favorable flow conditions. To this end, we designed a hydrodynamic maze with spatially varying mean flow and turbulence, creating a controlled heterogeneous flow landscape for understanding fish movement strategies. We found that fish escape energetically unfavorable regions by yawing their bodies relative to the flow. These yawed orientations appear to facilitate lateral migration through lift forces and may improve sensitivity to local flow variations. Notably, fish maintain body orientations near, but below, predicted stall conditions to exploit lift without a significant increase in drag. These findings provide insight into how fish navigate heterogeneous hydrodynamic environments, with potential relevance for both natural and engineered flow systems.

Graph-based surrogate models offer a promising route to accelerate computational fluid dynamics (CFD) simulations on unstructured meshes. However, their development is limited by the scarcity of benchmark datasets spanning multiple flow regimes and standardized protocols for long-horizon autoregressive prediction. We introduce ONECYL (ONE CYLinder), a new benchmark for unsteady flow past a circular cylinder across laminar, transitional, and high-Reynolds-number regimes. The benchmark comprises 450 high-fidelity Variational Multiscale finite-element simulations (270,000 flow snapshots) with randomized cylinder geometries, providing time-resolved velocity and pressure fields together with mesh connectivity, geometric descriptors, Reynolds numbers, and integrated aerodynamic quantities. Beyond the dataset, ONECYL establishes a unified evaluation framework combining full-field rollout errors, virtual probes, and drag and lift predictions to assess numerical accuracy and physical fidelity. To accompany the benchmark, we develop a Graph Transformer as a reference baseline predicting velocity and pressure fields autoregressively on unstructured meshes. Using ONECYL, we investigate geometric representations and physics-based regularization across the three Reynolds-number regimes. The results show that explicitly encoding the cylinder geometry through a level-set representation consistently improves long-horizon prediction accuracy and generalization to unseen geometries, while divergence-based regularization becomes increasingly beneficial as flow complexity increases. The ONECYL benchmark and its Graph Transformer baseline provide a reproducible framework for evaluating graph-based surrogate models and establish a foundation for future research on long-horizon prediction of unsteady bluff-body flows.

Pulsatile flow in corrugated tubes arises in hemodynamics and microfluidics, where oscillatory forcing and geometric constrictions jointly determine transport and wall loading. We extend Womersley's classical solution for oscillatory flow in a rigid circular tube to rigid axisymmetric tubes of slowly varying radius. Within the lubrication approximation, we derive closed-form expressions for the axial velocity profile, volumetric flow rate, phase lag, and wall shear stress at an arbitrary Womersley number. Three-dimensional lattice Boltzmann simulations are used to assess the regime of validity of the theory. The analysis shows that the local velocity profile varies strongly along the tube, ranging from plug-like in wide sections to more parabolic near bottlenecks. The cycle-maximum flow rate decreases with increasing corrugation, but this reduction weakens as pulsatility increases, reflecting a crossover from the quasi-steady scaling $\langle R^{-4}\rangle^{-1}$ to the high-frequency scaling $\langle R^{-2}\rangle^{-1}$. The wall shear stress is maximal at the bottleneck and decreases with Womersley number. For sinusoidal corrugations, the bottleneck wall shear stress depends non-monotonically on the corrugation because of the competition between local shear amplification and global hydraulic resistance. Closed-form expressions for the time-averaged wall shear stress and oscillatory shear index further connect the theory to standard hemodynamic metrics.

We examine two major factors that influence the optimum projection angle: aerodynamic forces and the effect of run-up. With respect to aerodynamics, we consider not only the drag but also the lift generated by spin during flight. By linearizing the equations of motion that include these forces, we derive perturbation solutions with respect to drag and lift coefficients and clarify their qualitative effects. The results show that both drag and lift reduce the optimum projection angle, with the latter exerting a stronger influence. To investigate the effect of run-up, we use an extended projection model in which the initial speed depends on the initial angle. Analysis of this model reveals that a stronger run-up increases the relative projection angle but decreases the launch angle observed from the ground. These findings provide a mechanical explanation for the release angle in shot put and the takeoff angle in long jump. The present study establishes a simple theoretical framework for clarifying the respective roles of aerodynamic and run-up effects in determining the optimum projection angles in sports.

We investigate flow-induced scission of wormlike micelles under different flow kinematics using dissipative particle dynamics simulations of surfactant solutions in shear, uniaxial extensional, planar extensional, and biaxial extensional flows. The average lifetime of wormlike micelles is used to quantify the degree of scission. While flow-induced scission occurs in all flow types when the deformation rate is sufficiently high, the dependence of the average lifetime on the deformation rate differs among flow types. To provide a unified description, we introduce an effective extension rate determined by the velocity gradient tensor and micellar orientation. When expressed in terms of this effective extension rate, the average lifetimes obtained under all flow types considered collapse onto a single curve. These results demonstrate that a unified description of flow-induced scission requires not only the strength and kinematics of the imposed flow, but also the micellar orientation relative to the extensional direction.

We derived a resolvent operator to analyze the coupled flame-acoustic effect in a model two-stream coaxial combustor. The theoretical analysis accommodates both the hydrodynamic effect of the active flame and chamber acoustic effect, as well as their coupling effect. Utilizing the coupled thermoacoustic resolvent, we are able to identify the optimal forcing of different mechanisms and their corresponding optimal responses. When this new modeling tool is applied to a two-stream coaxial model combustor, it reveals distinctly different forcing-response characteristics in the coupled system compared to those in a purely hydrodynamic linear system. Acoustic energy peaks, indicative of resonance, are observed. Additionally, it has been found that the acoustic forcing does not maintain a rank-one property. Furthermore, the modes most receptive to the flame-acoustic coupling effect can be identified using a novel sensitivity analysis approach. Interestingly, by employing the coupled thermoacoustic resolvent, we demonstrate that forcing can be designed to negate or counteract perturbations caused by the forcing of another attribute, potentially aiding in the development of effective thermoacoustic control strategies.

We study the local errors of classical machine-learning surrogate models, which approximate the time evolution of the one-dimensional viscous Burgers equation. Four models are compared on the same prediction task, using the spatial grid values directly: radial basis function (RBF) kernel ridge regression (KRR), linear Ridge, ExtraTrees, and Random Forests. Across all four models, the one-step residual, defined here as the true value minus the predicted value at each grid point, forms clear curved branches near predicted maxima and minima. A more detailed analysis of KRR shows that these errors are much more strongly related to the second spatial derivative, which measures local curvature, than to the first spatial derivative. Near a smooth extremum, predicted value and curvature form a local two-branch fold. Under our local curvature-based model of the residual, this fold predicts a leading-order near-parabolic relation between predicted value and residual. This geometric result motivates a direct test of the Burgers advection (transport) and diffusion (smoothing) terms. For KRR and Ridge, regression tests on held-out trajectories, a control that breaks the spatial alignment of the diffusion term, and a spectral test of high-frequency content are consistent with insufficient viscous smoothing at moderate and high viscosity. In this case, the surrogate retains more small-scale structure than the true future state. The same physical explanation is much weaker for the tree models. Finally, a correction that uses only predicted quantities reduces both one-step error and error during recursive rollout, where each prediction is used as the next input.

Grid-based fluid dynamics solvers routinely struggle with exhaustive meshing demands and ill-posed inverse problems. A practical mesh-free alternative is given by Physics-informed neural networks (PINNs) but, applying them to highly elastic Oldroyd-B fluids results in many training failures. The High Weissenberg Number Problem (HWNP), driven by the exponential stress growth near stagnation points is a major issue, which causes standard PINN optimizers to diverge. To prevent the network from crashing, we apply a Cholesky decomposition to the conformation tensor. This mathematical constraint stabilizes the gradients by guaranteeing a positive-definite stress field. Beyond mathematical stability, the inherent spectral bias of deep learning models can hinder the network from accurately capturing the highly elastic wake structures. Therefore, we used sparse data assimilation to force the model toward the actual physical solution. By anchoring the physics loss with targeted CFD data points and accelerating training via transfer learning, we successfully pushed the network past non-physical local minima. We validated this Cholesky-PINN approach on flow past cylindrical geometries for Reynolds numbers (Re) between 5-25, for the single-cylinder setup. In addition, the relaxation time ({\lambda}) is increased from 0.1 to 0.5 to test the stability of the network. Finally, we scale the framework to a complex 3-cylinder array which proved our constructive solid geometry approach completely bypasses the tedious re-meshing steps of traditional CFD. The combined framework accurately captured sharp viscoelastic wakes, providing a stable computational tool for complex rheological modeling.

The wakes of a lift + cruise aircraft's vertical lift propellers interact with the wing during the transition from hover to forward flight. This study investigates how variations in axial and longitudinal separations between the vertical lift propellers and the wing affect aerodynamic performance during this critical phase. Axial variations were introduced by orienting the motors either upright or inverted at two longitudinal positions relative to the wing. Wind tunnel tests were conducted on the resulting lift + cruise wing configurations over a Reynolds number range of 52,000 to 377,000, using tufts, pressure taps, and load cells to capture aerodynamic behaviour. Results show that the early transition phase (front propeller advance ratios between 0 and 0.25) is particularly sensitive to configuration changes. Rear motor orientation had a pronounced effect: when oriented upright at the shortest longitudinal separation, the active lift propellers increased the lift-drag ratio of the design by approximately 4 units, whereas in the rear motor inverted case the design suffered a 4-point reduction in the lift-drag ratio. Decreasing the longitudinal separation amplified both the beneficial lift contribution of the rear propeller and the generally adverse effects of the front propeller. However, placing the front propeller closer to the wing in the upright orientation enhanced performance at advance ratios between 0.11 and 0.25, due to favourable interactions between the wing and the front propeller's trailing vortices.

In this article, we study the flow induced by crystallization of sodium chloride in sessile droplets. We measure flow velocities on the order of 1 $\mathrm{cm.s^{-1}} during crystallization, two orders of magnitude higher than those reported in previous studies. We show that this discrepancy is due to surface contaminants in earlier experiments. Numerical simulations reveal that in the clean case, the flow is driven by Marangoni stresses, whereas it is density- driven in the contaminated case. Consequently, droplet cleanliness significantly influences the flow which, in turn, determines the growth rate of crystals.

This work presents a comparative analysis of Reduced-Order Models (ROMs) applied to incompressible fluid dynamics within geometrically parametrized domains. Two distinct reduced-order solution strategies are investigated and compared: a monolithic coupled solver and a segregated SIMPLE-based algorithm. Their performance is assessed on two steady, two-dimensional benchmark cases: a lid-driven cavity flow and a flow past a cylindrical obstacle. The two algorithms are compared in terms of fields evaluation and aerodynamic coefficients prediction. The computational results highlight a fundamental trade-off between accuracy and numerical efficiency. On the one hand, after an opportune supremizers enrichment, the coupled approach guarantees a faster convergence, despite the need of a larger number of degrees of freedom. On the other hand, the segregated SIMPLE algorithm yields superior reconstruction accuracy, particularly for lower-dimensional reduced spaces, at the cost of a slower convergence rate.

Physics-informed neural networks (PINNs) represent a growing frontier in using artificial intelligence to solve partial differential equations (PDEs). Automatic differentiation (AD) plays a central role in this paradigm, which is mesh-free and replaces traditional iterative solvers with gradient-based optimization in continuous space. However, the inherent limitations of AD, particularly in handling higher-order derivatives and discontinuous solutions, pose significant challenges for complex problems. This has motivated a growing number of researchers to explore discretization-based constraints as an alternative path. Yet, the respective applicability of these two paradigms remains largely unexplored. In this work, we conduct systematic experiments across a wide spectrum of problems, from simple linear Poisson to high-Mach hypersonic flows with strong discontinuities. Through a rigorous decomposition of approximation, optimization, and truncation errors, we systematically elucidate the fundamental trade-offs and error-governing mechanisms of both paradigms, as well as two representative network architectures: multi-layer perceptron (MLP) and graph neural network (GNN). Our results reveal a consistent trend: as nonlinearity strengthens, the accuracy advantage of discretization-based constraints becomes increasingly pronounced, with smaller optimization errors compensating for the truncation errors. Moreover, the more complex the nonlinearity and boundary conditions, the greater the advantage of GNN over MLP. These insights offer a robust practical guideline for configuring neural PDE solvers in demanding engineering applications. Our source data and code are available at https://github.com/guoxing0809/neuropde_analysis.

Heterogeneous exascale systems are reshaping computational fluid dynamics, yet rewriting mature high-order solvers for accelerators can fragment code bases and weaken reproducibility. We present a single-source OpenMP target modernisation of UCNS3D, a high-order unstructured finite-volume solver for compressible flows. The common CPU/GPU implementation preserves its numerical formulation, Fortran code base, and workflows. Rather than porting isolated kernels, we enable the complete explicit time-advancement path: high-order reconstruction, gradient evaluation, inviscid and viscous fluxes, boundary treatment, halo exchange, and solution update. The implementation uses persistent target data regions, flat run-time arrays, compile-time sizing of temporary storage, explicit local algebra, target-callable routines, and GPU-aware MPI with device-resident buffers. These choices address the irregular stencils, complex data structures, and substantial temporary storage of high-order unstructured CFD. Verification using the compressible Taylor-Green vortex shows CPU and GPU dissipation histories agreeing to machine precision on LUMI and with published reference data. A single-node run on the ARCHER2 GPU platform provides an independent portability check. End-to-end performance is evaluated on fully populated nodes using Taylor-Green vortex, LM1021 sonic-boom, and NASA high-lift CRM benchmarks. Relative to the previous production implementation, the refactored CPU path is 1.27-1.67 times faster, while GPU offload delivers same-node speed-ups of 2.71-4.05 and 84-101 percent strong-scaling efficiency. The results show that standards-based OpenMP provides portable, production-scale acceleration without sacrificing numerical fidelity, CPU performance, or software sustainability.

In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint–Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier–Stokes equations with surface tension, discretized using the standard $P2-P1$ Taylor–Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh–Taylor instability.

We employ weakly nonlinear theory to investigate how an externally imposed simple shear flow affects the onset of spontaneous dynamics of an inertialess active filament deforming in Stokes flow. The filament, clamped to a wall at one end, is subjected to a compressive "follower force" applied tangentially at its free end. By extending my earlier weakly nonlinear analysis of the shear-free case (J. Fluid Mech., 1007 A65, 2025), we derive a generalized amplitude equation governing the near-onset dynamics under weak shear. Analysis of the amplitude equation shows that, besides inducing a steady deflection, the shear damps the filament's intrinsic oscillations. This damping arises from a subtle nonlinear resonance between the shear and the intrinsic oscillations, scales quadratically with the shear rate, and is anisotropic—stronger in the flow direction than normal to it. Without shear, stable whirling states, where the filament tip traces a circular orbit in a plane parallel to the wall, and unstable planar-beating states are known to simultaneously emerge at a critical follower-force value, with circular whirling typically observed beyond this threshold. Shear breaks this degeneracy, driving a sequence of dynamical transitions: from circular to elliptical whirling, then to transverse beating (normal to the shear), and ultimately to steady deflection.

The Volume-of-Fluid implementation in the \href{basilisk.fr}{Basilisk} flow solver is employed to study mass transfer after coalescence-induced jump-off of bubbles on solid substrates at four combinations of bubble radius ($R_m=150$ and 25 $\mu$m, hydrogen-water properties) and Schmidt number ($\text{Sc}=210$ and 1). The results show a relatively strong downward entrainment of low-concentration liquid, induced by a rapid movement of the bubble interface at approximately 0.5 to 1 inertio-capillary time units after the moment of coalescence. At $\text{Sc}=210$, this leads to a highly local increase of the Sherwood number at a core region (roughly an area of radius $R_m/2$) below the south pole of the merged bubble, which persists long after the bubble departure due to the slow diffusion at large $\text{Sc}$. The enhancement factor of the Sherwood number is highly dependent on the state of the mass-transfer boundary layer at the moment of coalescence, increasing with smaller boundary layer thicknesses. Shortly after the jump-off, the velocity of the bubble is considerably damped and rapidly approaches its free-rise terminal velocity. The effect of micro-convection on the wall mass transfer coefficient at this stage is insignificant when isolated, similar to what is reported in the literature for purely buoyancy-driven bubble rise – but slightly stronger.

Flapping insect wings generate leading-edge vortices (LEVs) that produce much of the lift required for hovering, yet the frequency governing their formation has not been connected to classical vortex shedding. Roshko scaling for bluff-body wakes, together with the Sigurdson extension to wall-bounded separated flows, identifies a universal vortex-formation Strouhal-number range of approximately 0.15 to 0.17. Here we show that this same range governs LEV formation on both stationary wings and hovering insect wings. We first develop an approximate scaling for stationary flat-plate wings in which discrete LEVs are generated by periodic leading-edge perturbations, and show that maximum lift consistently occurs within the universal Strouhal range. In hovering insects, one LEV forms during each translational half-stroke, allowing the same framework to be applied to published flight data. Despite large differences in morphology, kinematics and Reynolds number, the insect data recover the same Strouhal range. These results reveal a common vortex-formation timescale linking classical separated flows, artificially generated LEVs and the natural LEVs that sustain insect hovering.

This study proposes a hybrid reduced-order modeling (ROM) framework for the simulation of turbulent flow. The central idea is to decompose flow dynamics according to their temporal characteristics and predict the resulting components individually. The full field is first divided into a sub-field represented by a limited number of proper orthogonal decomposition (POD) modes (named as POD-retained field) and the corresponding residual sub-field (named as POD-truncated field). A frequency-informed POD strategy identifies the retained modes by considering both modal energy and dominant frequency. The evolution of retained POD coefficients, which feature similar temporal scales, is described using a vector autoregressive (VAR) model. In parallel, the POD-truncated field is compressed into a low-dimensional latent space using a Fourier-neural-operator-based Koopman $\beta$-variational autoencoder (FK-$\beta$-VAE), with the latent variables subsequently predicted by a switching-VAR model. Turbulent statistics of the full field are recovered by combining the contributions from the two components. The framework is assessed using turbulent channel flow at a friction Reynolds number of $110$. The predicted Reynolds-stress components, turbulent kinetic energy (TKE), and dominant wavenumber spectra show good agreement with the reference. Moreover, in comparison with an alternative framework of full-field modeling (i.e., without field decomposition), the proposed framework yields more accurate and robust long-term statistical predictions.

In viscous flow, the circulation enclosed by a deterministic material loop generally changes through vorticity diffusion. It is shown that the source-bearing unsteady Kiknadze–Krasnov vortex possesses a distinguished cylindrical material surface on which this viscous circulation transfer vanishes identically. For a single distributed mode, the scaled squared radius $x=\beta(t)r^2$ satisfies \[ \frac{\mathrm D x}{\mathrm D t} = 4\nu\beta(t)\big[(s-1)-x\big], \] where $\beta(t)$ is the inverse squared radial scale, $\nu$ is the kinematic viscosity, and $s$ is the incomplete-gamma shape parameter. For $s>1$, the cylinder $x=s-1$ is transported exactly by the radial flow and preserves the inside/outside ordering of fluid trajectories. The same factor $(s-1)-x$ governs the radial vorticity gradient and the material circulation-transfer rate. Consequently, the magnitude of the distributed axial vorticity $|\omega_z|$ attains its annular maximum on this material cylinder, $\partial_r\omega_z=0$ there, and the enclosed circulation remains exactly $\Gamma P(s,s-1)$ for every admissible prescribed strain history. Neighbouring material cylinders continue to exchange circulation viscously, while the distinguished moving cylinder carries a fixed fraction of the distributed circulation throughout the admissible evolution. In the steady source–strain limit, the surface reduces to the radial stagnation cylinder. The complete velocity and pressure fields, exact radial-scale evolution, admissible parameter ranges, and qualifications for multiple radial scales are also derived. The resulting solution-specific material-circulation invariant provides an exact benchmark for numerical material-surface tracking, vortex-core evolution, and viscous circulation transport, with the principal analytical results additionally supported by machine-checked formal verification.

Aero-optic effects distort light wave propagation near a high-speed aircraft, thereby degrading performance in airborne imaging and communication systems. Measuring aero-optic data through experiment is costly and the resulting data often has a limited spatial size. Further, alternative methods for simulating this data, including computational fluid dynamics and conventional phase screen generation algorithms (e.g., boiling flow), face drawbacks such as large computation time or inaccurate statistics. More recently, data-driven algorithms have been proposed that can synthesize data that matches relevant statistics of measured aero-optic data. However, these methods cannot spatially extend aero-optic data. In this paper, we introduce ReVAR-ext (Re-whitened Vector AutoRegression-extender), an algorithm that builds on an existing data-driven approach, ReVAR, to spatially extend measured aero-optic data (a process called outpainting) and match the spatial and temporal correlations of the measured data. ReVAR-ext generalizes the generation process of ReVAR by combining multiple sets of synthetic data with the input measured data. This approach generates multiple fixed-sized synthetic images, each of which overlaps with the input data, and then stitches them together. When paired with ReVAR, the ReVAR-ext algorithm can generate aero-optic data with arbitrary temporal duration and arbitrary spatial size. Our experiments show that extended data generated by ReVAR-ext closely matches the temporal power spectrum of two measured aero-optic data sets. Further, the extended data approximately matches the spatial autocorrelation, with reduced accuracy at large spatial lags and at vertical lags.

The Navier-Stokes equation for a compressible Newtonian fluid is reassessed, in view of recent investigation results on the foundations of aeroacoustics. In the process, the role and necessity of the so-called Stokes' hypothesis is reconsidered, which in its current practice omits the bulk viscosity. In contrast, the relevance of a new generalized kinematic viscosity is proposed, along with a new methodology that will enable estimation of second coefficient of viscosity completely obviating the necessity of making the Stokes' hypothesis. This opens up the vista of a new formulation for the Navier-Stokes equation applicable for both the subjects of fluid mechanics and aeroacoustics in a unified approach.

Motile microorganisms inhabit oscillatory flows encountered in physiological and engineering systems, yet the influence of flow unsteadiness on their shear-induced preferential concentration remains less understood. We investigate transverse transport of elongated microswimmers in oscillatory pressure-driven channel flow using complementary Langevin simulations and two- and one-dimensional Fokker-Planck models. Agreement between particle-based and continuum descriptions across governing parameters establishes the fidelity of the Fokker-Planck formulation for swimmer transport in oscillatory shear flows. Our analysis demonstrates that oscillatory forcing fundamentally modifies classical steady-flow shear-trapping. We find that increasing Womersley number $Wo$ reduces centerline depletion by confining oscillatory shear to thinner near-wall regions. In contrast, increasing frequency ratio $\beta$, of swimmer rotational diffusion rate and flow oscillation frequency, promotes sustained orientational anisotropy, and leads to a saturating increase in centerline depletion. In the weak-swimming limit, we derive a hierarchy of coupled orientational moments, enabling analytical solutions at arbitrary temporal harmonic order. The asymptotic solutions establish a universal transfer law showing that, for a given swimmer shape, the normalized leading-order orientational response depends solely on $\beta$. Reconstruction of the orientational distribution yields closed-form expressions for the swimmer concentration profile and depletion index, $I_D$. Our asymptotic solution recovers the steady-flow weak-shear scaling of $I_D$ with flow Peclet number, $Pe_f$, of $I_D \propto Pe_f^2$, and reveals that oscillatory forcing attenuates this response by a factor $16\beta^2/(1+16\beta^2)$. These results provide a theoretical framework to predict transverse transport of microswimmers in oscillatory channel flows.

Our understanding of inertial particle dynamics in turbulence is mostly based on flows held in a statistically stationary state, a particular regime that differs from many natural flows where energy input can often be intermittent or cyclic, or may abruptly cease. Here we investigate inertial particle and bubble dynamics in freely decaying turbulence through complementary experiments and direct numerical simulations. While particle accelerations decay monotonically in time, we find evidence that the clustering can exhibit a non-monotonic evolution, intensifying sharply before subsequently weakening. We demonstrate that both the acceleration and clustering behaviors can be mapped onto their counterparts in stationary turbulence using a dynamic rescaling of the evolving length and time scales of the turbulence. Validity conditions for the dynamic rescaling, satisfied by both the experimental and numerical datasets, are derived. The proposed mappings remain applicable across a broad range of density ratios, from light to heavy particles, and particle sizes spanning two orders of magnitude in Stokes number.

Strongly enforced Dirichlet boundary conditions require highly refined near-wall meshes to resolve steep velocity and thermal gradients. This introduces high computational costs, especially for practical flow simulations. Weakly enforced boundary conditions alleviate this burden by acting as a variationally consistent near-wall model. By allowing a controlled slip at the solid wall, weak enforcement recovers accurate flow quantities on coarse boundary-layer meshes across both incompressible and compressible regimes. Furthermore, weak boundary conditions serve as the fundamental enabling technology for immersogeometric analysis. Because the weak operator evaluates boundary integrals independently of the background mesh, high-fidelity flow analysis can be performed directly on complex geometries without fitting a mesh to the surface. This capability has facilitated direct geometry-to-analysis workflows for boundary-representation CAD models, raw point clouds, photogrammetric reconstructions, and segmented medical images. This review examines the unified mathematical development of the weak boundary condition framework from scalar advection-diffusion equations to the full Navier-Stokes equations, illustrating its versatility and robustness across incompressible and compressible flows, whether in traditional boundary-fitted, sliding-interface, or advanced immersogeometric applications.

The automatic derivation turns a declared system of conservation laws into a lattice Boltzmann scheme, giving each conserved physical quantity a set of q populations whose linear equilibrium embeds the physical flux in their first moment. When the flux depends on gradients of the conserved state, those gradients are supplied by tracking them as additional transported fields. Since lattice Boltzmann is commonly memory-bound, these additional degrees of freedom reduce the achievable throughput. To reclaim it, we reconstruct the gradients from the moment structure of the equilibrium instead of transporting them. To leading order, the first moment of a conserved quantity's non-equilibrium part carries its gradient. Because the reconstructed flux enters its own equilibrium reference, that moment is the image of the gradient under a linear operator built from the diffusive-flux Jacobian. The reconstruction is that operator's algebraic inverse, generic across gradient-form constitutive closures and generated automatically from each declared flux. The resulting scheme carries the conserved quantities alone, reconstructing the required gradients from the populations and forming the fluxes locally. It converges at second order in double precision across advection-diffusion-reaction, Allen-Cahn, Navier-Stokes, resistive magnetohydrodynamics and homogenized compressible Navier-Stokes-Fourier systems, matching the accuracy of gradient tracking at equal resolution. On an NVIDIA RTX A5000 it is up to 3.7 times faster in single precision, the memory-bound kernels reaching up to 97% of peak memory bandwidth.

We develop a theory that determines the radial profile of the mean velocity in a coherent geostrophic vortex forming in a turbulent rapidly rotating fluid. Following the conditions of our experiments, we assume that the flow in the vortex is sustained by the absorption of short-wavelength inertial waves arriving from the vortex periphery. The nonlinear interaction between waves is assumed negligible in the theory. Comparison with experimental data supports the validity of the developed model.

Low-frequency cavity breathing oscillations can strongly affect flame stabilization and operability in cavity-stabilized supersonic combustors, yet their hydrodynamic origin and suppression remain insufficiently understood in opposed twin-cavity configurations. We investigate the breathing dynamics of an opposed twin-cavity supersonic combustor under low- and high-enthalpy conditions using synchronized high-speed Schlieren imaging, wall-pressure measurements, numerical simulations, nonlinear phase-space reconstruction, Hilbert-transform analysis, and reduced-order modelling. Under low-enthalpy conditions, a self-sustained breathing mode is observed at a dominant frequency of approximately 156 Hz, with large phase differences between cavity-floor and ramp pressures. Measurements and simulations show that periodic mass exchange between the cavity and freestream drives cyclic cavity depressurization and repressurization, establishing a pressure-shear-layer feedback loop that sustains the oscillation. A two-pressure-state reduced-order model, coupled with a shear-layer displacement coordinate, reproduces the measured frequency, pressure phase relationship, and stability characteristics, demonstrating that both bulk-cavity and reattachment/shock-foot pressure states are required to capture the dynamics. Upstream nitrogen injection produces only transient attenuation, with the oscillation recovering as the injected gas convects downstream. In contrast, ethylene injection followed by ignition permanently suppresses the oscillation, with the nonlinear attractor collapsing to a stable equilibrium. Heat release reorganizes the cavity pressure field and alters density, compressibility, and pressure-response timescales, thereby weakening the feedback mechanism responsible for sustaining the breathing mode.

Sloshing is an inevitable phenomenon in an ocean-going vessel that can have adverse effects. In this work, the mitigation of sloshing is investigated using multiple thin porous baffles of various configurations in a partially filled swaying tank. The boundary value problem is solved within the framework of a linearized potential flow theory using the scaled boundary finite element method (SBFEM). The flow through the thin porous baffles is assumed to follow Darcy's law. The computational domain is divided into a minimum number of subdomains due to the presence of porous baffles and to ensure star convexity. Higher-order polynomials are used along each subdomain edge to represent the unknown field, i.e., velocity potential. The developed numerical model is validated with the known results in the literature. Subsequently, various results, such as the amplification factor and the forces of the tank wall, are presented and discussed for the effect of configuration, porosity, slosh tank width, depth of baffle submergence and the space between adjacent baffles. From the parametric study, it is observed that top-mounted baffles enhance sloshing suppression by $50\%$ compared to bottom-mounted vertical baffles, considering all sloshing modes. Assessing the overall effectiveness, top-mounted convex baffle configuration emerges as the most efficient configuration for sloshing suppression, achieving a well-balanced reduction across all modes.

A coupled analytical framework is developed to predict the internal boundary layer (IBL) height, wall shear stress and the mean velocity profile downstream of a surface roughness transition in a neutral atmospheric boundary-layer. The new model combines a three-layer analytical velocity formulation with a modified diffusion analogy for the IBL growth rate. The diffusion analogy links the growth rate of the IBL to turbulent diffusion and to mean vertical advection. Our formulation rectifies physical inconsistencies in a previous model that assumed that the turbulent diffusion is controlled only by the upstream surface conditions and that the characteristic streamwise velocity difference caused by streamline displacement is independent of downstream distance from the roughness transition. Key model parameters, namely the turbulent diffusion coefficient and the eddy viscosity augmentation coefficient, are modelled as functions of the upstream-to-downstream aerodynamic roughness length ratio. The coupled model, along with three other analytical models, is tested against twelve datasets covering a wide range of roughness ratios, including wind-tunnel experiments and large-eddy simulations. The new model accurately predicts wall shear stress, mean velocity, and IBL height for all combinations of upstream and downstream roughness values evaluated, for both smooth-to-rough and rough-to-smooth transitions.

Rotating magnetic microparticles are building blocks for field-driven assembly and microrobotic control. As the elementary interaction rule for larger assemblies, pair motion in these systems is governed not only by magnetic forcing, but also by hydrodynamic coupling and other long-range interactions. Here we develop a reduced framework for two synchronized rotating magnetic particles by resolving the interactions into radial components that change the interparticle distance and transverse components that rotate the line of centers. The competition between magnetic dipolar interaction, additional radial repulsion, and rotation-induced transverse coupling selects three pair-motion modes: rigid-body rotation, contact-separation rotation, and irreversible separation. We derive transition criteria for the rigid-body state, reversed orbital motion, and the separation boundary, and obtain an asymptotic solution for the separation dynamics. Lattice Boltzmann simulations of particles rotating near a wall provide a hydrodynamic realization of the model, in which inertial secondary flow generates radial repulsion and rotational flow produces transverse coupling. The resulting phase diagram in the physical $(\mathrm{Re},C_m)$ plane is consistent with the reduced-model predictions. These results provide design rules for programming elementary pair interactions in rotating magnetic-particle systems and may help guide the control of microrobotic assemblies.