Papers

A sub-grid closure of the scalar-dissipation rate for the Large Eddy Simulation (LES) of turbulent premixed flames is assessed experimentally. Hotwire anemometry is performed to characterize the background turbulent flow, and the Rayleigh scattering measurements are conducted to acquire instantaneous temperature fields, which are used to obtain the scalar dissipation rate. Either methane or hydrogen-enriched (40% by volume) methane is used as the fuel. The Karlovitz number varies between 1.7 and 34.5. The LES filter size is changed from 0.1 to 3.0 times the thermal thickness of the corresponding laminar flames. Both Gaussian and top-hat filtering methods are used. Statistical analyses are performed to investigate the characteristics of the measured, resolved, and unresolved scalar dissipation rate as well as how these are influenced by the normalized filter size, filter type, and the Karlovitz number. It is shown that the algebraic model allows for acceptable prediction of the Favre-filtered, temporally and spatially averaged scalar dissipation rate across the examined test conditions. The experimental measurements are used to gain insight into a key parameter used in the algebraic model. While differences between the previously proposed and our measured value of the model parameter for small Karlovitz number flames are reported, good agreement between our measured values and previously suggested values is obtained for relatively larger Karlovitz number flames. This finding is shown to be consistent across the examined filter sizes and filtering methods, despite the differences in the examined flame configuration of the present experimental study and those of past numerical investigations. This motivates future investigations to assess use of the algebraic model for simulating turbulent premixed flames with an extended range of operation.

A unified linear theory is developed for the unsteady loading of finite-chord aerofoils, rigid or porous, in compressible subsonic flow. The formulation combines Possio's integral operator with a convective permeable boundary condition, allowing chordwise-varying admittance while retaining the wake and unsteady Kutta condition. The loading exponents at aerofoil edges and admittance discontinuities keep their incompressible form in terms of the local permeability parameter, so weighted-Jacobi collocation carries over. The solution is verified against published incompressible results and an independent compressible formulation. Gust and heave responses and their indicial counterparts reveal that permeability controls the sensitivity of unsteady loading to compressibility. As permeability increases, the material impedance rather than the surrounding flow sets the pressure jump, but only gradually: at Mach number 0.7 the gust load on a weakly permeable surface changes by a third to a half, and closed-form steady and high-frequency limits for resistive surfaces show that it vanishes only when the permeability parameter greatly exceeds the Mach number. The porous-to-impermeable load ratio, by which a treatment is judged, cannot be obtained by combining incompressible porous and compressible rigid theories, which misjudge it by up to a factor of two. Incompressible theory overestimates this ratio for an acoustically compact chord and underestimates it for a non-compact one, by factors of 1.4 to 4.3 at Mach numbers 0.5 to 0.7 and reduced frequencies 5 to 20, overstating the load reduction. Since compactness depends on Mach number times reduced frequency, the error persists at low speed, exceeding 10 per cent at Mach number 0.05 for reduced frequencies above 10.

An analytical criterion for the disappearance of turbulent flow in a channel is developed within the Alexeev hydrodynamic equations (AHE). The analysis builds on an analytical representation of the streamwise velocity as a superposition of a parabolic component and a nonlinear turbulent component coupled to the transverse velocity field. The critical Reynolds number is obtained from the balance of viscous dissipation of kinetic energy associated with the turbulent component. The resulting critical Reynolds number is expressed analytically as \(Re_c=f(\delta,\gamma,n)\), where \(\delta\) is the Reynolds-independent AHE similarity parameter, \(\gamma\) is the weighting coefficient of the turbulent component, and \(n\) is the transverse-velocity mode number. The criterion describes the disappearance of the turbulent solution as the Reynolds number is decreased and therefore addresses the turbulent-to-laminar transition rather than the linear instability of the laminar solution. Unlike a criterion based on a single universal critical Reynolds number, the AHE criterion predicts a transition threshold that depends on the parameters characterizing the flow. For representative channel-flow parameters, the predicted critical Reynolds number is approximately \(Re_c=1000\text{--}1200\). The predicted threshold is compared with experimental observations of transition and of the persistence of laminar flow in channel flows. The analysis suggests that viscous dissipation provides a mechanism limiting the persistence of the turbulent solution below a critical Reynolds number.%

The wave-particle decomposition is presented as a framework for multiscale kinetic transport, comprising a theory and an algorithm. Along the characteristics of the kinetic equation, the equilibrium integral of the solution over a local kinetic horizon defines a wave, which depends only on the conservative variables, and its exact complement defines a particle. Both obey kinetic equations whose moments are extended Navier-Stokes equations, and the conservation laws together with the particle equation form a closed system that is equivalent to the kinetic equation for every horizon. Parametrized by the ratio of the horizon to the relaxation time, these systems form a continuous spectrum from kinetic theory to Navier-Stokes hydrodynamics that adapts to the flow from cell to cell. The algorithm is a coupled wave-particle iteration for steady flows. It alternates a macroscopic iteration for the conservative variables, with the particle frozen, and a kinetic iteration for the particle, with the wave fixed. Its fixed point is the discrete kinetic solution, it is asymptotic preserving, and its near-continuum convergence factor is bounded by the share of the transport carried by the particle, a share that decays exponentially with the horizon-to-relaxation ratio. The collision model enters only through a conservative remainder, and the equations and the iteration are written out for the Bhatnagar-Gross-Krook, Shakhov and ellipsoidal statistical models, the Boltzmann and Landau equations, neutron transport and radiative transfer. The decomposition is related to the unified gas-kinetic wave-particle method, the micro-macro decomposition, penalization and synthetic acceleration. Computations of hypersonic flows past a cylinder and around the three-dimensional X38 vehicle illustrate how the division of the distribution adapts to the flow and how strongly the iteration is accelerated.

Whether orthogonalising the moment basis changes a central-moment lattice Boltzmann scheme is decided by the geometry of the velocity set. The basis enters the collision only through the conjugate $\mathit{T}^{-1} \Lambda \mathit{T}$, so two bases related by a constant matrix $\mathit{A}$ define exactly the same scheme if and only if $[\Lambda,\mathit{A}]_{ij}=\mathit{A}_{ij}(\lambda_i-\lambda_j)$ vanishes, and on physical states only its columns for the non-conserved moments matter. We prove that on lattices with velocities in $\{0,\pm1\}^d$ and symmetric weights orthogonalisation reaches the shear moments only through the face and body diagonals: whatever the orthogonalisation, the shear rate is free on D2Q9 and D3Q15, whereas on D3Q19 and D3Q27 the scheme changes whenever the fourth-order moments do not relax at the shear rate. On rectangular lattices, where the symmetry is broken, an independent bulk rate yields an orthogonal counterpart that does not share the transport coefficients of the published scheme, which is itself orthogonal in the inner product of the rest equilibrium up to the one relaxation entry that consistency requires. Where the formulations differ but share their hydrodynamics, a basis orthogonal in the inner product of the rest equilibrium, which guarantees linear stability at rest, was never less robust in the least stable flow direction by more than a few per cent, often much more robust, and the more accurate against a Taylor-Green DNS. Computed through the non-orthogonal transforms with a conjugated relaxation matrix, it costs at most $2\%$ more on D3Q27.

Plume-laden convection plays a fundamental role in thermal transport in geophysical and industrial flows. While the dynamics of isolated laminar plumes have been extensively studied, their collective interactions and evolution in a multi-plume system remains poorly quantified due to the lack of four-dimensional (4D, in space and time) flow measurements for viscous convection, common in the turbulence community. Here we present a time-resolved experimental study of clustered plume dynamics in a high-Prandtl-number Rayleigh-Bénard system with temperature-dependent viscosity from 4D velocity measurements. Building on our companion methodology (Bao and Lithgow-Bertelloni, 2025), we characterize the spatiotemporal distribution, morphological evolution, and interaction modes of tens of coexisting plumes. We identify a wide spectrum of dynamical behaviors–merging, splitting, branching, pulsing, and head detachment–that arise from coupled interactions among plumes, multiscale flow, and the evolving thermal boundary layers. We synthesize prior behaviors into a unified, time-resolved framework of plume evolutionary pathways. Characteristic length and timescales, including spacing and initiation times, are compared with previous theoretical and experimental studies. We find thinner plumes with greater minimum spacing. The fraction of isolated plumes (e.g., Hawaii-like) varies dramatically (0–60%) as the flow evolves. Our results provide new insight into plume self-organization and spatiotemporal variability under Earth-like conditions, crucial for understanding geochemical evolution and mapping geochemical anomalies from hotspot lavas to deep sources. These results quantitatively complement previous experimental work and numerical studies on interacting plumes, serving as a benchmark for comparison with geodynamical simulations of mantle convection.

Laboratory investigation of convective flow in viscous fluids is crucial for various engineering and geophysical applications, including vigorous convection in planetary mantles, which involves multiple rising plumes. Many experimental techniques have been developed to visualize the flow and plumes, but most previous measurements remain largely qualitative. Here we present a method to measure and analyze four-dimensional (4D) plume-bearing viscous fluid flow, extending volumetric velocimetry approaches to the high Prandtl-number laminar regime relevant to mantle convection. First, a customized three dimensional (3D) Scanning Stereoscopic Particle Image Velocimetry (SSPIV) system is applied to a Rayleigh-Bénard experiment suitable to study the dynamics of Earth's interior. We report the first quantitative 4D velocity measurements of multiple interacting laminar plumes at high Prandtl numbers. The raw velocity data are postprocessed with a Lagrangian Coherent Structure (LCS) and cluster analysis pipeline, tailored for clusters of viscous plumes, which allows quantitative, transport-based material boundary tracking of the plumes in space and time. We show example results to demonstrate the power of our method while fully exploring the dynamics in a companion paper Bao and Lithgow-Bertelloni (2025). Our analysis quantifies the rich dynamical behavior of multiple interacting plumes. We suggest our method of measurement and analysis can help better quantify the morphology, interaction, and evolutionary pathways of plumes feeding Earth's volcanic hotspots and other planetary interiors.

On unstructured grids, the tangent of hyperbola for interface capturing (THINC) method with quadratic surface representation and Gaussian quadrature (THINC/QQ) requires topology-dependent numerical quadrature for cell and face integrals and Newton iteration for the surface constant. This study introduces a quadratic moment-matched sigmoid (QMMS) approximation that evaluates these quantities from the mean and variance of the quadratic field while retaining the hyperbolic-tangent reconstruction profile and the boundary variation diminishing (BVD) formulation. A slope-matched Gaussian cumulative distribution function and a moment-matched Gaussian model provide closed form approximations for the surface constant and face averages, eliminating Newton iteration and topology-dependent runtime quadrature from these evaluations. Single-cell tests and nine two- and three-dimensional benchmarks assess reconstruction accuracy, flow-field differences, and computational cost. Across the tested cases, the principal transported and shock structures remain closely aligned with those obtained using THINC/QQ, with local differences concentrated mainly near discontinuities, contact regions, and developed shear layers. Reconstruction-stage profiling gives mean THINC/QQ-to-QMMS time ratios of 2.12 in two dimensions and 1.85 in three dimensions. QMMS therefore reduces reconstruction-stage cost while replacing topology-dependent runtime integral evaluation with a common moment-based formulation

The effect of a porous coating on the water-exit dynamics of a circular cylinder is investigated experimentally. Cylinders comprising a $30~\mathrm{mm}$ solid core surrounded by a $10~\mathrm{mm}$-thick porous foam layer with pore densities of 10, 20, and 60 pores per inch (PPI) are compared with a smooth cylinder of the same outer diameter. Experiments are performed over $1.50\times10^{4}\leq Re\leq5.00\times10^{4}$ and $0.37\leq Fr\leq4.08$. Time-resolved particle image velocimetry characterizes the wake and reconstructed pressure field, while proper orthogonal decomposition (POD) examines its energetic organization. All porous cylinders reduce free-surface elevation relative to the smooth cylinder, with the largest reduction generally obtained for 60 PPI. The submerged wake, however, is not simply weakened. Porous cases generally develop larger circulation and vortex area, with a non-monotonic dependence on pore density and operating condition. The 10 PPI cylinder frequently produces the largest vortex region, whereas 60 PPI generates stronger negative pressure within the vortex and the largest integrated vortex-associated pressure deficit for $Fr=1.02$, $2.00$, and $4.08$. During the submerged approach to contact, this pressure deficit co-evolves strongly with circulation, with Pearson correlation coefficients typically between $0.90$ and $0.98$. POD shows that 9–18 modes recover 95% of the modal energy, with 20 PPI requiring only 9–10 modes. Overall, porous coating reorganizes wake strength, extent, pressure signature, and energetic structure while reducing the free-surface response.

Turbulent flows span a wide range of scales, making direct numerical simulation (DNS) prohibitively expensive at high Reynolds numbers. Large eddy simulation (LES) offers a pragmatic alternative by only resolving the large-scale motions, but its accuracy hinges on the subgrid-scale (SGS) model. We introduce the Tau-orthogonal (TO) framework to the lattice Boltzmann method (LBM) using a macroscopic-velocity forcing. The TO method shifts the modeling target from a high-dimensional SGS field to the time dynamics of a small set of spatially integrated quantities of interest (QoIs). Training data are generated by a predictor-corrector tracking procedure that nudges coarse simulations toward reference QoI trajectories. Lightweight linear regression models with stochastic, multivariate Gaussian residuals (LRS) then drive the LES autonomously. Compact convolution-based kernels replace the sharp Fourier filters of the original formulation, lifting its restriction to rectangular periodic domains. We first evaluate the closure on two-dimensional Kolmogorov flow, where TO-LRS yields stable, statistically accurate online LES. However, bounded high-frequency oscillations are observed in the solution fields. The decisive test is three-dimensional turbulent channel flow, simulated on a grid five times coarser in every direction than the high-fidelity reference. Here the plain BGK solver is unstable, and even calibrated Smagorinsky and WALE models over-dissipate the near-wall flow. TO-LRS, applied on top of an eddy-viscosity substrate and with the QoI set augmented by mean-profile QoIs, reproduces the reference distributions and holds the DNS mean velocity profile, at $40\times$ lower online cost per simulated time unit than the high-fidelity simulation. These results establish reduced, QoI-based closures as an interpretable and inexpensive alternative to high-dimensional neural SGS models for LBM.

Neural surrogates are trained to predict 3D turbulent flows in place of direct numerical simulation (DNS). For chaotic flows, the goal is short-term pointwise accuracy followed by long-term physical and statistical fidelity. However, small prediction errors can carry a surrogate away from the flow's attractor. Off-attractor states are poorly represented in training data, leaving their evolution weakly constrained. The learned dynamics can then amplify deviations and lead to blow-up, freezing, or statistical drift. We propose off-attractor supervision (OAS) to supervise neural surrogates where they leave the attractor. OAS teaches the model how the true Navier-Stokes dynamics would evolve from these states. Each selected state is paired with its own future computed by DNS. Three generators select a few hundred states for relabeling. The first collects states from the surrogate's own rollouts. The second uses surrogate attacks to target freezing, excessive amplification, and violations of incompressibility and energy balance. The third perturbs training states along an amplified direction and a strongly damped random direction of the dynamics. All attacks run on the surrogate alone, and DNS relabeling is performed offline once per selected state. Experiments on $128^3$ turbulence show that OAS increases the median time to failure from 21 to 721 steps. The compared baselines achieve medians of at most 110 steps, and the advantage holds across training seeds. OAS also achieves the lowest pointwise error at step 15 and the best long-horizon statistics among the compared methods. OAS integrates physical models into neural simulation by extending supervision from fixed reference trajectories to states where the surrogate is likely to fail. This principle can guide the development of more reliable scientific surrogates when deployment takes models beyond the coverage of their training data.

Improvised explosives used for fishing on shallow Indonesian reefs shatter coral skeleton, yet the damage they cause has been described largely through empirical radii and ecological surveys. We formulate an idealized model of how free gas held within a coral canopy modifies the shock loading that such a charge delivers to skeletal plates. The canopy is treated as a relaxed bubbly mixture whose shock impedance follows from the conservation of mass and momentum, and the reef is represented as a layered column of water, canopy, skeletal plate, and canopy struck at normal incidence. Three closed-form results emerge. Above a crossover pressure set by the void fraction and the stiffness of seawater, the canopy becomes nearly transparent to the shock. The impulse transmitted through any lossless layered stack is independent of the canopy, so gas redistributes the pulse in time without changing its total push. A plate carries tension after reflection from its lower face only when the canopy impedance falls below a threshold fixed by the plate thickness and the pulse duration, which defines a critical thickness. For a one-kilogram charge directly overhead, a gas-rich canopy more than triples the standoff at which a twelve-centimeter plate spalls while shortening the standoff at which it is crushed. A prescribed daily cycle of photosynthetic gas makes the same charge markedly more damaging at noon than at night. Bubble dynamics show that the canopy does not reach equilibrium within the pulse, so the results are best read as upper bounds.

Convolutional Neural Networks (CNNs) are used as analytical tools to investigate the relationship between the progress variable field and the local chemical source term in lean premixed hydrogen flames. Rather than employing machine learning for modelling, CNNs are leveraged to analyse the physical information contained in spatially resolved fields from direct numerical simulations. CNNs are particularly well suited for this task because they exploit spatial correlations and multi-scale structures, allowing an assessment of how spatial organisation influences the source term. The analysis demonstrates that the progress variable based on water, $C_{\rm H_2O}$, contains all the information required to accurately parametrise the chemical source term whereas $C_{\rm H_2}$ alone does not. The inclusion of the mixture fraction $Z$ improves the accuracy of the latter but provides no significant additional information to the CNN when the spatial field of $C_{\rm H2O}$ is used as input. The same behaviour is observed in both a laminar thermodiffusively unstable flame and a turbulent slot-jet hydrogen flame, indicating that $C_{\rm H_2O}$ is a robust single variable for parametrisation. A complementary scale analysis in the laminar case shows that spatial features extending over at least two laminar flame thicknesses are required to reconstruct the source term accurately, thereby identifying the characteristic scale in the progress variable field that carries this information. These results demonstrate how machine learning can uncover physical dependencies that remain hidden to classical statistical analyses.

In the nonlinear source of the pressure Poisson equation the fluctuating enstrophy and strain nearly cancel. We ask where the cancellation is complete, which we call silent, and how the source escapes it. Pointwise the source depends only on the eigenvalues of the velocity gradient. Pure shear has none, so it is silent. It is the origin of the normalised invariant plane, whose second-invariant coordinate is the normalised source. Let $f$ be the shear fraction of the gradient and $m$ its distance from that origin. We prove that $m\le1-f\le3m$ at every point of every incompressible flow. Wherever the source nearly vanishes and the third invariant is small, the gradient is nearly pure shear. Otherwise the cancelling gradient is a balanced vortex, a swirl its own strain cancels at any strength. At a no-slip wall the silent object is exact: the wall shear-stress fluctuation, a rank-one sheet. Away from the wall we assume the same sheet, dressed with a small residual, and derive how it escapes. The escape passes through one element of the residual, the along-sheet variation of the sheet-normal velocity. Its amplitude is the geometric mean of sheet and residual, and its sign selects swirl or strain. A rank-two silent object has the same source through the same gates but balanced eigenvalues, so the assumption fixes the escape's topology, not its source. The shear fraction is thus a pointwise proxy for cancellation by shear, and a model of the source must be built on what escapes.

The introduction of the approximated streaming to the standard Lattice Boltzmann Method (LBM) decouples the space and velocity discretizations. Although many no-slip implementations knwon from LBM can be directly adopted to the models with approximated streaming, their exact behavior in the off-lattice setting remains unexplored. In this work, we investigate the meshfree off-lattice D2Q9 model equipped with several no-slip implementations – non-equilibrium extrapolation, simple and interpolated bounceback, and moment-based boundaries – applied to a Stokes flow around a cylinder. We compare the pressure, velocity and velocity gradient fields obtained with various no-slips, on polar and hybrid polar-scattered discretizations. We find that non-equilibrium extrapolation performs the best of all the studied no-slip realizations, giving smooth stresses and zero velocity on the solid walls. Other no-slips suffer from oscillations and/or discontinuities in the hydrodynamic fields. Hybrid discretizations are found to give higher errors than the polar grid, but improve the stability of the solution. Finally, we simulate the deformation of an elastic ring under the stresses obtained with the studied no-slips to highlight the importance of the sensible choice of the no-slip realization in more complex problems.

We develop entropy-stable isothermal-wall conditions for the compressible Navier–Stokes equations at continuous and semi-discrete levels. For a stationary, impermeable, no-slip wall at constant positive temperature, adding total-energy density divided by wall temperature to the canonical convex entropy cancels the wall contribution without suppressing heat transfer. This affine modification preserves the entropy Hessian, relative entropy, and volume entropy production. It is proportional to total ballistic-energy density and yields a conditional $L_2$-type bound based on the initial field under the stated assumptions. Two wall formulations use a common discontinuous Galerkin discretization with the summation-by-parts property and simultaneous approximation terms. Both give zero adapted wall contribution without a penalty and a nonpositive contribution with it. The complete-residual formulation penalizes the full wall-data residual and balances fluid energy through its complete numerical wall flux. The Fourier-energy-exact formulation combines an entropy-neutral skew correction with a momentum-projected penalty so that the complete numerical outward energy flux equals the one-sided numerical Fourier heat flux at every wall node and spatial resolution. Pointwise tests verify the local identities. Manufactured-solution studies with entropy-stable interior coupling demonstrate convergence rates consistent with order $p_s+1$ in the discrete $L_2$ norm, where $p_s$ is the solution polynomial degree. Thermal-relaxation calculations verify the semi-discrete energy and adapted-entropy balances. Three-dimensional calculations demonstrate balance closure in a closed domain, convergence of curved-wall traces, and applicability to a complex supersonic separated flow.

Deterministic micro–macro simulation of polymer solutions requires the coupled evolution and spatial transport of a configuration distribution, together with the conversion of its moments into macroscopic stress and feedback to the flow. We develop a Fokker–Planck/lattice-Boltzmann solver for this coupling in two-dimensional dilute Hookean polymer solutions. The solver represents the distribution on the unbounded configuration space by Hermite coefficient fields, advances local configuration dynamics and physical-space transport in separate steps, and recovers Kramers stress from the second moment to achieve two-way coupling with a purified two-relaxation-time lattice-Boltzmann flow solver. To assess whether this configuration description recovers the corresponding macroscopic response, we use the exact second-moment closure of the continuous Hookean model as a macroscopic reference for comparison with analytical and independently discretized macroscopic solutions. The calculations reproduce velocity overshoot and damped oscillations in start-up Poiseuille flow, with velocity profiles approaching the analytical start-up transient under grid refinement; in four-roll flow with spatially nonuniform extension and stress feedback, the maximum full-domain relative differences in velocity and polymer stress are approximately $0.0309\%$ and $3.84\%$, respectively, over the tested Weissenberg numbers at corresponding sampling times. These comparisons support the solver's ability to recover the Hookean macroscopic response from configuration-distribution evolution. Further calculations of wall-bounded recirculation and open cross-slot flow exhibit the corresponding conformation responses and symmetric and asymmetric flow states, extending this deterministic micro–macro method to viscoelastic flows under different boundary constraints.

Molten pool flow significantly influences bead geometry, defect formation, and solidification microstructure in wire-arc directed energy deposition (DED). However, direct flow sensing remains an open challenge due to extreme temperatures, intense arc illumination, and complex flow patterns. Traditional research has relied either on computationally intensive fluid dynamics simulations, which require assumed boundary conditions and lack empirical anchoring, or on vision-based tracer particle tracking, which yields sparse, noisy, and physically unconstrained velocity estimates. This work bridges these two paradigms by reconstructing physics-constrained 2D surface flow fields from high-speed imaging of a GTAW-based wire-arc DED process under distinct flow regimes: quasi-steady convection and periodic droplet impact. The pipeline begins with homography correction to calibrate the oblique camera view, followed by dense optical flow extraction to provide raw velocity observations. For quasi-steady pools, a physics-informed neural network (PINN) reconstructs the surface velocity field by jointly enforcing data fidelity, incompressible Navier-Stokes momentum equations, no-penetration boundary conditions, and an arc-forcing prior through composite loss minimization. For pools subject to periodic droplet impact, a phase-conditioned time-dependent PINN is further developed to resolve the cyclic flow evolution throughout the impact period. This work provides a unified framework that bridges high-speed visual sensing and fluid mechanics, enabling physics-grounded flow diagnostics for wire-arc DED processes.

We introduce a dataset of approximately 10,000 Reynolds-Averaged Navier-Stokes (RANS) simulations of steady, incompressible, two-dimensional subsonic flow around downforce-generating NACA 4-digit airfoils, targeting aerodynamic regimes relevant to automotive and motorsport applications (openly available on https://huggingface.co/datasets/ratiolabs/downforce-airfoils). Using this resource, we study geometry-conditioned neural surrogates for fast flow prediction, comparing neural fields with neural ODEs, MLPs with graph-based models, and several spectral geometry-conditioning methods. We further propose Airfoil2Vec, an airfoil-specific spectral geometry encoder that combines the joint contour spectrum with separate spectral representations of camber and thickness, for predicting continuous pressure and velocity fields. We evaluate generalization through angle-of-attack interpolation, interpolation and extrapolation to unseen NACA 4-digit geometries, and generalization to unseen non-NACA airfoils. The resulting surrogate accurately captures aerodynamic quantities and qualitative flow features while providing orders-of-magnitude speedups over conventional computational fluid dynamics.

The origins of strong magnetic fields observed in many white dwarfs are uncertain. Recent observations show that such fields are more common for white dwarfs with crystallized cores. Crystallization creates a destabilizing composition gradient that drives thermohaline convection in the star's fluid envelope, which may play an important role in magnetic field emergence. We perform 3D magnetohydrodynamical simulations of thermohaline convection with magnetic fields of various strengths and orientations, using the Boussinesq approximation in periodic Cartesian boxes. Our simulations suggest that thermohaline convection can generate magnetic fields when the magnetic Prandtl number is large (i.e., low magnetic diffusivity), but they are likely too weak to account for those observed in magnetic white dwarfs. However, the simulations indicate that strong magnetic fields can be advected outwards by the thermohaline convection without being destroyed, depending on the net magnetic flux. Hence, crystallization-induced thermohaline mixing may transport magnetic fields initially trapped in white dwarf interiors to their outer layers, allowing them to be observed. However, additional simulations using more realistic geometry and magnetic field configurations will be needed to confirm this possibility.

Using diffuse-interface theory, we uncover unexpected phase-change phenomena that are absent from widely used models of evaporation and condensation. In the inviscid limit, the same adjacent thermodynamic states admit stationary evaporation and condensation with equal and opposite mass fluxes, even when the vapor pressure lies below saturation. Viscosity breaks this reversibility but gives rise to multiple stationary condensation rates for the same vapor state. Lattice Boltzmann simulations dynamically recover these states, showing that these phenomena are dynamically realized by the diffuse-interface equations rather than arising solely as mathematical solutions of the reduced interfacial relations. Our results reveal previously unexplored behavior in a well-established theory of liquid–vapor interfaces.

We present a parallel strategy for the study of the vortex-induced vibrations (VIV) of a rigid, massless cylinder mounted on translational springs, in two and three dimensions. Without mass or damping, its motion is governed solely by the fluid forces and the spring restoring force, and is an immediate response to the flow. We focus on low spring stiffness, yielding high reduced velocity and maximal oscillation amplitude. A monolithic finite element method in an arbitrary Lagrangian-Eulerian framework with implicit time stepping is proposed, solving the fluid flow, cylinder dynamics, and mesh motion simultaneously. Mesh movement is modelled with a linear elastic pseudo-solid with variable Lamé coefficients, and the no-slip condition on the cylinder is enforced with a Lagrange multiplier coupled to the position degrees of freedom; three strategies are explored to enforce this force-position coupling in a distributed framework. To the best of our knowledge, this work is the first to propose a distributed solver for three-dimensional fluid-structure interaction at zero mass ratio. The solver is verified with manufactured solutions, and exhibits second-order accuracy in time. A numerical study of two- and three-dimensional VIV for Reynolds numbers from 100 to 300 reproduces the VIV responses obtained in previous two-dimensional studies, and predicts nonperiodic 3D oscillations starting at $Re = 300$. Using the direct solver MUMPS, the proposed method scales to up to 768 compute cores.

We consider the problem of controlling a three-dimensional falling liquid film using same-fluid blowing and suction through the substrate. Building upon recent results for the corresponding two-dimensional problem, we employ a reduced-dimensional weighted-residual model for the film height and downstream flux as the basis for controller design. Linear stability analysis is used to estimate the number of actuators required to stabilise the film, while a linear-quadratic regulator (LQR) framework is used to construct feedback controls for the linearised system. The resulting gain matrix is then combined with observations from direct numerical simulation (DNS) of the three-dimensional Navier-Stokes equations, allowing controls derived from the reduced-dimensional model to be applied directly to the full flow. Through systematic numerical tests, we demonstrate that these controls successfully stabilise the flat-film solution across a physically relevant range of Reynolds numbers and domain configurations. We further show that both the number and placement of actuators play a crucial role in control performance, with spanwise instabilities requiring additional actuator coverage in the cross-stream direction. Although the extension from two to three dimensions substantially increases the cost of controller construction, this cost is incurred entirely offline during the computation of the gain matrix, making the overall framework computationally tractable. Our results demonstrate that LQR feedback controls derived from a three-dimensional weighted-residual model retain predictive value when applied to fully resolved DNS, extending previous two-dimensional control methodologies and helping bridge the gap between theoretical control design and experimentally relevant falling-film flows.

Recirculating flows are central to transport phenomena, but their generation in potential flows requires additional physical mechanisms. We show experimentally that recirculation at vanishing Reynolds number can be produced at prescribed locations by coupling oscillations of a Hele-Shaw cell ceiling with an off-center passive obstacle. The net drift is well described by a potential flow model with no adjustable parameters. The resulting flows are localized around the obstacles and can be combined to generate programmable flow patterns at the microscale.

Data-driven turbulence models for the Reynolds-averaged Navier-Stokes (RANS) equations offer a promising route to improving predictions of complex flows. Such models, specifically the turbulence constitutive relations, can be learned efficiently from high-fidelity Reynolds-stress data without evaluating the RANS equations during training. However, conventional losses weight all tensor-component and spatial errors equally, although their influence on a quantity of interest (QoI) can differ significantly; reducing the aggregate stress error therefore does not necessarily lead to an improved QoI prediction. Training against flow-level observations accounts for this dependence but requires repeated, potentially expensive RANS solutions. In canonical shear flows, physical reasoning can identify the shear component as the only one relevant for the mean-flow prediction. Motivated by this example, we propose a goal-oriented method to select and weight Reynolds-stress training data for complex flows. For a specified QoI, a single offline adjoint evaluation quantifies its sensitivity to local perturbations of each Reynolds-stress component. These sensitivities are converted into fixed weights in the supervised loss, enabling training without further RANS solutions. We validate the weighting in square-duct and periodic-hill flows, then apply it to a film-cooling jet in crossflow, where it improves velocity and cooling-effectiveness predictions over uniformly weighted training despite using a velocity-only QoI. Beyond turbulence modelling, this work suggests a broader strategy for aligning supervised learning with downstream prediction goals while preserving training efficiency.

We investigate fully nonlinear water waves and fluid-particle dynamics generated by the horizontal motion of a seabed obstacle with prescribed time-dependent velocity. The governing equations are the full Euler equations, formulated in a time-dependent conformal domain that simultaneously maps the moving free surface and seabed onto fixed boundaries. The main contribution of this work is a Lagrangian formulation for computing particle trajectories in the resulting genuinely unsteady conformal domain. We derive a closed-form trajectory system in the canonical domain in which the time dependence of the conformal map is entirely represented by the real and imaginary parts of an analytic function that can be evaluated spectrally from the surface. We apply the formulation to waves generated by horizontal submarine landslide motion and characterize particle displacements throughout the fluid as functions of the initial particle position and Froude number. Our findings identify distinct regions in which particle motion is predominantly associated with the moving seabed, the generated wave, or the combined action of both. The results reveal a transition in the dominant mechanism driving particle motion: at low Froude numbers, particle displacements are primarily associated with the moving seabed, whereas at high Froude numbers the generated wave becomes increasingly dominant, particularly near the free surface and away from the obstacle path.The numerical predictions are benchmarked against laboratory data available in the literature, showing good agreement and providing a quantitative assessment of the model accuracy. Moreover, laboratory topographies beyond those considered here can be readily incorporated into the numerical framework through a Hermite interpolation procedure.

Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample localized features and let the residual be dominated by regions that are already well resolved. We propose a feature-tracking PINN (FT-PINN) in which the solution network is defined on a fixed reference domain and composed with a diffeomorphic deformation map from a parameterized nonlinear manifold. The deformation and solution-network parameters are trained jointly by minimizing the pulled-back conservation-law residual. This lets collocation points concentrate along features of essentially arbitrary geometry, including curved, oblique, and merging shocks, without prior knowledge of their locations. The framework is agnostic to the choice of parameterization. Boundary preservation is enforced exactly through a tangential projection of the displacement, and folding is discouraged by a one-sided penalty on the Jacobian determinant. On four test problems (space-time viscous Burgers with merging shocks, a decelerating Burgers shock, the space-time Euler shock tube, and steady 2D Euler regular shock reflection), FT-PINN resolves shocks at their correct locations with a limited collocation budget. A vanilla PINN with the same architecture, budget, and training either misplaces the shocks or fails to form them.

Exact periodic solutions of the unforced incompressible Navier-Stokes equations require the convective field to be a pure gradient, absorbed into the pressure; for the cyclic trigonometric families studied previously this occurs only at isolated phases and, over the range so far classified, only at n = 3 and 4. The forced problem, we show, admits an exact construction for every phase vector and every n >= 3. For an n-parameter family of two-term cyclic fields, solenoidal and a Laplacian eigenfunction, the transverse part U^0 of its convective field serves as the body force, giving a closed-form solution with velocity, pressure and force explicit. We prove closed forms for the pressure and for both magnitudes, in every dimension and with no upper bound on n: the forcing is never trivial, and the L^2 magnitude of U^0 stands to that of the whole convective field in the constant ratio 2*sqrt(2)/3, whatever the dimension, phase or units. The forcing does no net work, so the kinetic energy decays purely viscously at arbitrary Reynolds number, giving an exact benchmark in any dimension. A numerical study of vorticity concentration at zero applied work uses it as a reference, and shows that apparent saturation can be a resolution artefact.

Smoothed Particle Hydrodynamics (SPH) is well suited to a range of problems, particularly those involving large deformations in fluid dynamics. In recent years, in addition to the advancement of SPH formulations, the development of differentiable solvers has also progressed. However, unified frameworks that flexibly accommodate diverse numerical schemes, including advanced and implicit methods, while supporting continuous extension and updating remain limited. In this study, a high-accuracy and composable differentiable SPH solver, CraftSPH, has been developed. In CraftSPH, major computational operations are implemented as independent modules, which can be combined according to the intended purpose of constructing a solver. This design enables different computational schemes to be intuitively constructed from combinations of common components and allows newly developed high-accuracy discretization methods to be flexibly incorporated and extended. Furthermore, each module supports automatic differentiation, enabling applications to physical-parameter estimation and to optimization that combines SPH solvers with deep learning models. Accordingly, CraftSPH provides an SPH computational framework in which high-accuracy discretization, explicit and implicit computations, and automatic differentiation can be handled in a unified and extensible manner. To demonstrate the applicability of CraftSPH to a wide range of problems, forward analyses are conducted for Poiseuille flow, two- and three-dimensional dam-break problems, and a rising-bubble problem. In addition, the performance of automatic differentiation is evaluated through inverse problems involving parameter estimation for the Taylor-Green vortex and lid-driven cavity flow.

Accurate and rapid prediction of the aerodynamic drag coefficient ($C_D$) is essential for vehicle design, particularly during early-stage design, where many candidate geometries must be evaluated. Although computational fluid dynamics (CFD) provides reliable aerodynamic estimates, its high computational cost limits large-scale design exploration. This paper proposes the hierarchical graph-pooling Transolver (HGPTrans), which combines hierarchical graph pooling with Transolver-based attention to directly predict $C_D$ from vehicle surface meshes. Motivated by the fact that vehicle aerodynamics depends on both local geometric features and long-range interactions among spatially distant surface regions, HGPTrans integrates three complementary components. Graph isomorphism convolutions encode discriminative local geometry, Transolver-style slice attention captures global interactions with linear computational complexity, and information-redundancy-aware hierarchical pooling progressively removes redundant nodes while preserving informative geometric structures. The model is trained and evaluated on the large-scale DrivAerNet and DrivAerNet++ datasets, where it achieves the lowest mean absolute error and mean squared error among the evaluated baselines. Its generalization capability is further assessed through transfer learning on a real-vehicle dataset containing both sedans and sport utility vehicles (SUVs), achieving relative $L_1$ errors of 1.56% (sedans) and 2.12% (SUVs) with an inference time of approximately $0.293$ s per vehicle. This corresponds to an acceleration of several orders of magnitude relative to high-fidelity CFD while keeping the predicted drag coefficients within a few percent of the CFD reference. Ablation studies confirm each component's contribution and reveal the effects of depth and pooling ratio.