Laser-induced forward transfer (LIFT) is a nozzle-free laser-assisted printing method that provides an advanced manufacturing route for spatially selective deposition of functional inks, nanoparticle suspensions, polymers, hydrogels, biological materials, and other difficult-to-nozzle formulations. The apparent simplicity of LIFT, however, conceals a strongly coupled laser-liquid interaction. Laser energy is absorbed within a confined donor architecture, converted into thermal and plasma responses, and then transformed into bubble-mediated motion of the donor material. The cavitation bubble provides the transient mechanical bridge between optical energy deposition and the hydrodynamic ejection process. This chapter presents LIFT from a multiscale perspective centered on bubble dynamics and material ejection. It first reviews major LIFT donor architectures. Then, it examines how donor ribbon design, absorbing-layer properties, laser parameters, material rheology, control bubble inception/growth, jet formation, droplet breakup, and final deposition. Modeling approaches are discussed as tools for connecting experimental observations across time and length scales, ranging from reduced-order estimates to interface-resolving simulations and data-driven process maps. As one illustrative mechanistic example, thermal-only, plasma-mediated, and coupled plasma-thermal-thermoelastic frameworks for early-stage bubble inception are briefly compared to show how different inception assumptions can provide initial conditions for downstream bubble growth and jetting models. This chapter concludes by identifying opportunities for bubble-aware donor design, time-resolved diagnostics, benchmark datasets, and predictive LIFT process maps based on intermediate bubble and jet observables.

This study investigated how additively manufactured nozzles with body-centered cubic lattice structures reduce the flame flashback propensity in a hydrogen jet flame burner. Five different configurations of a jet flame combustor were investigated, with a focus on mixing duct walls incorporating porous media. The nozzles were manufactured by the powder bed fusion of metals using a laser beam process. The lattice parameters were varied by the volume fraction and the strut diameter. For the experiments, pure hydrogen was used as fuel under atmospheric conditions at various equivalence ratios and Reynolds numbers of 9,000 - 12,000. Flow field measurements, flame imaging, and spectral proper orthogonal decomposition of the flame dynamics were employed to identify possible transition mechanisms from a stable operation to flashback. The flow fields and the flame shapes showed only minor effects from wall modifications, preserving general flow characteristics across configurations. The flow dynamics in the combustion chamber were dominated by large-scale coherent structures in the shear layer, specifically Kelvin-Helmholtz instabilities. The results demonstrated that the nozzle with the coarsest porous wall structure significantly improved the flashback resistance compared to a nozzle with a solid wall. It is concluded that the primary mitigation mechanism was a cooling effect by unburnt mixture flowing through the porous media. The findings confirmed that the integration of lattice structures through additive manufacturing provides a viable strategy for hydrogen flashback mitigation by manipulating the coupled interaction between the flame and the thermal conditions of the wall.

Diffuse-interface models are a widely used framework for interfacial dynamics in complex fluids, in which interfaces are represented through smooth transition layers and capillary effects are encoded by a free-energy functional. For incompressible mixtures with more than two phases, however, robust computation is substantially more difficult because the numerical method should preserve the balance structure of the continuum model, maintain the saturation constraint, dissipate energy, and treat all phases symmetrically even when density ratios are arbitrary. Existing structure-preserving methods are largely developed for binary flows or for formulations that distinguish a reference phase, so a genuinely symmetric N-phase discretization remains lacking. The practical problem is therefore to construct a fully-discrete method for N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture models that retains the key thermodynamic and conservation properties of the continuum equations for arbitrary density ratios. Here we propose a symmetric fully-discrete method for the N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture model with arbitrary density ratios. The method yields a fully-discrete problem in which every solution satisfies exact phase volume conservation, phase mass conservation, total volume conservation, total mass conservation, and a discrete energy-dissipation law. In addition, if the volume-saturation constraint holds for the initial data, then it is preserved at every time step. We numerically verify these structure-preserving properties and demonstrate the robustness of the method in representative multiphase flow problems. The resulting scheme provides a computational framework for incompressible N-phase mixture flows with complex interfacial dynamics and arbitrary density contrasts.

Accurate modeling of tsunamis (such as those generated by landslides) requires capturing both wave dispersion in the deep ocean and wave breaking near the shore. The shallow water equations are often preferred for working with tsunamis, but neglect dispersion and may be inaccurate in scenarios where dispersive effects are significant. In this work, we develop an approach that seeks to incorporate the best aspects of both hyperbolic and dispersive models by combining either of two hyperbolic reformulations of the Serre-Green-Naghdi equations away from the shore with the non-dispersive shallow water equations near the shore. The model is discretized and implemented within the GeoClaw software, and incorporates adaptive mesh refinement as well as shared-memory parallelism. We validate it through comparison with benchmarks and real tsunami data. The results and performance compare favorably with the existing dispersive water wave solvers, including a speedup of about 2x relative to GeoClaw's existing dispersive solver for a large-scale tsunami simulation.

Particulate contaminants decrease the power output of solar panels, the transparency of windows, and are detrimental to microelectronics, where even a single particle can induce a short circuit. Despite significant research on particle adhesion and self-cleaning, it remains unclear when and how a drop can remove a particle from a surface, thus efficiently cleaning the surface. Here, by combining lattice Boltzmann simulations and confocal microscopy experiments, we show that at least six different scenarios arise from the complex interplay between capillary and friction forces when a drop collides with a particle. Notably, the capillary force plays a dual role in particle removal: while its tangential component always drives removal, its normal component can also hinder it. By introducing a dimensionless capillary capture parameter, we can predict particle removal across a wide range of particle and surface properties. These results provide quantitative design principles for easy-to-clean surfaces that minimize water and chemical usage.

Thin films draining on top of curved surfaces occur in coating, manufacturing, and geophysical flows, where predicting accumulation and thinning is crucial. Unlike singularities associated with contact lines, boundaries, defects, a smooth saddle alone can produce a locally singular drainage thickness distribution. The singularity stems from competing converging and diverging flow and is regularized within a dynamically selected region where drainage, hydrostatic pressure, and capillarity balance. Saddles thus emerge as generic building blocks for thin-film drainage on complex topographies.

We propose a minimal, rotation-free model of magnetohydrodynamic (MHD) dynamo action driven by laminar thermal convection in a regular tetrahedral cavity. Unlike canonical planetary-dynamo settings, where flow helicity is supplied by global rotation, the present system generates robust flow helicity purely through the geometric constraints imposed by tetrahedral boundaries. Direct numerical simulations show exponential amplification of a weak seed magnetic field and a nonlinear saturated state in which the magnetic energy exceeds the kinetic energy. The convective flow organizes into a highly symmetric pattern with \(D_4\) dihedral symmetry. The dynamo-generated magnetic field obeys a corresponding signed \(D_4\) symmetry involving antisymmetry under \(\pi\)-rotations about the two horizontal axes of the tetrahedron. The tetrahedral dynamo provides a conceptually transparent setting for isolating geometry-induced helicity, magnetic-field amplification, and a closed induction cycle in a non-rotating laminar flow.

Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a 256^2 DNS dataset at Re_f \approx 2250, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25% to 94% in reconstruction and from 20% to 79% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias -0.70 that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias -0.117 at just 20 function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of S_3, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of S_3 suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.

Mangroves are increasingly promoted as nature-based solutions for coastal protection, yet many existing models neglect the vertical variation of vegetation biomass, leading to oversimplified representations of root-flow interactions. In this study, we introduce a generalised parametrisation of the mangrove vegetation profile that is applicable across multiple mangrove species and derive a wave attenuation model that explicitly accounts for the mangrove root characteristics. Based on this parametrisation, we propose a simplified mangrove representation that reproduces a prescribed drag force profile and is suitable for both computational fluid dynamics simulations and experimental fabrication. The hydrodynamic performance of the proposed model is evaluated using OpenFOAM simulations. Our results show that the wave attenuation effectiveness of mangroves is frequency-selective and species dependent. This nonlinear behaviour contrasts with classical vegetation models and reveals a previously unrecognized mechanism by which mangrove root characteristics govern coastal protection.

The translation dynamics of two binary mixture droplets is investigated theoretically and is corroborated with experiments. The proposed model accounts for the effects of Marangoni stresses generated by evaporative cooling and concentration gradients, as well as vapour diffusion, for both components of the binary mixture. We consider thin droplets, allowing us to use the lubrication theory to derive the evolution equation for the droplet profiles. We numerically solve the evolution equations using the finite element method and examine various cases of pure and binary droplet pairs exhibiting translational behaviours like attraction, repulsion, and 'chasing'. The results show that the combined effect of solutal Marangoni, capillary effect, and thermal Marangoni determines the movement of the droplets. The non-uniform evaporation generated from 'vapour shielding' creates such effects. We observe that for droplets with the same initial composition, solutal Marangoni and capillary forces induce droplet attraction, while thermal Marangoni effects drive their repulsion. For droplets with different initial compositions, the drop with a higher concentration of the more volatile component pushes, or `chases', the drop with a lower initial concentration of this component, completely driven by the solutal Marangoni. We carried out experiments involving water-morpholine binary mixture droplets to validate the results predicted by our model.

The current study presents a three-dimensional linear stability analysis of particle-laden Couette-Poiseuille flow suspended in a Newtonian fluid between two parallel plates, with the lower plate coated by a porous medium. The influence of suspended particles is examined using a two-domain formulation in which particles are confined to the fluid layer and do not penetrate the porous substrate. The particle-laden suspension is modeled using the dusty-gas framework, while the flow within the porous layer is described by the volume-averaged Navier-Stokes (VANS) equations. In particle-laden flows over impermeable walls, particle inertia may either stabilize or destabilize the flow depending on the governing parameters. In contrast, the presence of a porous layer introduces an additional permeability-dependent destabilizing mechanism that fundamentally modifies these classical trends. Consequently, particle loading can reduce the critical Reynolds number at sufficiently high permeability, even in parameter regimes where particles stabilize the corresponding rigid-wall flow. The coupled formulation also introduces additional disturbance branches associated with fluid-particle coupling near the permeable interface. Although these modes remain stable across the parameter space investigated, they modify the eigenspectrum and influence the dominant instability by altering coupling pathways. Furthermore, unlike impermeable-wall Couette-Poiseuille flow, where increasing the Couette component generally stabilizes the flow, the porous-wall configuration exhibits a monotonic decrease in the critical Reynolds number over the range examined. These results demonstrate that porous boundaries can fundamentally alter established stability behavior in particle-laden shear flows through permeability-dependent coupling between the suspension and the porous substrate.

Rendezvous is a critical task for multi-agent systems, requiring agents to coordinate to meet at an unspecified location. However, achieving this in fluid environments presents a challenge, as it remains unclear how agents can exploit underlying fluid kinematics to facilitate convergence. In this study, we adopt a multi-agent reinforcement learning (MARL) approach to develop physics-informed rendezvous strategies in vortical flows. Compared to a naive strategy, where agents navigate toward their counterparts, MARL strategies significantly improve the rendezvous rate. MARL strategies also show transferability across varying vortex intensities, vortex scales, and swarm sizes. By breaking the symmetry of the state-action map, MARL strategy leverages a non-intuitive mechanism that prevents agents from becoming trapped in separate vortices, thereby enhancing rendezvous success. Additionally, a heuristic strategy is extracted from the learned strategy and also outperforms the naive strategy. Furthermore, a theoretical analysis demonstrates that fluid deformation impedes the rendezvous process. Large finite-time Lyapunov exponents identify where fluid effects separate adjacent agents, suggesting that targets should be planned in weak-deformation regions. Our findings reveal the important role that agent-fluid interactions play in multi-agent tasks and highlight the MARL capability to explore swarm intelligence in complex flow environments.

We tackle two key difficulties in the simulation of the viscous hydrodynamics of a large dense collection of rigid particles: (i) the poor convergence rate of an iterative solution of the discretized linear system as particle gaps shrink, and (ii) the large number of unknowns needed to accurately discretize the resulting lubrication-driven flows. Our focus is the 2D Stokes resistance and mobility boundary value problems for nearly-touching disks. To address both challenges, we introduce a general two-body preconditioning strategy, and implement it with the method of fundamental solutions. For each close particle pair, the hard-to-resolve interaction is represented in a basis precomputed by solving a local boundary value problem on a fine grid. In an iterative solve, the resulting flow field corrects that obtained from a coarse representation of all particles. The local fine-grid correction can even be compressed so that all particles except the pair itself are affected by an equivalent set of coarse sources. Numerical experiments demonstrate rapid GMRES convergence in challenging multi-particle settings, with iteration counts remaining low even in densely packed suspensions. For example, the mobility problem is solved for a random close packing with area fraction $\phi = 0.65$, $P = 10000$ monodisperse disks, and minimum separation $10^{-3}$, in just 47 GMRES iterations, achieving five digits of accuracy with 72 vector unknowns per body.

Droplet and particle grouping can be influenced by applying an acoustic field and have practical applications such as particle scavenging and aerosol filters of engine exhaust and air purifiers. The present work experimentally investigates the influence of a standing acoustic wave on a single stream of droplets. The experimental setup consists of an acoustic transducer and a reflector plate through which the droplet stream passes in the presence or absence of an external pressure field generated by a standing acoustic wave. A droplet stream is generated with the help of a nozzle connected to a pressurized working fluid supply and piezoelectric transducer to control the spacing between droplets. The effect of the acoustic pressure field on the droplet stream generated by the nozzle operated at different piezoelectric excitation frequencies and fluid pressures is investigated. Droplet stream characteristics at every nozzle excitation frequency are observed with a high-speed camera when the acoustic field is switched OFF and ON. The competing effect of nozzle excitation frequency and acoustic field is observed. At lower nozzle frequencies, the nozzle generates an unstable stream of droplets having different sizes and spacings between them. When the acoustic field is applied at these lower frequencies, the stream of droplets becomes organized, and in some cases, it becomes equispaced and of the same size. However, an opposite behavior is observed at higher frequencies. In these cases, as the acoustic field is applied, an equispaced mono-disperse droplet stream becomes unstable due to the coalescence of droplets within the stream.

Data-driven modeling shows significant promise for faster-than-real-time forecasting of fluid flows. For real-world engineering applications (e.g., flow control), models must contend with limited, imperfect, and incomplete experimental measurements. In this work, we present an analysis of data-driven surrogate models trained to forecast the time-evolution of experimentally measured cylinder wakes in the subcritical vortex shedding regime. Using a dataset of two-dimensional, two-component particle image velocimetry measurements, we train fully convolutional neural networks, U-Nets, Fourier neural operators, and dynamic mode decomposition-based models to forecast the development of experimentally measured velocity fields. To characterize data-driven approaches contending with transient flow features and limited, imperfect observations, the development of predictions over extended forecast horizons is examined at a fixed Reynolds number (Re = 590). Next, models are trained at a range of Reynolds numbers (Re = 230 to Re = 2920) to investigate the impact of increasingly turbulent and three-dimensional flow phenomena, and the challenges associated with measuring them, on forecast quality. We find that experimentally trained surrogate models can provide meaningful predictions over short time horizons, propagate low-frequency dynamics over longer forecast periods, and achieve faster-than-real-time evaluation. However, the data-driven models struggle to preserve transient flow features and high-frequency energy content when faced with noisy measurements and incomplete state observations. This emphasizes the underlying challenges that remain for data-driven modeling approaches to effectively contend with fluid dynamics in real-world engineering applications, where observations are often imperfect and limited.

Immersed boundary methods (IBMs) are widely used to simulate flows around complex geometries and moving bodies, but they often involve a trade-off between precision and computational efficiency. Eulerian formulations require special treatments for moving walls and may generate spurious force oscillations, whereas Lagrangian formulations can suffer from slip errors at the immersed surfaces. We propose a novel sharp-interface IBM for incompressible flows involving moving, deformable, and arbitrary-thickness bodies. The method combines a fast tagging algorithm, a two-sided Eulerian forcing strategy, and a consistent mass correction that reduces the splitting error of fractional-step schemes, while preserving the structure of the discrete Laplacian operator. This formulation retains the efficiency of direct Poisson solvers, thus avoiding the overhead of cut-cell, multigrid, and projection-based approaches. The method naturally handles moving boundaries, and yields small transpiration errors with second-order accuracy in the enforcement of the no-slip condition. Numerical tests using rigid, deformable, turbulent, and biologically inspired flows demonstrate the accuracy, robustness, and efficiency of the method, without compromising computational cost.

It is shown that the lowest (second) order truncation of the Carleman linearization of the fluid equations (C2) recovers the late stage of the evolution, namely the steady-state solution, although to a decreasing degree of accuracy at increasing Reynolds number. This asymptotic property is first proved analytically for the decaying logistic with external forcing and then shown to hold to a significant degree of accuracy also for the more complex case of two-dimensional Kolmogorov-like fluid flow at low Reynolds numbers, below $Re \sim 10$. This time-asymptotic property may open interesting prospects for the quantum simulation of low-Reynolds steady-state fluid flows.

The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data. This addresses a key limitation of a-priori learning where direct numerical simulation (DNS) data is used to approximate the subgrid stress with the assumption of a low-pass filter. Closures trained in this a-priori manner frequently lead to unstable deployments due to the mismatch between the assumed filter and the effect of numerical discretizations and coarse-graining. In comparison, while typically stable during deployment, a-posteriori learning incurs high computational costs due to the need to backpropagate through a large eddy simulation (LES) solver. Furthermore, a-posteriori methods are challenging to apply broadly since they require significant modification of existing solvers. Finally, both approaches are limited when generalization is desired across different numerical schemes with their implicit filtering characteristics. In this work, we present a deep-learning approach for turbulence closure modeling built on the continuous data assimilation framework. Our approach enables the a-priori training of closures using sparsely observed DNS data without modifying or differentiating through the LES solver, while preserving stability during deployment for the recovery of invariant statistics. We focus on the model's ability to adapt to different discretizations by explicitly conditioning it on the numerical scheme. We use two- and three-dimensional canonical cases to test our framework and show that the learned correction systematically tracks the discretization error of the coarse solver.

Lagrangian measurements of tracer particle dispersion in stratified turbulence are presented from a large-scale experiment achieving both high buoyancy Reynolds numbers and low Froude numbers -- a regime characteristic of oceanic conditions. Stratification has a pronounced effect on the vertical particle dispersion, which is observed to be constrained to distances on the order of the buoyancy scale $w_{\mathrm{std}}/N$, where $w_{\mathrm{std}}$ is the standard deviation of the vertical velocity and $N$ is the Brunt-Väisälä frequency. As expected in strongly nonlinear, stratified turbulence, the frequency spectrum of the Lagrangian velocity becomes isotropic at frequencies higher than $N$. The spectral decay follows a $1/f^3$ scaling, which contrasts with the $1/f^2$ behavior typical of homogeneous isotropic turbulence. At time scales corresponding to internal waves, the statistics of velocity increments remain Gaussian, consistent with the weakly nonlinear regime of wave turbulence. At smaller scales, however, the flow exhibits strongly non-Gaussian statistics, indicative of fully nonlinear turbulent dynamics driven by wave breaking.

Data assimilation (DA) for compressible flows with shocks is challenging because many classical DA methods generate spurious oscillations and nonphysical features near uncertain shocks. We focus here on the ensemble Kalman filter (EnKF). We show that the poor performance of the EnKF may be attributed to the bimodal forecast distribution that can arise in the vicinity of an uncertain shock location; this violates the assumptions underpinning the EnKF, which assume a forecast which is close to Gaussian. To address this issue we introduce the new neural EnKF. The basic idea is to systematically embed neural function approximations within ensemble DA by mapping the forecast ensemble of shocked flows to the parameter space (weights and biases) of a deep neural network (NN) and to subsequently perform DA in that space. The nonlinear mapping encodes sharp and smooth flow features in an ensemble of NN parameters. Neural EnKF updates are therefore well-behaved only if the NN parameters vary smoothly within the neural representation of the forecast ensemble. We show that such a smooth variation of network parameters can be enforced via physics-informed transfer learning, and demonstrate that in so-doing the neural EnKF avoids the spurious oscillations and nonphysical features that plague the EnKF. The applicability of the neural EnKF is demonstrated through a series of systematic numerical experiments with the inviscid Burgers' equation, the Sod shock tube, and a two-dimensional blast wave.

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

We present evidence of the dynamical hysteretic nature of dissipation in unsteady turbulent flows. Wind tunnel experiments and direct numerical simulations in oscillating flows show that, at stationary mean Reynolds number, the dissipation constant is larger for decelerating flows. Consequently, a periodic behavior of the flow produces a hysteresis cycle, whose area scales with a parameter combining the Strouhal number and the relative amplitude of the forcing. This phenomenon can be explained and quantified through the influence of the unsteady term in the Karman-Howarth equation, with implications for a wide range of out-of-equilibrium systems.

In this work, Galerkin projection is used to build reduced-order models (ROM) for two-dimensional Rayleigh-Bénard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for velocity and temperature with a coupled formalism where the equations are projected onto a single basis combining velocity and temperature components. Orthonormal bases for modal projection are obtained as the eigenfunctions of the controllability Gramian of the linearized RB equations, eliminating the need for DNS snapshot databases required by traditional POD-based approaches. Various coupled and uncoupled ROMs with different numbers of modes are generated and validated against direct numerical simulations (DNS) over a wide range of Rayleigh numbers. One of the objectives is to determine their domain of validity as a function of the system dimension and the Rayleigh number. DNS and ROM results are compared in terms of mean vertical profiles, heat flux, flow structures, dynamical regimes and energy spectra. Crucially, unlike previous POD-based Galerkin models for thermal convection, these ROMs do not require closure models and remain numerically stable. The coupled approach shows better agreement with DNS in terms of mean vertical profiles and Nusselt number scaling. The capabilities of these models are exploited to conduct a detailed bifurcation analysis at $Pr = 10$ using Poincaré sections and Lyapunov exponents, precisely identifying the transitions between periodic, quasiperiodic, and chaotic states with significant reductions of computational cost.

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly turbulent flows are not feasible in the foreseeable future, and reduced-order models must capture dynamics that involve interactions across scales. In the present work, we propose a novel framework, Graph-based Learning of Effective Dynamics (Graph-LED), that leverages graph neural networks (GNNs), as well as an attention-based autoregressive model, to extract the effective dynamics from a small amount of simulation data. GNNs represent flow fields on unstructured meshes as graphs and effectively handle complex geometries and non-uniform grids. The proposed method combines a GNN based, dimensionality reduction for variable-size unstructured meshes with an autoregressive temporal attention model that can learn temporal dependencies automatically. We evaluated the proposed approach on a suite of fluid dynamics problems, including flow past a cylinder and flow over a backward-facing step over a range of Reynolds numbers. The results demonstrate robust and effective forecasting of spatio-temporal physics; in the case of the flow past a cylinder, both small-scale effects that occur close to the cylinder as well as its wake are accurately captured.

Fluidic injection offers a promising solution to improve the performance of the overexpanded single expansion ramp nozzles (SERNs) during vehicle acceleration. However, determining the injection parameters that yield the best overall performance across multiple nozzle operating conditions remains a challenge. The gradient-based optimization method requires gradients of injection parameters at each design point, which can lead to high computational costs when using computational fluid dynamics (CFD) simulations. This paper uses a pretrained neural network to replace CFD during optimization, enabling quick calculation of the nozzle flow field at multiple design points. Considering the physical characteristics of the nozzle flow field, a prior-based prediction strategy is adopted to enhance the model's accuracy. In addition, the neural network's back-propagation algorithm computes gradients quickly by running the computation only once, thereby greatly reducing gradient computation time compared to the finite difference method. As a test case, the average nozzle thrust coefficient of an SERN at seven design points is optimized, resulting in a 1.14\% improvement. The time cost is greatly reduced compared with traditional optimization methods, even when the time required to establish the training database is included.

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured or unstructured grids. The framework integrates multi-level information to generate high fidelity time sequences of the system dynamics. We demonstrate the effectiveness and versatility of our framework with two case studies in incompressible, two dimensional, low Reynolds cylinder flow on an unstructured mesh and incompressible turbulent channel flow on a structured mesh, both parameterized by the Reynolds number. Our results illustrate the framework's robustness and ability to generate accurate flow sequences across various parameter settings, significantly reducing computational costs allowing for efficient forecasting and reconstruction of flow dynamics.