The weak wall-normal pressure variation in pressure-driven rarefied Poiseuille flow is a stringent test of higher-order constitutive models: it is almost invisible in the total-pressure norm, yet it is generated by anisotropic molecular stress. A tangent-form nonlinear coupled constitutive relation (NCCR) reproduces its convex topology, but the physical reason for its quantitative success remains unresolved. We ask whether the constitutive stress relation and reduced streamwise forcing are independently accurate or whether their effects compensate. A direct simulation Monte Carlo (DSMC) campaign is analysed using two-dimensional momentum budgets, a pressure-error norm based on the transverse signal, a matched-outlet-Knudsen comparison and componentwise tests of the pre-elimination NCCR balance. The non-equilibrium wall-normal stress over-supports the measured pressure defect, while streamwise transport of shear stress supplies an opposing correction. The state map, momentum budgets and forcing diagnostics show that neither outlet Knudsen nor outlet Mach number alone organises the pressure amplitude; along the fixed-ratio sequence, rarefaction is accompanied by larger changes in the constitutive diagnostics than in pressure amplitude. The DSMC-inferred stress relation departs from the fixed reduced coefficient, and even the best common scalar closes the dominant shear component far more accurately than the normal components that carry the pressure field. Correcting the coefficient alone can therefore worsen the reconstruction, whereas restoring omitted streamwise-momentum terms reduces the amplitude bias in strongly accelerated cases. The reduced law can remain accurate through stress–momentum compensation, showing that agreement of a weak non-equilibrium observable need not imply correct internal closure mechanics.

The collision process is essential to the Direct Simulation Monte Carlo (DSMC) method, as it incorporates the fundamental principles of the Boltzmann and Kac stochastic equations. The primary impetus of this paper is to rectify a long-standing theoretical flaw in the widely used no-time-counter (NTC) collision algorithm. We demonstrate that the standard NTC scheme is fundamentally non-Markovian, relying on a fixed majorant product that introduces a system 'memory' and leads to inaccuracies at low particle counts. We propose a new algorithm, NTC-Pre-Scan, which transforms the scheme into a fully Markovian process. When repeated collisions are not crucial, our new NTC scheme, called NTC-Pre-Scan, can operate accurately with a very low number of particles per cell (PPC), with average PPC < 1 (e.g., PPC = 0.01), resulting in several empty cells in simulations. This contrasts with the standard NTC schemes, which typically require a PPC greater than 1. Then, a systematic evaluation of different Bernoulli-Trial (BT)-based collision partner selection schemes, including the simplified Bernoulli trials (SBT), generalized Bernoulli trials (GBT), symmetrized and simplified Bernoulli trials (SSBT), and the newly proposed symmetrized and generalized Bernoulli trials (SGBT), is conducted to treat some benchmark rarefied gas dynamics problems. The results show that the BT-based collision algorithms and NTC-Pre-scan successfully maintain the collision frequency as the number of particles per cell decreases. Simulation of the Bobylev-Krook-Wu (BKW) problem, for which an exact solution of the Boltzmann equation is available, indicates that, like the GBT, the SGBT algorithm yields the same results as theory for the average of the fourth moment of the velocity distribution function (VDF). The simulation on the three-dimensional computational grid for the GBT and SGBT schemes matches the fourth moment of the velocity component of the VDF exactly with the analytical solution. Performance analysis in a micro cavity reveals that the GBT, SSBT, and SGBT decrease the computational cost of simulation. Specifically, the computational cost of the SGBT scheme has been reduced by around 40 % when an appropriate selection number (N-sel) is chosen, and this scheme requires a sample size of 0.62 of the NTC scheme. Finally, we demonstrate that all algorithms successfully capture complex flow phenomena, such as shock waves, in the case of hypersonic flow over a cylinder. Moreover, in the cylinder problem, the SGBT scheme can achieve the same level of accuracy with 28 % less computational cost and an outstanding sample size of 0.319 of the nearest neighbor (NN) scheme, which is the modern invariant of the NTC scheme. These advancements enable accurate simulation of rarefied gases with fewer particles (NTC-Pre-Scan) and lower computational cost (SGBT), which is directly beneficial for the design of complex vacuum systems.

This paper presents a novel computational framework for the Direct Simulation Monte Carlo (DSMC) method that utilizes two distinct adaptive strategies: an initial mesh refinement algorithm to determine the primary sampling grid, and an innovative Time-Averaged Inverse Transient Adaptive Sub-cell (TAI-TAS) method to manage the collisional sub-cells dynamically. Contrary to standard TAS approaches, the principal advantage of the TAI-TAS method is its allocation of the highest computational resolution (i.e., the maximum number of sub-cells) to the lowest-density regions of the flow, ensuring physical accuracy in these critical, highly rarefied zones. The framework's effectiveness is demonstrated in challenging one-dimensional shock tube simulations, including a case with a 10:1 density ratio and a complex double-diaphragm shock tube problem designed to study wave interactions. This approach, particularly when paired with the Simplified Bernoulli Trials (SBT) collision scheme, demonstrates the ability to produce high-fidelity results with remarkably low numbers of particles per cell. Furthermore, the proposed SBT collision scheme combined with the TAI-TAS method accurately resolves the above shock tube problem with a significantly smaller number of particles per cell than previously reported in the literature.

Neural surrogates for molecular scattering provide a route to continuously evaluable and differentiable direct simulation Monte Carlo (DSMC) collision kernels, but a small pointwise deflection-angle error is not sufficient evidence that a learned map is kinetically reliable. Diffusion, viscosity, representative collision rates, angular redistribution, and mixture relaxation are nonlinear functionals of the same scattering measure. We therefore develop a multiscale validation framework for neural ab initio scattering kernels that combines angular regression, transport cross sections, Ohr-style representative quantities, cumulative angular measures, Fourier spectral content, impact-grid and angular-noise robustness, loss-ablation diagnostics, and three solver-level DSMC mixture tests. The framework is demonstrated on a refined argon–argon Jäger table and on helium–argon ab initio EPAPS data of Sharipov and Benites represented by a neural equal-area scattering surrogate. For He–Ar over /≥10 K, the surrogate preserves , , /, , and within 0.75%, 1.37%, 0.84%, 1.21%, and 1.46%, respectively. The cumulative angular measure agrees within 1.43%, the median relative L_2 error of χ(q) is 3.4×10^-3, and the high-mode spectral-energy ratio is essentially unbiased. The same neural He–Ar kernel is then embedded in periodic DSMC mixture problems that separately probe mass diffusion, momentum diffusion, and two-dimensional field-level mixing. A sinusoidal composition mode is reproduced over three independent realizations with a mean normalized-history error of 1.28±0.22% and D_/D_=1.015±0.013. A transverse shear wave is reproduced with a 1.58% history error and ν_/ν_=0.989.

Rarefied gas dynamics spans a wide spectrum of applications: micro–nano devices where the mean free path becomes comparable to characteristic lengths, vacuum and porous systems where Knudsen diffusion emerges, and high-speed (including hypersonic) flows where non-equilibrium effects shape transport and surface interactions [...]

The Direct Simulation Monte-Carlo (DSMC) method is based on splitting the rarefied gas process evolution into two ballistic and collision steps within a time step. The collision step is the more complicated, requiring a rigorous theoretical analysis to discover its relation to the fundamental kinetic equations. In this work, we present a systematic derivation and examination of the Bernoulli-Trial (BT) family of collision schemes. The master Kac equation describes the binary collision interactions as a stochastic process lying in the background of the DSMC probabilistic rules, and it serves as a starting point for our derivation of the BT family. This study is limited to the analysis of four BT members, including Simplified Bernoulli Trials (SBT), Generalized Bernoulli Trials (GBT), Symmetrized Simplified Bernoulli Trials (SSBT), and Symmetrized Generalized Bernoulli Trials (SGBT). These schemes are implemented in the DSMC code, and a simple relaxation problem is simulated to determine optimal values for the pair-selection parameter Nsel.

This study investigates the aerodynamic performance of an Audi A4 sedan using computational fluid dynamics (CFD) and machine learning (ML) analysis. The CFD setup was first validated against published DrivAer Notchback wind-tunnel data, showing a Cd deviation of 3.25%, and was subsequently applied to the Audi A4-like sedan geometry. The ride height varied from 1.336 to 1.536 m, and the rake angle ranged from 0° to 5° across the four Reynolds numbers (Re = 4.87 × 106, 9.75 × 106, 14.61 × 106, and 19.48 × 106). In our ML analysis, gradient boosting emerged as the most accurate predictive model (R2 ≈ 0.91 for Cd and 0.96 for the lift coefficient, Cl), outperforming random forest and LightGBM. Differential evolution optimization was performed under balanced, drag-focused, and downforce-focused conditions. The Reynolds number had a minimal effect on the optimum location; therefore, detailed results are reported for Re = 9.75 × 106, with other Re values showing similar trends. The baseline geometry (ride height = 1.436 m, rake angle = 0°) had Cd = 0.313 and Cl = +0.029. Balanced optimization resulted in Cd = 0.287 (–8.31%) and Cl = –0.083 (corresponding to a net change in Cl of –0.112 relative to the baseline). The minimum drag condition reached Cd = 0.285 (–8.95%) with a slight positive lift (Cl = +0.014), whereas the maximum downforce optimization reached Cl = –0.108 with a 6.71% drag penalty (Cd = 0.334). Recognizing the resolution limits of the dataset, near-optimal solutions were found within approximate ride-height ranges of ≈ 1.34–1.36 m and rake angles of ≈ 0.1°–4.6°, indicating robust aerodynamic performance rather than singular precise geometrical points. The machine learning predictions were validated against CFD with < 3% error in Cd. However, owing to the limited training set of 100 CFD samples, Cl predictions exhibited higher validation errors, with the most notable discrepancies occurring in the balanced condition. Finally, under simplified energy estimation assumptions, the minimum-drag configuration indicates an idealized decrease in aerodynamic energy/fuel consumption of approximately 9.1%, whereas the maximum-downforce configuration substantially increases the downforce at the expense of higher drag.

Rarefied gas flow over a micro backward-facing step (BFS) is a canonical non-equilibrium benchmark featuring separation, recirculation and strong Knudsen-layer effects that are highly sensitive to both the Knudsen number and the step-height ratio. High-fidelity Direct Simulation Monte Carlo (DSMC) simulations resolve these phenomena but are prohibitively expensive for parametric studies, uncertainty quantification and design exploration. In this work, we develop a Deep Operator Network (DeepONet) surrogate for rarefied step flows that maps the Knudsen number ( Kn ) and the geometric ratio (h/H) to the full two-dimensional velocity field in a micro-step geometry. The architecture is augmented with a physics-guided zonal loss that assigns higher weights to errors in the recirculation region ( U < 0 ), thereby enforcing accurate prediction of separation and reattachment. Systematic comparisons with DSMC data in the slip and early transition regimes show that the surrogate reproduces key physical trends, including the shortening and eventual disappearance of the separation bubble with increasing Kn and the non-monotonic variation of the reattachment length with h/H. A low-data study (reported in the supplementary material) demonstrates that the model attains more than 90% of its asymptotic accuracy using only about 40– 50% of the available high-fidelity simulations, substantially mitigating the cost of data generation. Furthermore, stochastic weight averaging Gaussian (SWAG) provides epistemic uncertainty estimates that are naturally localized near the shear layer and separation point, i.e. in the most non-equilibrium regions of the flow. The resulting framework offers a fast, robust and data-efficient tool for exploring rarefied micro-step flows, enabling many-query analyses in regimes where direct DSMC sampling is computationally intractable.

We examine the structure of Direct Simulation Monte Carlo (DSMC)-resolved internal compression layers in rarefied micro-nozzle flows and show that their apparent parametric complexity is largely a registration and finite-thickness scaling effect. A density-gradient diagnostic identifies the compression-layer station x_s, while a jump-based thickness δ_j=Δρ/max|/∂ x| defines a shock-centered coordinate ξ_j=(x-x_s)/δ_j. In physical coordinates, the leading proper orthogonal decomposition (POD) mode of the centerline density profiles captures only 83.33% of the fluctuation energy, whereas the jump-scaled coordinate increases this value to 98.33%. A two-dimensional shock-window POD further confirms that this compactness is not a centerline artifact: in the registered (ξ_j,η) frame, the first density mode captures 94.98% and the first two modes capture 99.05% of the fluctuation energy. The same region is identified by density-gradient and gradient-length Knudsen-number diagnostics, linking the reduced representation to localized short-gradient-length rarefaction rather than to shock motion alone. We then use this structure as an inductive bias in a shock-aligned Fusion–Deep Operator Network (DeepONet) surrogate for density, velocity components, temperature, Mach number, and pressure. For held-out back-pressure cases, density, temperature, and pressure errors remain below 6.8%, 4.3%, and 6.8%, respectively, and the hardest case reduces the shock-window mean error from 9.75%–22.27% for standard baselines to 4.51%. The results show that improved prediction follows from the reduced shock-centered structure of the DSMC fields rather than from network capacity alone.

Wall traction in a rarefied gas is a half-range functional of molecules arriving at and leaving a surface, whereas hybrid solvers, moment methods, and learned wall models often transmit only finite full-range moments. We determine which directional information is lost and what restores the wall functional using direct simulation Monte Carlo (DSMC) of Mach-6 flow over three triangular-protrusion orientations. Output-specialized neural networks interpolate a 57-condition DSMC database. A distinct ExtraTrees regression holds learner capacity, auxiliary features, train/test split, and seeds fixed while comparing the primitive state S_0, the momentum-flux-augmented state S_1, and the heat-flux-augmented state S_2. Adding the momentum-flux tensor P_ij reduces aggregate pressure error by 31% but does not make signed shear transferable. An analytic null-space construction supplies the mechanism: strictly positive distributions can share all full-range moments through degree three while producing different pressure and opposite signed shear because the wall kernel selects the incident half space. A finite-distance off-wall ExtraTrees state S_off shows that partial directionality is useful but representation-dependent. Finally, a parameter-free kinetic reconstruction combines the incident half-range wall-arrival state S_HR with the prescribed diffuse kernel and agrees with both a same-window DSMC tally sharing the incident events and a separate 40,000-step DSMC wall-tally window. The resulting design principle is direct: a rarefied wall closure must preserve the incident normal–tangential correlations required by the target load rather than merely adding higher full-range moments.

We examine Direct Simulation Monte Carlo (DSMC)-resolved rarefied micro-nozzle flows with finite-thickness internal compression layers and develop a shock-aligned, scalar-conditioned surrogate for repeated field prediction. The study separates the physics of the moving compression layer, the shock-aligned trunk features, and the branch/trunk conditioning block. Density-gradient and gradient-length Knudsen-number diagnostics show that the dominant compression layer is a localized finite-width macroscopic compression region on the sampled DSMC grid rather than a mathematical discontinuity. A jump-based thickness defines the registered coordinate ξj=(x−xs)/δj, which makes the centerline profiles substantially more compact. For ρ, U, P, and Mach number, the leading proper orthogonal decomposition energy increases from 69.9%–78.9% in physical coordinates to 94.7%–98.0% after shock-centering and thickness scaling. This reduced structure motivates signed-distance and local envelope features in the surrogate. The evaluation includes per-feature ablations, parameter-count-aware and seed-robust baselines, fusion-isolation tests, near-boundary extrapolation stress tests, and a posteriori physical-consistency diagnostics. For the hard 16 kPa case, adding only the signed shock distance reduces the shock-window error of a Cartesian Hadamard branch/trunk model from 57.98% to 10.17% in the single-seed ablation. Across three random seeds, the reduced signed-distance model gives a shock-window error of 9.12±1.01%, comparable to a strong Cartesian multilayer perceptron with 8.86±1.26%. The contribution is, therefore, not a new fusion architecture but a physics-based shock-centered representation and a transparent assessment of when it improves shock-localized surrogate accuracy within a calibrated pressure range.

The direct simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity ab initio potentials. This work develops a unified, physics-constrained neural-operator framework that accelerates DSMC while preserving physical invariants and stochasticity required for long-time kinetic simulations. First, we introduce a local neural collision kernel replacing the phenomenological hard sphere (HS) model. To overcome the variance suppression and artificial cooling inherent to purely deterministic regression surrogates, we augment inference with a physics-constrained stochastic layer. Controlled latent-noise injection restores thermal fluctuations, while cell-wise moment-matching is introduced as a numerical stabilization device to suppress long-time energy drift. Remarkably, the proposed operator can be deployed without retraining in a two-dimensional lid-driven cavity after being trained on collision samples harvested from a one-dimensional Couette flow. Since the underlying HS collision law is geometry-independent, this test is intended to assess robustness across flow configurations and collision-state distributions rather than the transfer of a geometry-specific law. The surrogate accurately reproduces the primary fields and higher-order non-equilibrium moments in the cavity case. Second, to bypass the extreme cost of trajectory-based classical scattering, we develop a dedicated ab initio neural operator for the J & auml;ger interaction potential. Trained via a physics harvesting strategy on large-scale collision pairs, it efficiently captures the high-energy scattering dynamics dominating hypersonic regimes. Validated on a Mach 10 rarefied argon flow over a cylinder, the framework reproduces transport behaviors and shock features with high fidelity, achieving an approximate 20% cost reduction relative to direct numerical integration. Collectively, this work establishes physics-constrained neural operators as accurate, stable, and efficient drop-in surrogates for DSMC collision dynamics across both engineering HS setups and ab initio hypersonic simulations.

FlowMLLab is open-source educational and research software for a first rigorous encounter with artificial intelligence (AI) in thermal-fluid engineering. It was used in the Summer 2026 graduate course \emph{AI in Fluid Mechanics} at the University of MassachusettsAmherst and is also intended as an onboarding path for engineers entering industry. The software emphasizes validated numerical data, scaling, case-wise splitting, transparent baselines, multilayer perceptrons, proper orthogonal decomposition (POD), and restricted neural operators before introducing research-level kinetic closures in the final notebooks. One lid-driven cavity connects computational fluid dynamics (CFD), direct simulation Monte Carlo (DSMC), and reduced-order modeling. On three blind Reynolds-number cases, the maximum velocity error is $0.4941\%$ for POD--Galerkin and $0.6338\%$ for POD--DEIM (Discrete Empirical Interpolation Method); the latter provides a measured $9.24\times$ online speedup and a 7.84-query break-even count. Existing gates retain blind POD--DeepONet errors below $0.5\%$ and validate DSMC wall pressure against published data to $0.772\%$. Seventeen notebooks, five lecture PDFs, versioned evidence, command-line tools, and Python 3.10--3.12 tests connect every scientific claim to executable software.

Prescribed wall heat flux provides active control of rarefied micro-nozzle operation through coupled gas–surface energy exchange, viscous blockage, and pressure thrust. Direct simulation Monte Carlo (DSMC) examines nitrogen flow through a planar converging–diverging micro-nozzle under six uniform conditions spanning the entire diverging wall: two negative heat fluxes that extract gas energy (cooling), zero heat flux (adiabatic), and three positive heat fluxes that add gas energy (heating). Normalization by a fixed inlet kinetic-energy flux gives Qw/E=−2.763% to 20.722%; the largest positive value is treated as a high-intensity sensitivity bound. Wall–bulk response, gradient-length Knudsen measures, mass-flux profiles, blockage, thrust decomposition, and proper orthogonal decomposition (POD) of signed numerical-schlieren fields are examined. Positive prescribed heat flux raises the peak wall temperature above 5 times the inlet stagnation temperature, increases the dimensionless mean blockage fraction from 0.328 (32.8%) under the adiabatic condition to 0.477 (47.7%), and reduces the discharge coefficient from 0.701 to 0.677. The throughput penalty is accompanied by an impulse gain. Between the adiabatic condition and Qw=7.5×104Wm−2, the normalized total-thrust coefficient CF increases from 3.11 to 3.89, and the specific impulse increases from 156 to 201 s because the momentum- and pressure-thrust contributions increase sufficiently to exceed the mass-flow penalty. Direct profiles show a dominant forward-flow core with weak near-wall reverse flow; using signed instead of positive-only mass flux changes mean blockage by less than 0.84%. The first two POD modes contain 97.4% of the fluctuation energy, whereas leave-one-condition-out tests reveal limited extrapolation for the strongest cooling condition. Thus, prescribed heating trades reduced throughput for greater impulse, while the low-rank description remains limited to the sampled operating family.

Integrating the physically realistic Lennard-Jones (LJ) potential into the Direct Simulation Monte Carlo (DSMC) framework has historically been hindered by the computational cost of evaluating complex scattering dynamics. This study presents a high-fidelity, machine-learning-accelerated framework that bridges the gap between rigorous molecular physics and large-scale kinetic simulations. This new approach is implemented in the standard Bird's suite of DSMC algorithms (DSMC1, DSMC1S, and DS2V), offering a high-precision platform for rarefied-gas studies. To achieve this, two problems are addressed: incorporating Lennard-Jones-specific properties into the inherently total cross-section concept of the method and replacing the computationally intensive particle-scattering process with a surrogate machine-learning model. As a result, a universal Variable Effective Diameter (VED) model is developed through local viscosity matching, ensuring accurate capture of attractive-repulsive interactions across a wide range of temperatures, a critical advance over traditional models limited to narrow thermal bands. The surrogate model, crucial for the framework's efficiency, employs a Deep Operator Network (DeepONet) as a high-performance substitute for the computationally intensive LJ scattering integral. The framework reveals critical physical insights often missed by standard models. The framework is validated against three canonical problems: shock waves in helium and argon, supersonic Couette flow at low temperature, and hypersonic cylinder flow at two Mach numbers. In the argon shock-wave problem, we showed that although the density profile of the Variable Hard Sphere (VHS) model does not match the experimental data, its velocity distribution function follows the LJ prediction. In supersonic Couette flow with cryogenic walls (40 K), the LJ model predicts a smaller shear stress than the VHS model, highlighting the dominant role of long-range attractive forces in low-temperature shear layers. In parallel, for hypersonic flow over a cylinder at Mach=10, the LJ and VHS results agree well, even in the wake region where temperatures range above 800 K; in this regime, high-energy repulsive collisions dominate, rendering the attractive potential well negligible. As we reduced the cylinder and incoming flow temperatures to the cryogenic regime (Mach 5, Tw=40K), profound deviations became apparent: the LJ model predicted a larger, more elongated wake vortex than the VHS model, a direct macroscopic manifestation of long-range attractive forces that reduce the local effective viscosity. By leveraging Scientific Machine Learning (SciML)-based operator learning, the DeepONet surrogate preserves the intricate balance of molecular forces while accelerating the collision subroutine by 40% and reducing total simulation wall-clock time by 36%. This work establishes a scalable, physically grounded, and computationally efficient pathway for high-fidelity kinetic modeling in the era of scientific machine learning, while providing fluid physical insights beyond standard VHS predictions.

Time-resolved direct simulation Monte Carlo (DSMC) fields are used to test whether a detached rarefied hypersonic bow shock contains a slow collective displacement that can be separated from correlated particle-sampling fluctuations. Mach-10 rotationally relaxing nitrogen flow over a circular cylinder is analysed for diameter-based Knudsen number 0.01≤≤1, where =λ_∞/D, λ_∞ is the freestream mean free path and D is the cylinder diameter. A density half-jump front is extracted on body-normal rays, unsupported solid-side points are excluded, and temporal coarse graining is performed before feature extraction. Persistent and sampling covariance components are compared using a penalized composite-fit score, design-scale cross-validation, block resampling, synthetic controls and complementary full-field matched filters. Corrected field proper orthogonal decomposition (POD) is high rank at every Knudsen number, yet a weak, same-signed angular displacement is resolved at =0.01 and 0.025. Independent random-seed and simulator-particle-loading repeats recover the angular shape and relaxation time while the raw sampling variance changes with loading. Across the two resolved states the mean density layer broadens by 82%, while the angular shapes remain strongly aligned. Density and pressure recover the marker motion most strongly; the reduced Mach-number and translational-temperature participation at =0.025 is evidence consistent with moment-selective weakening, although observable-dependent signal-to-noise remains a possible contributor. The signal is interpreted as a low-pass bow-layer response embedded in broadband kinetic fluctuations, not as a newly discovered discrete oscillation or a demonstrated linear instability. The higher-Knudsen records are not sufficiently sensitive to establish physical disappearance.

Machine learning is beginning to influence rarefied-gas modeling at multiple levels, including equation-solving, operator learning, learned collision physics, moment closures, direct simulation Monte Carlo (DSMC) field surrogates, and gas–surface models. This Perspective argues that the central challenge is not demonstration-level success, but trustworthy use under realistic deployment conditions: multiregime Knudsen behavior, stochastic DSMC labels, sharp nonequilibrium structures, uncertain gas–surface interaction, and scarce direct experimental anchors. I classify the main method families by what is learned, distinguish soft physics penalties from structure-preserving designs, and propose evaluation standards based on extrapolation tests, noise-aware metrics, end-to-end cost accounting, and a three-level validation hierarchy. Most current evidence is solver-facing: it demonstrates surrogate fidelity to a teacher solver more often than direct physical fidelity to experiment. The aim is not to dismiss ML for rarefied and vacuum-related gas transport, but to separate what is already credible from what remains provisional, and to define a reporting standard that makes future claims auditable.

Integrating a physically realistic Lennard Jones LJ potential into Direct Simulation Monte Carlo DSMC has long been hindered by the high cost of evaluating detailed scattering dynamics. We present a high-fidelity, machine-learning-accelerated framework that bridges rigorous molecular physics and large-scale kinetic simulation, implemented within Bird standard DSMC algorithm suite. Two challenges are solved incorporating LJ consistent properties into DSMC total cross-section formulation, and replacing the expensive particle scattering step with a surrogate model. First, we develop a universal Variable Effective Diameter model via local viscosity matching, capturing attractive repulsive interactions over a wide temperature range an advance over traditional models restricted to narrow thermal bands. Second, we employ a Deep Operator Network as a fast, accurate substitute for the LJ scattering integral, enabling efficient high-precision collisions. The resulting framework exposes physical effects often missed by standard models and is validated on three canonical problems: shock waves in helium and argon, supersonic Couette flow with cryogenic walls, and hypersonic cylinder flow at two Mach numbers. In the argon shock case, we show that while the Variable Hard Sphere VHS model fails to match the experimental density profile, its velocity distribution function closely follows the LJ prediction. In low temperature supersonic Couette flow, the LJ model predicts smaller shear stress than VHS, underscoring the dominant influence of long-range attractive forces in cryogenic shear layers.

The present investigation examines an innovative method for improving the efficiency of thermal separation of binary gas mixtures in a parallel plate configuration. The Direct Simulation Monte Carlo (DSMC) approach was employed for precisely modeling flow in rarefied regimes at micro-scales. The study explores separating a 50 %- 50 % helium-xenon mixture between two plates, highlighting the potential of using specular and diffusive surfaces to generate effective separation flows. We investigated the influence of Knudsen numbers (Kn), i.e., 0.001

Film cooling is a key technology for protecting turbine blades from high thermal loads, directly influencing component durability, efficiency, and operational safety. Micro vortex generators (MVGs) offer a passive approach to enhance near-wall mixing, suppress cooling jet lift-off, and stabilize the coolant film, enabling more uniform and effective surface cooling. Despite their widespread use, the detailed influence of MVG geometry, axial placement, and tip angle on aerodynamic and thermal performance remains insufficiently understood. This study examines MVG height (1.5 to 5.5 mm), axial location (− 7.5 to + 7.5 mm relative to the cooling hole), and tip angle (tested within ± 5° of the baseline design) on film cooling over a stator blade. Aerodynamic and thermal effects are evaluated using turbulence kinetic energy (TKE), surface pressure distributions, temperature, film cooling effectiveness, enthalpy, stagnation density, cfRe (friction Reynolds number), Nusselt number, adiabatic film cooling effectiveness, and pressure-loss measurements. Heights below 1.5 mm fail to generate coherent vortices, acting mainly as surface roughness, while heights above 5.5 mm induce local separation, vortex breakdown, and increased pressure loss, reducing overall cooling. Heights of 2.5–4.0 mm produce stable streamwise vortices that enhance near-wall mixing and extend the cooling film’s effectiveness. Axial placement strongly influences vortex–jet interactions: upstream positions allow premature vortex dissipation, while positions too close to the jet disrupt the core flow and induce instabilities. Our study shows that the best cooling occurs for MVGs placed 5–7.5 mm upstream, where vortices remain coherent, jet lift-off is suppressed, and lateral spreading is promoted. Tip angle variations within the tested range have minimal impact. Compared to the baseline case, the best MVG configuration improves surface cooling by 33–46% along the blade, with maximum gains near the root and mid-chord (X/D ≈ 0.05–0.2), highlighting the importance of well-designed MVGs for sustaining effective film cooling across critical blade regions.