ABSTRACT. Since many years, the use of genuinely multidimensional methods is advocated as the best solution for the next generation of CFD solvers by many, including P.L. Roe, H. Deconinck, T.J.R. Hughes, R. Abgrall, and others. The notion of multidimensional has taken many forms. The most classical view is the idea of replacing differences along grid directions with differencing along physical directions, also referred to as multidimensional upwind differencing. Another take on this notion is that directional differences should be replaced by approximations of full multiD differential operators, as e.g. in the streamline upwind method, in residual distribution schemes, and in most versions of the active flux method.

In this talk, we discuss this issue under the prism of the preservation of stationary states, a property widely advocated in geophysical and astrophysical applications, where it is often referred to as a well-balanced property.

Starting from P.L. Roe’s original idea of integrating the source along characteristics, the talk will review by steps of increasing complexity the issue of constructing methods which have enhanced approximation properties for multi-dimensional equilibrium states. The use of discrete multidimensional operators emerges as a must in this setting. A novel framework to obtain stationarity preserving schemes is discussed and the impact of stationarity preservation on other enhancements as reduction of mesh imprinting and low Mach compatibility, are discussed and illustrated via several examples.

ABSTRACT. The accurate numerical solution of singularly perturbed problems remains a significant computational challenge due to the presence of thin boundary and interior layers where gradients are extremely steep. This work develops a high-order Chebyshev spectral collocation framework augmented with adaptive coordinate stretching to efficiently resolve these localized features without the need for complex mesh refinement. The proposed method is applied to four representative test cases: linear reaction-diffusion, nonlinear boundary layers described by the Falkner-Skan equation, and multi-dimensional convection-diffusion problem. Spatial derivatives are approximated using Chebyshev differentiation matrices and transformed to the physical domain via algebraic, hyperbolic tangent and Bayliss-Turkel mappings, while boundary conditions are imposed directly at the collocation points. Numerical results and validation against analytical solutions demonstrate that this mapped approach recovers spectral accuracy and rapid convergence across all cases. By precisely clustering degrees of freedom within the layers, the method provides a robust and computationally efficient alternative for high-precision simulations of transport processes in singular perturbation regimes.

ABSTRACT. Accurate shock capturing is a fundamental requirement for numerical methods in compressible CFD, as even small errors in shock speed or position may lead to significant global inaccuracies. In hyperbolic systems of conservation laws, shock waves propagate according to the Rankine–Hugoniot conditions, which critically rely on the conservative form of the governing equations. Any loss of conservation may therefore alter the predicted shock trajectory. In practical CFD applications, however, non-conservative effects may arise for several reasons, for instance when using non-conservative interpolation procedures between meshes in adaptive or re-meshing strategies, or when solving the governing equations in non-conservative variables.

In this work, we systematically investigate how controlled non-conservative perturbations to the conservative variables affect shock propagation in one-dimensional conservation laws. We consider both the inviscid Burgers equation and the compressible Euler equations. Simple analytical or approximate relations, derived from the Rankine-Hugoniot jump conditions, are proposed to predict the modified shock speed as a function of the reference conservative shock speed and the imposed perturbations. The analysis reveals a systematic deviation of the shock trajectory that accumulates in time. Numerical experiments, conducted with a high-order finite volume solver, confirm the theoretical predictions with high accuracy.

The results quantify the intrinsic sensitivity of shock dynamics to conservation errors and provide practical predictive tools for assessing the impact of non-conservative formulations in the propagation of discontinuities.

ABSTRACT. Partial differential equations (PDEs) on surfaces arise in various situations. Historically, surface equations have first been numerically solved using fitted approaches, by triangulating the surface and using discrete spatial operators on this discretization. Since the work of Bertalmio in 2001, an alternative way of solving surface equations, qualified here as "unfitted" (or embedded or immersed) approach, has been used. The idea is to extend the original surface equations to volume equations and to solve them in some volume embedding the surface of interest. In this approach, the surface is described implicitly with a level-set function rather than explicitly with a mesh.

Different types of PDEs have been addressed with the unfitted approach, starting with elliptic and parabolic equations. Furthermore, unfitted advection equations were successfully solved by Ruuth and Merriman and other studies. However, these equations are either linear transport equations, or solved on structured (and often Cartesian) meshes using finite differences.

The present work applies the unfitted approach for non-linear hyperbolic systems on unstructured meshes. To do so, the tangential gradient defined by Greer is used in combination with the discontinuous Galerkin method to solve non-linear surface hyperbolic systems of equations. The choice of this specific gradient is crucial as the waves associated with hyperbolic systems must be correctly solved everywhere in the volume to prevent any harm to the surface solution.

In this work, the presented method is applied to two 2D cases and one 3D case. The convergence is assessed on the 2D test cases, while the 3D test case exhibits an excellent qualitative agreement with the reference solution. Furthermore, the method convergence is proved to be independent from the tubular radius of the embedding volume, which drastically limits the extra cost of the method since only a thin band of embedding cells is necessary.

ABSTRACT. In this talk, we propose to review recent advances that have been obtained on the computation of low Mach number flows with the finite volume methods and the discontinuous Galerkin method. Based on a two time scales asymptotic expansion of the barotropic Euler system, we have been able to identify a link between the good or wrong accuracy of a numerical scheme for the Euler system, and the ability of a numerical scheme to correctly capture the long time limit of the linear acoustic wave system. This led us to the following results on the behaviour of high order discontinuous Galerkin methods for the computation of low Mach number flows: • In general, using triangular/tetrahedral meshes and a correct numerical flux (e.g. Roe, Godunov,Osher, HLLC, but not Rusanov or HLL) leads to a method that is low Mach number accurate, with the optimal order of accuracy. • In general, if quadrangular meshes are used, or if Rusanov or HLL schemes are used, numerical experiments show that the numerical method is one order less accurate than the optimal order. • It is possible to enrich the velocity approximation space for recovering an optimal order of accuracy at low Mach number on quadrangular meshes provided the correct numerical flux is used, see the pdf abstract for more details.

This talk proposes an overview of these different results, that were published in the following articles: - Pascal Bruel, Simon Delmas, Jonathan Jung, and Vincent Perrier. A low Mach correction able to deal with low Mach acoustics. Journal of Computational Physics, 378:723–759, 2019. - Jonathan Jung and Vincent Perrier. Long time behavior of finite volume discretization of symmetrizable linear hyperbolic systems. IMA Journal of Numerical Analysis, 43(1):326–356, 2023. - Jonathan Jung and Vincent Perrier. Steady low Mach number flows: identification of the spurious mode and filtering method. Journal of Computational Physics, page 111462, 2022. - Jonathan Jung and Vincent Perrier. Behavior of the discontinuous Galerkin method for compressible flows at low Mach number on triangles and tetrahedrons. SIAM Journal on Scientific Computing, 46(1):A452–A482, 2024. - Jonathan Jung and Vincent Perrier. A curl preserving finite volume scheme by space velocity enrichment. Application to the low Mach number accuracy problem. Journal of Computational Physics, 515:113252, 2024. - Jonathan Jung, Ibtissem Lannabi, and Vincent Perrier. On the spurious modes associated with the pressure centred low mach number fix for compressible flows. Computers & Fluids, page 106945, 2025. - Vincent Perrier. discrete de-Rham complex involving a discontinuous finite element space for velocities: the case of periodic straight triangular and Cartesian meshes. Annales Henri Lebesgue, 8:417–452, 2025. - Vincent Perrier. Development of discontinuous Galerkin methods for hyperbolic systems that preserve a curl or a divergence constraint: the case of linear systems. Journal of Computational Physics, page 114445, 2025.

ABSTRACT. High-fidelity simulation of turbulent fluid flows governed by partial differential equations is computationally expensive, particularly at high Reynolds numbers where resolving multi-scale interactions requires costly Direct Numerical Simulations(DNS). We introduce Augmented wavelet Fourier Neural Operator (AW-FNO), a synergistic architecture fusing the Fourier Neural Operator(FNO) with the Wavelet Neural Operator (WNO). The Adaptive Gated Fusion Mechanism (AGFM) induces a piece-wise trust map that encodes the relative importance of FNO and WNO. Our model achieved 3 times improvement compared to vanilla FNO on the incompressible two-dimensional Navier-Stokes equation.

ABSTRACT. 1. Introduction Computational Fluid Dynamics (CFD) based on traditional numerical methods is computationally expensive for tasks such as large-scale three-dimensional aerodynamic optimization [1]. Recently, several studies have constructed efficient surrogate models for aircraft using artificial intelligence (AI) to achieve high-performance simulation in aerodynamic design [2,3]. However, a significant challenge for current AI methods in engineering tasks is that while models infer efficiently and accurately within the training distribution, their prediction errors often increase sharply and uncontrollably in out-of- distribution (OOD) scenarios [3]. In practical engineering, OOD scenarios are unavoidable, as it is difficult to sufficiently sample all possible geometries of interest during the dataset construction phase, especially for higher-dimensional 3D problems. Therefore, enhancing the OOD generalization performance of AI surrogate models is critical to improving their engineering utility.

In recent years, some work in the field of AI has sought to improve OOD generalization by integrating numerical solvers with neural networks, enforcing physical constraints during flow field inference. For instance, ANCHOR [4] invokes traditional numerical methods within the inference framework when residuals exceed a specific threshold, achieving stable predictions for 3D unsteady diffusion equations. PIRF [5] serializes complex mappings and utilizes equation residuals to constrain generated results in real-time during inference, thereby improving OOD predictions. However, these approaches have not yet been applied to fluid dynamics problems characterized by stronger nonlinearities. Inspired by these ideas, this study plans to construct an innovative fast inference framework that fuses traditional numerical methods with deep learning, applied to airfoil flow field inference to enhance OOD generalization. The specific methodology is introduced in the following section

2. Methodology The schematic of the proposed framework is shown in Figure 1, consisting of the following three core components: (1) A pre-trained initial field generation model: This provides a relatively reliable initial flow field for the framework. It predicts the global flow field distribution from the global airfoil geometry using a Fourier Neural Operator [6], which possesses strong field-learning capabilities. (2) A BERT-like conditional generative operator trained: A local flow field generator based on the Transformer [7] architecture is trained using a paradigm mimicking BERT [8]. During the training phase, flow fields at random grid locations are masked, requiring the model to generate the corresponding masked fields conditioned on the remaining portions. While previous work has implemented BERT-like conditional flow field generation schemes [9], no work has yet constructed a complete workflow based on this to the best of our knowledge. (3) A numerical solver: The open-source ADFlow [10] solver is reconstructed within the deep-learning-compatible PyTorch environment to enable highly parallel execution. The flow field inference process configured by these components is as follows: first, the initial field generation model provides an initial prediction U0 based on the complete geometry. This flow field may be unreliable in OOD scenarios. Subsequently, the numerical solver and the conditional generative operator are invoked alternately to refine the flow field. The numerical solver performs only a single-step time marching on Ut in each iteration to provide the residual distribution Rt. A masking strategy is designed to obtain Mt based on Rt, where high-residual regions are masked and low-residual regions serve as conditions. The conditional generative operator then predicts the refined flow field Ut+1 based on the masked field Mt∙ Ut, yielding an improved flow field for the next step. By alternating these steps, the global prediction for OOD geometries is simplified into residual-guided local conditional generation, thereby improving the OOD prediction performance of the deep learning model.

3. Conclusions This study constructs a deep learning inference framework integrating real-time flow field residuals. The model is trained on a small-scale geometric dataset (as shown in Figure 2, left) and tested on a candidate airfoil set collected from real aerodynamic optimization (as shown in Figure 2, right). The results demonstrate that, compared to traditional global prediction, the proposed framework reduces the mean flow field prediction error on the OOD test set by an order of magnitude, while maintaining an inference time per flow field of approximately one second. these results prove the potential of the framework for application in real-world aerodynamic design scenarios such as aerodynamic optimization.

References [1] J. Li, X. Du, and Joaquim R. R. A. Martins. 2022. "Machine Learning in Aerodynamic Shape Optimization." Progress in Aerospace Sciences，vol. 134, no. 1, 2022. [2] Z. Zhu, G. Zhao, and Q. Zhao. "Fast and high-precision compressible flowfield inference method of transonic airfoils based on attention UNet." Physics of Fluids, vol. 36, no. 3, 2024. [3] W. Tang, C. Wu, Y. Yang, et al., "A fast transonic airfoil flow field prediction model based on a modified Fourier neural operator." Sci. China Phys. Mech. Astron, vol. 69, 214604, 2026. [4] R. Rajyasri, N. Dibyajyoti, G. Somdatta, "The Best of Both Worlds: Hybridizing Neural Operators and Solvers for Stable Long-Horizon Inference." arXiv preprint arXiv:2512.19643. 2025 [5] M. Yuan, P. Jin, N. Li, et al., "PIRF: Physics-Informed Reward Fine-Tuning for Diffusion Models." arXiv preprint arXiv:2509.20570 [6] Z. Li, B. K. Nikola, A. Kamyar, et al., "Fourier Neural Operator for Parametric Partial Differential Equations," 9th International Conference on Learning Representations. 2021. [7] A. Vaswani, N. Shazeer, N. Parmar, et al. "Attention is all you need." Advances in neural information processing systems 30, 2017. [8] J. Devlin, M. Chang, K. Lee, et al. "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding." In Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, vol 1, pp. 4171–4186. [9] B. Xu, Y. Zhou, X. Bian, "Self-supervised learning based on Transformer for flow reconstruction and prediction", Physics of Fluids, vol 36, 023607, 2024. [10] C. A. Mader, G. K. W. Kenway, A. Yildirim, and J. R. R. A. Martins. "ADflow—an open-source compu- tational fluid dynamics solver for aerodynamic and multidisciplinary optimization." Journal of Aerospace Information Systems, 2020.

ABSTRACT. Sensitivity analysis based on adjoint operators is a cornerstone of modern computational fluid dynamics, serving as an essential foundation for applications such as aerodynamic shape optimization, data assimilation, and resolvent analysis. However, its practical application is often hindered by high implementation costs and the requirement for intrusive modifications to existing solvers. To overcome these barriers, this study proposes a data-driven, non-intrusive framework named the Continuous Local Ensemble Trained Linear Model (CLETLM).

The CLETLM framework identifies the sparse discrete Jacobian matrix of the governing equations by directly relating state disturbances to the corresponding residual responses from a solver. By exploiting the spatial locality of fluid interactions through a solver-dependent 13-point numerical stencil, the sparse Jacobian matrix is explicitly constructed without internal code modification except for residual output. A significant advantage of this framework is that the approximated adjoint operator is immediately accessible through simple matrix transposition, eliminating the need for dedicated adjoint code development.

The proposed method is validated through global stability analysis of two-dimensional compressible flow over a circular cylinder at Reynolds numbers ranging from 47 to 100 and Mach numbers from 0.1 to 0.3. The identified eigenvalues corresponding to unstable modes effectively capture the physical trends observed in previous studies. Furthermore, the characteristic spatial structures of both direct and adjoint modes are successfully extracted. These results demonstrate that CLETLM can accurately and robustly identify the system Jacobian and the associated adjoint properties using only existing forward solvers.

ABSTRACT. This paper systematically investigates a rapid prediction method for two-dimensional airfoil flow fields based on U-Net, focusing on multi-objective optimization and gradient competition issues in multi-variable joint outputs. By constructing a stable baseline network through hyperparameter ablation and comparing single-variable and multi-variable models under a unified evaluation framework, it quantitatively reveals gradient conflict phenomena within the shared parameter space. Furthermore, this paper introduces an irrational constraint regularization mechanism and a gradient projection-based multi-objective optimization strategy (PCGA) to mitigate the inconsistency in parameter update directions. Experimental results demonstrate that, compared to the baseline joint-output model, physical constraints reduce the average relative error in the V-direction velocity field near the wall by up to 69.2%. PCGA achieves a maximum reduction of 30.1% in the average relative error of the pressure field without increasing model complexity, while significantly improving the balance of multivariate predictions.

ABSTRACT. Performing wall-resolved Large-Eddy Simulations (WRLES) of high-Reynolds number industrial flows remains computationally prohibitive. This limitation stems from the stringent grid resolution required to capture the inner boundary layer, with requirements scaling as Re^(13/7). Consequently, an overwhelming fraction of degrees of freedom must be clustered near the wall, restricting WRLES to relatively low Reynolds numbers. To alleviate these costs, Wall-Modeled LES (WMLES) avoids resolving the inner layer by prescribing a modeled wall shear stress, tau_w, at the wall. Discontinuous Galerkin (dG) methods are particularly well-suited for the implicit Large-Eddy Simulation (iLES) of compressible turbulent flows, as their inherent numerical dissipation effectively acts as a subgrid-scale model. In this work, a Wall-Modeled implicit LES (WMiLES) strategy is pursued within an explicit, entropy-stable dG solver. The approach replaces the standard no-slip condition with a slip wall coupled to a modeled wall shear stress. This stress is inferred from a reconstructed velocity profile based on flow variables sampled at a prescribed wall-normal donor location.

In the present dG framework, the solution is approximated within a discrete polynomial space in physical (mesh) coordinates. For this polynomial space, a set of orthonormal and hierarchical basis functions is computed. The use of orthonormal basis functions yields an identity mass matrix when advancing in time the conservative variables, while the L2 projection onto the entropy variables guarantees robustness by enforcing a discrete structure-preserving property, such as entropy stability. The numerical convective fluxes are treated with an exact Riemann solver, while the viscous fluxes contribution follows the second scheme of Bassi and Rebay (BR2). To avoid the need for over-integration, discrete entropy stability is guaranteed by the Direct Enforcement of the Entropy Balance (DEEB) correction.

The WMLES approach is implemented as a boundary condition enforced at each wall quadrature point, p_d. During preprocessing, for each p_d, a donor point p_D is identified by intersecting the wall-normal direction with the first interior mesh face. The solution at p_D is sampled to compute the local density, viscosity, and tangential velocity. The friction velocity is then obtained by solving a non-linear algebraic relation via a Newton method. We considered Reichardt's law for the dimensionless velocity and, for isothermal walls, the law of Kader is used to evaluate the heat flux. The computed wall shear stress and heat flux are then imposed through a modeled viscous numerical flux, while enforcing the slip condition. This strategy allows using substantially larger wall-adjacent cells and therefore relaxes the time-step restriction proper of explicit schemes, resulting in overall computational efficiency.

Preliminary results are presented for turbulent channel flows at friction Reynolds numbers Re_tau = {590, 2,000} in the near-incompressible regime with isothermal walls. Despite the use of a coarse mesh (20x10x10 cells), the high-order dG solver accurately resolves turbulent structures, as illustrated by Q-criterion iso-surfaces. Mean velocity profiles obtained with seventh- and eighth-degree polynomials show good agreement with reference DNS data. As typical of WMLES, the profiles align with the benchmark from the second cell away from the wall onward. The presentation will provide a comprehensive validation, with particular emphasis on the impact of donor-point location on the turbulent statistics. To account for non-equilibrium effects, we will also present first results on implementing wall models based on coupled wall-normal ordinary differential equations.

ABSTRACT. This study investigates the dynamics of pulsating Kolmogorov flow using direct numerical simulation data. The main aim is to examine the evolution of the turbulent energy spectrum and turbulent length scale. Most engineering turbulence models, including standard two-equation closures, rely exclusively on two scalar quantities, for instance: the turbulent kinetic energy and its dissipation rate. Pope's analytical model spectrum is built precisely on these two parameters, assuming that the entire spectral distribution can be reconstructed from these values together with universal correction functions. However, this assumption is fundamentally rooted in equilibrium turbulence theory and its applicability to non-stationary, externally forced flows remains an open question. To assess the the validity of the two-parameter description under non-stationary conditions, the resulting energy spectrum is compared against Pope's theoretical model spectrum. At a dimensionless excitation frequency of 0.79, the phase-averaged energy spectrum aligns well with the model spectrum. In addition, a wave-like propagation of energy is observed, with spectral maxima and minima appearing at high wavenumbers after a distinct time delay. Furthermore, the analysis reveals that the normalized integral length scale oscillates near unity, indicating that energy-containing structures are physically constrained by the domain geometry. These findings highlight the need for geometry-aware turbulence models, which serves as the main objective for our future research.

ABSTRACT. Three-dimensional turbulent boundary layers (3D TBLs) are ubiquitous in engineering applications such as swept wings, turbomachinery, and marine vessels. The three-dimensionality arises from the misalignment between the pressure gradient and the primary flow direction, inducing a crossflow component. This crossflow, combined with streamline curvature and pressure gradients, significantly alters the turbulence structure, leading to phenomena like stress depletion and relaminarization. Despite their importance, our understanding of 3D TBLs lags behind that of canonical two-dimensional (2D) flows, due to the scarcity of high-fidelity experimental or numerical data and the lack of reliable theoretical models. Most existing DNS studies of 3D TBLs use idealized configurations (e.g., impulsive transverse pressure gradients in channels or moving-wall-driven crossflows) that decouple crossflow evolution from surface geometry and neglect spatial history effects. Moreover, databases are largely limited to incompressible or subsonic regimes. There is a critical need for high-fidelity simulations of spatially developing 3D TBLs under realistic conditions, especially at high speeds where compressibility and thermal effects are important. This study addresses these gaps by performing high-resolution DNS of a spatially evolving 3D TBL over a hypersonic swept blunt leading edge—a configuration representative of realistic hypersonic vehicle geometries. The swept blunt body naturally bridges 2D and 3D TBLs, offering a continuous spatial evolution from a quasi-2D attachment-line flow to a highly 3D, non-equilibrium downstream state under strong geometry-induced pressure gradients. The primary objectives are: 1. To establish a high-fidelity benchmark database for a spatially developing 3D non-equilibrium TBL. 2. To investigate the flow characteristics, mean flow evolution, and turbulence statistics under strong favorable pressure gradients and crossflow. 3. To derive and validate a generalized log-law for 3D TBLs that accounts for crossflow and pressure gradient effects.

ABSTRACT. This paper quantitatively compares implicit large-eddy simulation (iLES) and explicit eddy-viscosity LES (eLES) varying a range of grid resolutions. The iLES and three eLES models are evaluated with the benchmarking Taylor-Green vortex using a fourth-order finite-volume gas-kinetic scheme. The total dissipation is decomposed into physical, numerical, and subgrid-scale (SGS) modelling components. With coarsening grid, the SGS contribution decreases, while numerical dissipation becomes dominant in the under-resolved grid. Comparisons against filtered direct numerical simulation show that iLES consistently achieves better agreement than eLES from under-resolved to moderately resolved grids. Since volume-averaged statistics may obscure discrepancies in local structure, probability density functions of velocity gradients are further evaluated. The PDF-based analysis confirms the superior accuracy of iLES across grid resolutions, accurately reproducing gradient distributions even on coarse grids. In contrast, explicit SGS models show no clear strength and may introduce spurious effects that degrade resolved-scale flow dynamics.

ABSTRACT. 1. Introduction

For magnetically confined nuclear fusion devices, a continuous fuelling system is necessary for supplying hydrogen (deuterium and tritium) into the core of the plasma. The current leading, proven approach for this is the injection of solid hydrogen pellets: these are extruded and cut at cryogenic temperatures, before launching them into the plasma at high speeds.

Extrusion of solid hydrogen is possible above its yield stress, where it behaves as a non-Newtonian viscous fluid with strongly temperature-dependent material parameters. Reliable numerical modelling of this plastic flow behaviour requires a coupled thermo-viscoplastic simulation with an appropriate material model. A key part of the model is the accurate prediction of the heat generated due to viscous dissipation, since the temperature of the extruded material must remain below its triple point during extrusion to prevent melting: this usually limits the maximum achievable mass flow rate for a specific design.

This contribution focuses on the effects of the nozzle geometry (i.e., the initial, contracting part of the die) on the resulting temperature distribution inside a cryogenic solid deuterium extruder. First, a FEM-based CFD model for the non-Newtonian flow of solid hydrogen inside the extruder is presented, validated with experimental measurements. Then, the effects of changing the nozzle geometry are considered.

2. Methodology

A prototype cryogenic hydrogen extruder of batch type has been designed and built at the Fusion Plasma Physics Department of the HUN-REN Centre for Energy Research (EK-CER). It is capable of supplying a continuous solid deuterium rod of d=3.2 mm at a temperature of approximately 15 K, which is then cut into separate pellets. This device has been used for experimental measurements to validate the presented numerical model.

For the numerical model of the thermo-viscoplastic flow, the FEM-based CFD solver ANSYS Polyflow is used. The solid deuterium is assumed to behave as a Herschel--Bulkley fluid in accordance with the measurements of Leachman 2010, with a temperature-dependent yield stress and viscosity, and a flow index of n=1/2.

Additionally, the strong temperature-dependence of the solid deuterium material parameters such as its thermal conductivity and specific heat is also modelled. The dependence of material parameters on the ratio of para-ortho isomers are not considered, normal deuterium is assumed.

The basic design of the extruder nozzle is a conical throat connecting the die to the main chamber: the length of this throat is varied to explore the effects on the developing temperature profile and the required extrusion force.

At lower mass flow rates, numerical simulations identify a well-defined high-temperature region in the material that develops due to the increased viscous heat generation near the nozzle throat. Different geometries are explored, including a parabolic nozzle profile: this results in a more homogeneous axial temperature profile.

Curiously, the qualitative temperature distribution changes significantly at higher mass flow rates due to the strong nonlinearity of the material behaviour: this highlights the need for optimized design with regards to the target mass flow rate. The effect of the nozzle geometry on the total viscous heating generated is also explored. Some design recommendations are given for different operating mass flow rates.

3. Conclusions

The presented numerical model is found to agree with experimental measurements to an acceptable degree, and recommendations are made to further improve the accuracy. The nozzle geometry is shown to have a significant effect on the steady-state temperature distribution inside the material, highlighting the need for careful design choices regarding the die for different target mass flow rates.

ABSTRACT. Submarine flank collapses at volcanic islands can generate impulsive, highly directional waves, yet most events are poorly observed in real time, limiting the validation of numerical tools used for hazard assessment. Here we combine repeated multibeam surveys from the 2011-2012 submarine eruption south of El Hierro (Canary Islands) with 3D multiphase CFD to investigate collapse-driven near-field waves. Bathymetric differencing documents rapid edifice evolution with three collapses and provides estimates of the source area and mobilized volume for the largest event. Two OpenFOAM-based approaches are evaluated: a computationally efficient viscoplastic mixture model and a more detailed Eulerian-Eulerian two-phase model that resolves phase interactions and pore pressure effects. Validation against a submerged granular-slide benchmark shows that both models reproduce the main features of slide motion and wave generation, while the two-phase model offers additional insight at the local scale at higher cost. Field-scale simulations of the largest collapse indicate a strongly directional wave field whose nearshore response is shaped by refraction and shoaling over the island shelf, with small coastal amplitudes consistent with the absence of reported impacts. This approach is transferable to future submarine eruptions, where rapid mapping can provide realistic collapse inputs for scenario-based forecasts of near-field waves.

ABSTRACT. Given the ubiquity and significance of fluid-solid systems composed of non-Newtonian fluids and non-spherical particles in nature and industry, the deep investigation of their interaction dynamics is crucial for geological studies and engineering applications. In this paper, a resolved coupling model based on Smoothed Particle Hydrodynamics (SPH) and the Discrete Element Method (DEM) is proposed to simulate the interaction between non-Newtonian fluids and non-spherical particles. The non-Newtonian fluid is modeled using SPH with the power-law model, while the dynamics of the non-spherical particles is simulated using DEM incorporated with the super-ellipsoid and polyhedral particle models. A modified boundary repulsive force model, combined with the fixed ghost particle method, is developed to handle boundary conditions. For super-ellipsoid and polyhedron boundaries, an improved approach is proposed to generate uniformly distributed, body-fitted boundary dummy particles on their surfaces, thereby ensuring computational accuracy near boundaries and in fluid-solid interactions. To rigorously validate the framework, four benchmark cases are conducted, and the resulting numerical simulations are subsequently compared with experiments in this study. The SPH and DEM methods are first independently validated using a 3D non-Newtonian dam-break and a dry granular column collapse, respectively. The coupled framework is then assessed through two fluid-solid interaction cases: cube entry into a non-Newtonian fluid and complex dam-break scenarios involving mixtures of non-Newtonian fluids and non-spherical particles. The simulated flow behaviors (e.g., the cube penetration depth and downstream propagation of fluid-solid mixture) agree well with the corresponding experiments, validating the effectiveness of the proposed boundary treatment method and the accuracy of the framework to simulate the fluid-solid interaction systems involving non-Newtonian fluids and non-spherical particles.

ABSTRACT. Mucociliary clearance (MCC) is an important defense mechanism of the human respiratory system, which is coordinated by the combined effects of viscoelastic mucus, cilia, and airflow. Although previous studies have focused on cilia-mediated or airflow-driven transport separately, their combined effects in normal breathing and coughing events are relatively unexplored. The current study focuses on mucus transport under physiological airflow conditions using mathematical modeling and high-fidelity numerical simulations. The mucus layer is represented as a viscoelastic fluid using the Oldroyd-B model at low Reynolds and capillary numbers. Normal breathing is simulated using oscillatory shear stresses at the flat air-mucus interface, while cough-driven transport is simulated using direct numerical simulations with strong transient airflow. Parametric analyses are performed to explore the effects of mucus elasticity, viscosity ratio, airflow magnitude, and airway geometry on transport efficiency. The results indicate that high elasticity significantly inhibits transport in diseased states, while an increased viscosity ratio, indicative of mucolytic therapy, reduces elastic forces and promotes near-Newtonian transport, which is more efficient in clearing mucus. These results illustrate the combined effects of MCC mechanisms and emphasize the importance of mucus rheology and mucolytic therapy in efficient mucus transport in respiratory diseases like cystic fibrosis, COPD, and asthma.

ABSTRACT. This work presents a registration-based nonlinear model reduction method for the rapid and reliable solution of parametrized partial differential equations (PDEs), with applications to aerodynamic flows with shocks. Our interest is in many-query scenarios, which require the evaluation of quantities of interest, such as lift and drag, for many different values of configuration parameters, such as flow conditions and geometry. We aim to reduce the marginal cost of the solution by several orders of magnitude compared to standard full-order models (FOMs), while controlling the accuracy and equipping the solution with an a posteriori error estimate. To this end, we present a projection-based reduced-order model (ROM) that builds on the following ingredients: (i) adaptive high-order discontinuous Galerkin method, which provides efficient and reliable FOM; (ii) reduced-basis spaces, which provide low-dimensional approximations of the parametric solution manifold; (iii) registration-based warping of the reduced spaces, which enables the method to overcome the Kolmogorov N-width barrier for flows with parameter-dependent shocks; (iv) reduced quadrature rules, which are tailored to the reduced basis and accurately evaluate the PDE residual; (v) dual-weighted residual error estimates for both the FOM and ROM, which assess the error in the FOM and ROM; and (vi) an adaptive training algorithm, which incorporates adaptive mesh refinement in physical space and adaptive sampling in the parameter space. We demonstrate the efficacy of the formulation for parametrized aerodynamics problems modeled by the compressible Euler and Reynolds-averaged Navier–Stokes equations.

ABSTRACT. Aerodynamic shape optimisation is computationally expensive, particularly for transonic configurations like NASA's Common Research Model (CRM), where spanwise-varying planform and airfoil sections introduce many coupled parameters under nonlinear flow physics and strict constraints. Gradient-based optimisation becomes inefficient as sensitivity computations scale with the number of active variables. To address this, we propose a stratified parameterisation based on class-shape transformation (CST) and reduced-order optimisation using dominant modes. By decoupling planform control from airfoil refinement and focusing on key design variables, we reduce computational cost. The use of dominant POD modes leads to faster convergence with fewer Hessian matrix evaluations. Results show that the stratified approach reduces computational cost while maintaining near full-space performance. The full 37-parameter optimisation converges to C_D=0.01860 in 500 evaluations, while optimising planform and airfoil POD modes simultaneously achieves C_D=0.01773 in 400 evaluations. The stratified multi-scale approach (SLSQP-MSG) reaches C_D=0.01780 in 360 evaluations, yielding a 12.7% drag reduction with 10% fewer CFD evaluations. The results outperform CRM SLSQP benchmarks, with smooth and interpretable geometric changes. The proposed stratified reduced-order framework effectively reduces computational cost while preserving optimisation quality, making it suitable for large-scale aerodynamic design optimisation.

ABSTRACT. Domain decomposition(DD) has emerged as a key strategy for constructing scalable reduced order models(ROMs) in large-scale computational fluid dynamics. Recent advances focus on enhancing computational efficiency and interface fidelity. Taddei et al. enhanced local efficiency using static condensation without Lagrange multipliers. Meanwhile, interface coupling has been improved through techniques such as direct flux matching, Schur complement equations, and boundary response maps. To better handle the complex interactions in multi-injector flows, our work proposes an intrusive ROM that uniquely combines the efficiency of domain decomposition with the global accuracy of full-domain snapshots. The framework is developed to readily handle configurations with increased numbers of injectors and stronger coupling effects.

ABSTRACT. Reduced-order models (ROMs) are widely employed to describe complex system dynamics when simulations with full-order models (FOMs) are computationally prohibitive, or to extract dominant features from high-dimensional data. This study presents {POD--AS--ROM}, a novel model-reduction framework based on the active subspaces (AS) technique, which performs dimensionality reduction in both the state and parameter spaces, enabling efficient and high-fidelity approximations of quantities of interest (QoI). The approach employs proper orthogonal decomposition (POD) to extract low-dimensional coefficients from computational fluid dynamics (CFD) snapshots, which are inputs to a residual neural network (ResNet) with linear layers to learns their nonlinear mapping to QoI. Reverse-mode automatic differentiation (AD) is utilized to compute gradients with respect to the coefficients, enabling AS analysis for identifying influential modes and performing global sensitivity assessment. A surrogate model is subsequently constructed using a polynomial response surface based on AS-derived active variables, retaining only the highly influential POD coefficients to ensure accurate and efficient QoI prediction. The framework is validated on periodic and chaotic bluff-body flows, demonstrating high accuracy with few influential parameters, while AD-based gradients achieve a two-order-of-magnitude speed-up over finite-difference approximations. Sensitivity analysis further reveals that the influential coefficients are not necessarily proportional to modal energy, highlighting the critical flow structures. Consequently, POD--AS--ROM identifies a low-dimensional manifold of dominant QoI sensitivity directions, revealing that few POD modes govern key flow variations, thereby elucidating essential flow structures and their coupling with control parameters enabling efficient and accurate QoI prediction.

ABSTRACT. Introduction Multiphase flows are ubiquitous in nature and industry, from cloud formation and slurry reactors to emerging processes like battery slurry coating. These flows involve multiple interacting phases (gas, liquid, solid) with complex interface dynamics. Their behavior is governed by coupled partial differential equations (PDEs) that capture mass, momentum, and energy transfer across phases. Traditional numerical solvers have greatly advanced our ability to simulate nonlinear flow physics, but high-fidelity simulations remain computationally expensive for large-scale or long-term multiphase systems. Machine learning (ML) offers a promising data-driven alternative for modeling such complex systems with greater efficiency and scalability. In particular, the neural operator framework learns mappings from input fields to full spatiotemporal solutions, bypassing explicit PDE integration. Notable examples include the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), which have demonstrated rapid, high-accuracy predictions for fluid dynamics problems. However, directly extending existing ML surrogates to multiphase flows is challenging due to the discontinuous phase interfaces, sharp nonlinearities, and the high dimensionality of multiphase data. To address these challenges, we propose MultiOKAN, a composite reduced-order latent-space operator framework based on the Kolmogorov-Arnold Network (KAN). MultiOKAN comprises two KAN-based components: an autoencoder (KAE) that compresses high-dimensional phase volume-fraction fields into a low-dimensional latent representation, and a Deep Operator KAN (DOK) that predicts the time evolution of this latent state. In essence, the KAE encoder-decoder filters and reduces the multiphase flow field to capture essential interface structures, while the DOK serves as a neural operator mapping the initial latent vector to future latent states which are then decoded back to physical space. This architecture enables efficient forecasting of multiphase flow evolution without solving the governing PDEs directly. We validate MultiOKAN across a broad range of multiphase scenarios, including canonical two-phase flows (bubble rise, particle sedimentation, and a fluidized bed) and a coupled three-phase flow. Our framework is the first to achieve simultaneous spatiotemporal prediction in diverse gas-liquid, gas-solid, liquid-solid, and gas-liquid-solid systems using a unified model. It demonstrates excellent accuracy and speed, reducing prediction errors by a substantial margin compared to baseline operator networks, while maintaining similar computational cost. Extensive experiments with noisy input data show that MultiOKAN is highly robust: the two-stage design inherently filters out noise, preserving predictive performance. We also analyze the effects of temporal resolution and training data size on accuracy, providing practical guidelines for model deployment under data-sparse or high-frequency conditions. Furthermore, we extend the MultiOKAN framework to handle three-phase flows, showing that a single-encoder dual-branch strategy can efficiently capture multiphase interactions with minimal overhead. These contributions open a promising pathway toward real-time, ML-driven prediction of complex multiphase flow dynamics. Methodology Simulation data and problem setup. To train and evaluate the model, we generate a diverse dataset of multiphase flow simulations. Three two-phase flow cases (rising gas bubble in liquid, particle deposition, and a gas-solid fluidized bed) are simulated using high-resolution CFD solvers: the Volume of Fluid (VOF) method tracks sharp interface motion in the gas-liquid case, and an Euler-Euler two-fluid approach is used for particulate flows. These simulations provide spatiotemporal fields of phase volume fractions $\phi(\mathbf{x},t)$ on a fixed grid. Additionally, a more complex three-phase case (air-water-solid) is included by combining bubble rise and particle settling dynamics in one system. From each scenario, we collect sequences of volume-fraction field snapshots over time, which serve as training and test data for MultiOKAN. MultiOKAN architecture and training. The MultiOKAN framework consists of two neural network models that are trained separately: the KAN-based autoencoder (KAE) and the Deep Operator KAN (DOK). The KAE is a feed-forward network that compresses an input multiphase field into a latent feature vector, and then reconstructs the field from this latent representation. By using KAN high-order activation functions within the encoder and decoder, the KAE can efficiently capture complex interface geometries in a very low-dimensional embedding. The encoder's output $\xi_0$ represents the initial state of the flow in latent space, preserving essential structures while filtering out noise and redundant details. The DOK operator is built on the DeepONet paradigm, enhanced with KAN-based activation units. It learns a nonlinear mapping $\boldsymbol{\xi}_0 \mapsto \hat{\boldsymbol{\xi}}_t$ that advances the latent state from the initial time to a future time $t$. The DOK comprises a branch network and a trunk network. For multiphase inputs, the branch network processes the latent vector of each phase; the resulting branch outputs are multiplied together element-wise to incorporate inter-phase coupling into the representation. The trunk network takes the target time coordinate and produces a time-dependent feature vector. The inner product of the fused branch features and trunk output yields the predicted latent vector at time $t$. This predicted latent vector is then fed into the decoder part of the KAE to reconstruct the full field $\hat{\phi}(\mathbf{x},t)$. All components of MultiOKAN utilize KAN-based neurons, wherein each layer's activation is parameterized by a learnable high-order polynomial. This design significantly enriches the model's expressive power, allowing it to represent steep gradients and interfacial discontinuities more faithfully than conventional neural networks. Training of the KAE uses unsupervised learning on instantaneous flow snapshots, optimizing a reconstruction loss. Training of the DOK uses paired data of initial latent vectors and corresponding latent vectors at future times, optimizing the prediction error in latent space. We employ mini-batch stochastic optimization for both components, along with learning rate scheduling to ensure convergence. The models are trained on thousands of sample trajectories from the simulated cases, and early stopping or model selection is based on minimizing validation error. Conclusions MultiOKAN effectively learns the spatiotemporal dynamics of complex multiphase flows, enabling fast and accurate predictions that would be prohibitively expensive with traditional CFD solvers. Our reduced-order KAN-based architecture captures the essential nonlinear behavior of gas-liquid-solid systems in a compact latent space and successfully propagates this state forward in time. In extensive evaluations, MultiOKAN exhibits significantly lower prediction error than baseline neural operator models: for example, it reduces reconstruction MSE by approximately 50\% relative to conventional (non-KAN) operator networks, without increasing computational cost. These gains highlight the advantage of using high-order polynomial activations (via KAN) for representing sharp interfaces and complex couplings in latent space. At the same time, our results indicate that the largest performance improvements come from the autoencoder stage; incorporating KAN into the operator yields more modest benefits when compared to purely convolution-based operator models, suggesting that optimal network design may depend on the nature of the data and task dimensionality. Crucially, MultiOKAN is robust to noise and data limitations. In tests where random noise was added to input fields, the model maintained accurate predictions: the KAE stage naturally filters out high-frequency perturbations, and the DOK operator focuses on coherent latent features, resulting in only minor degradation in output accuracy even at high noise levels. When trained on reduced datasets, MultiOKAN continues to perform well until the training set becomes very small; we observed a clear threshold (around 40\% of the full data) below which prediction errors rise sharply, underscoring the need for sufficient diversity in training examples. Similarly, increasing the temporal resolution of the predicted outputs has little effect on the autoencoder but gradually raises the operator's error, as expected from the higher task complexity. These analyses provide practical guidance: MultiOKAN can be applied reliably under moderate data scarcity or high output frequency, but extremely sparse data or overly fine time-step predictions may require model or training adjustments. Finally, we demonstrated that MultiOKAN can be extended to multiphase systems with more than two phases. In a three-phase flow application, the framework successfully predicted the coupled evolution of two distinct volume-fraction fields. Among several architectural variants tested, we found that using a single shared encoder for all phases with separate branch networks in the operator achieved the best balance between accuracy and efficiency. This extension showcases the model's scalability and flexibility in handling additional phases or physics. Overall, the proposed MultiOKAN framework opens a new avenue for real-time forecasting of multiphase flow phenomena. By replacing expensive PDE solvers with learned latent-space operators, it has the potential to greatly accelerate the design and analysis of multiphase processes in engineering and environmental applications.

ABSTRACT. Heat transfer in fully developed turbulent square duct flow subject to spanwise rotation is studied with the help of DNS. The global friction Reynolds number Reτ is fixed at 180, and the Prandtl number Pr is 0.71, while the global friction rotation number Roτ varies from 0 to 10. In this paper, two thermal boundary conditions are considered. For the CHF condition, secondary flow causes the mean temperature, temperature variance, and streamwise turbulent heat flux profiles to develop a far-wall peak at high rotation numbers. For the CTD condition, the mean temperature profile does not exhibit a peak, but it shows a steep local transition. Both the temperature variance and turbulent heat flux exhibit a double-peak structure already at low rotation numbers. The budget analysis further shows that, under different thermal boundary conditions, locally large temperature gradients intensify the production of temperature variance and heat flux in specific regions, thereby leading to peaks in the temperature statistics. The correlation coefficients show that ρuθ,1 is more sensitive to rotation under the CTD condition, and it decreases more sharply in the far-wall region. The present study also reports several parameters of engineering relevance, including the turbulent Prandtl number, Nusselt number, and time scale ratio.

ABSTRACT. Many industrial applications, including Organic Rankine Cycle (ORC) turbomachinery, are characterized by non-ideal compressible flows, and their design requires the coupling of CFD tools with advanced thermodynamic models. In the past, mainly Finite Volume frameworks have been considered, but nowadays the continuous growth in computational power, together with the demand for higher accuracy in increasingly complex designs, is driving renewed interest in high-order accurate methods such as Discontinuous Galerkin(DG) methods. The objective of this work is to evaluate the performance of an efficient high-order Discontinuous Galerkin (DG) method for turbomachinery simulations. The flow is solved within a multi-reference- frame framework; stationary and rotating domains are coupled through a mixing-plane approach, and non-reflecting boundary conditions are imposed at the inflow and outflow boundaries. A two-equation k–log(omega) turbulence model is employed in its high-Reynolds-number formulation, making use of wall functions. Furthermore, the governing equations are expressed in terms of primitive variables based on the logarithms of pressure and temperature. The working fluid can be described by the polytropic ideal-gas law, the Peng–Robinson–Stryjek–Vera cubic equation of state (EoS), or the Span–Wagner multi parameter EoS. A look-up table (LuT) interpolation strategy is employed to reduce the computational cost of thermodynamic property evaluations. The following testcases are considered to validate the solver: a 3D supersonic nozzle (operated with R134a as a working fluid), a 3D transonic axial compressor (operated with air as a working fluid), and the second-stage of a supersonic ORC axial turbine manufactured by Turboden (operated with siloxane MM as a working fluid). The results are compared with the experimental and numerical data available in the literature.

ABSTRACT. A compressible large-eddy simulation is performed to investigate film cooling from a 7-7-7 laidback fan-shaped hole in turbulent crossflow. The objective is to establish a validated high-fidelity framework for analyzing coolant transport mechanisms. The experimentally documented turbulent boundary layer is reproduced by explicitly resolving a tripping-wire configuration, ensuring physically consistent inflow conditions. The simulation accurately captures the mean jet–crossflow structure and the spatial distribution of film-cooling effectiveness, showing close agreement with experimental measurements. In particular, the centerline decay and lateral spreading of the coolant film are well reproduced. These results demonstrate that the simulation reliably captures the dominant transport processes governing shaped-hole film cooling. The validated framework enables further analysis of vortex dynamics associated with jet–crossflow interaction.

ABSTRACT. This study systematically investigates the transition mechanism from linear instability to localized turbulence within the stationary-disk boundary layer of an enclosed rotor-stator cavity. To accurately predict the flow dynamics, a multi-fidelity analytical framework is employed, integrating local linear theory, global linear stability analysis, and nonlinear direct numerical simulation (DNS) using the spectral element method. Local linear stability analysis reveals that the boundary layer exhibits convective instability that eventually evolves into absolute instability at a critical local Reynolds number of Re = 21.7 and an azimuthal wavenumber of beta = -2.50. Furthermore, global linear analysis demonstrates that an initial impulse perturbation successfully triggers an upstream mode, which evolves into a globally unstable mode with a minimum critical Reynolds number of approximately Re = 48. Finally, nonlinear DNS elucidates the core transition pathway: primary spiral waves (beta = 10) reach nonlinear saturation, causing continuous and profound mean flow distortion. This distortion excites inwardly convecting circular waves, which then undergo intense nonlinear interference with the fully developed spiral waves. This modal interaction rapidly induces high-frequency, small-scale fluctuations, ultimately triggering localized turbulence in the mid-radius region (45.4 <= Re <= 70). The findings quantitatively define the critical boundaries and fundamental physical mechanisms of flow transition, providing precise theoretical criteria for complex confined rotating flows.

ABSTRACT. The convective instability and subsequent transition to turbulence in the rotating disk boundary layer are investigated using direct numerical simulations (DNS), supported by local and global linear stability analyses. The flow field is modeled within the B\"{o}dewadt-Ekman-von K\'{a}rm\'{a}n (BEK) framework. Our global linear simulations show that roughness elements effectively trigger convective spiral waves, whose wavenumbers increase with the Reynolds number. Most significantly, DNS reveals the detailed nonlinear breakdown process. Following linear saturation, the instability waves undergo a two-stage nonlinear evolution. The first phase saturates without causing a transition. It is the second nonlinear growth phase that triggers full-spectrum energy filling, leading to the onset of localized turbulence at $Re \approx 485$. These results provide a comprehensive view of the transition pathway, highlighting the critical role of secondary nonlinear interactions in the breakdown of the von K\'{a}rm\'{a}n boundary layer.

ABSTRACT. 1.Introduction High-speed trains operate under unique aerodynamic conditions, as the vehicle runs close to the ground, and various underfloor components, such as bogies, wheelsets, rails, and ballast form a highly complex flow passage beneath the underbody. Previous studies have reported that a large-scale meandering flow structure develops within this underfloor passage and convects downstream [1, 2, 3]. In tunnel sections, this meandering flow expands toward the vehicle sidewall from the underfloor, inducing strong pressure fluctuations, which can cause lateral and yawing vibrations [2]. Although vibration control technologies have mitigated these motions in practice, an understanding of fluid phenomena and countermeasures for the meandering flow remains necessary. Similar meandering flow phenomena have been observed in gap flows around nuclear fuel rods, where they are known as gap vortex instability or gap vortex street [4]. These studies provide useful insights for understanding the characteristics of meandering flow around railway vehicles. Direct numerical simulations (DNS) of gap flows between a finite-span plate and an infinite plate, which is the simplified model of a train, have revealed fundamental characteristics of the meandering flow [5]. However, actual trains possess sidewalls, and the influence of sidewall geometry on the development and structure of the meandering flow has not yet been clarified. The objective of this study is to investigate how the train sidewall geometry affects the characteristics of the meandering flow. DNS is conducted for both a finite-span plate model and a rectangular-section model representing a simplified train with sidewall. Spectral analysis is used to evaluate the frequency characteristics of the meandering motion.

2.Methodology and Problem Settings 2.1 Computational Method Three-dimensional incompressible Navier-Stokes equations were used as governing equations. Energy-conservative finite difference schemes in nonuniform grids [6] were used to discretise the governing equations, and time advancement was performed using the fractional-step method. Second-order central schemes were used for spatial discretisation, and the third-order Adams-Bashforth method was used for temporal integration. The bulk Reynolds number was set to Re = 10,000, based on the characteristic length L = 1 and the inflow velocity. This corresponds to a friction Reynolds number of approximately Reτ ≈ 150 when converted using the channel half-width δ = 0.5. No-slip boundary conditions were imposed on both the object surface and the infinite plate (i.e., ground), with the plate treated as stationary ground. A uniform inflow condition was applied at the inlet, and a convective outflow condition was applied at the outlet. Slip boundary conditions were imposed at the far-field boundaries. All quantities are nondimensionalized using the channel-width H = 1. 2.2 Schematic of Finite-Span Plate and Rectangular Body An overview of the computational domain used in this study is shown in Fig. 1, and the detailed geometries of the finite-span plate (referred to as Plate case) and the finite-span rectangular body (referred to as Box case) are presented in Fig. 2. The object width was fixed at W = 5, while the height was varied between the Plate and Box case configurations. The leading edge of the Box case was shaped as a wedge to prevent flow separation at the front. The gap between the ground and the object was set to 1, and the object length was 600. The computational domain size was 640 × 400 × 46.5, which was sufficiently large in the y and z directions relative to the object. The total number of grid points was 6150 × 765 × 264. The numerical simulations were performed on a Cray XC50 system at RTRI using 3600 parallel processors. 2.3 Grid Dependency A finer grid-resolution simulation was conducted to confirm that differences in the mean velocity profiles and characteristics of the meandering flow remain small. Further details will be presented in the final paper.

3.Results and Discussion Figure 3 shows the instantaneous velocity magnitude field at the middle height between the object (light gray) and the ground. Because a boundary layer develops along the stationary ground, the velocity near the ground (z = 0.5) decreases downstream. Turbulent flow is generated near the leading edge and spreads spanwise as it convects downstream, with its starting point further upstream for the Box case than for the Plate case. Meandering flow structures appear as low-velocity regions within the cross-section and maintain their structures over a wide area. Figure 4 shows the time-averaged streamwise velocity distribution at the center of the middle height. The velocity decreases sharply behind the leading edge due to the stationary object and ground, with the decrement beginning further upstream for the Box case. After reaching a minimum, the velocity recovers by x = 200 and becomes nearly uniform after x = 300. The recovery location corresponds to the onset of spanwise fluctuations of flow in Fig. 3, indicating that the development of meandering flow enhances momentum mixing between high-speed mainstream and low-speed gap flow. Figure 5 shows the PSD of the spanwise velocity v at x = 150 and x = 550. For both geometries, the peak frequency decreases downstream while the peak height increases. At x = 550, where the meandering flow is fully developed, the Box case exhibits a higher peak and a lower frequency than that of the Plate case. Figure 6 shows the distributions of the time-averaged and RMS values of the streamwise velocity u at x = 550 cross-section. The time-averaged velocity field indicates that the velocity u becomes minimum at the center of the gap, while the velocity increases toward the outside of the gap. The flow around the gap becomes high-speed, excluding the boundary layer flow near the ground. The RMS distribution forms a high-value area connecting the low-velocity gap flow with the surrounding high-speed flow, representing the mixing promoted by the meandering flow. The Box case exhibits a wider spanwise extent of high RMS values, indicating that the influence of the meandering flow spreads over a broader region. This causes a higher velocity distribution in the downstream region in Fig. 4 in the Box case. These results show that, under Poiseuille-flow conditions, the presence of the sidewall strengthens the meandering flow and expands the momentum mixing region.

4.Conclusions Direct numerical simulations were conducted to investigate the influence of sidewall geometry on the spatially developing meandering flow between a finite span object and an infinite plate under Poiseuille flow conditions. The main findings are as follows: •A meandering flow develops regardless of the presence of sidewalls, and this flow contributes to the recovery of the gap flow velocity beneath the object. •When sidewalls are present, the meandering flow starts developing from further upstream. •The presence of sidewalls decreases the dominant frequency and increases the fluctuation intensity of the meandering flow in the fully developed region. This promotes momentum mixing and leads to a more pronounced recovery of the gap flow velocity.

ABSTRACT. Abstract Rough surfaces modify the near-wall flow and therefore play a crucial role in the torque response of Taylor-Couette (TC) flow, motivating extensive investigations over recent decades. Here, direct numerical simulations (DNS) are performed to examine the influence of dimple roughness and to elucidate the underlying mechanisms in a TC system with radius ratio η = 0.714, considering both laminar and turbulent regimes. In the laminar regime, the dimples reduce the wall shear stress and thus decrease the friction-induced torque Tτ, yielding a net torque reduction of 6.8%. In the turbulent regime, the dimples intensify flow fluctuations and modify the large-scale flow structures, which strengthens the pressure difference across each dimple and increases the pressure-induced torque Tp, leading to a net torque enhancement of 11.2%. These findings clarify how dimple roughness modifies torque in TC flow and provide physical guidance for the surface design of energy-efficient rotating machinery, such as electric motors and turbine shafts. Introduction When it comes to rotation systems, Taylor-Couette (TC) flow provides a canonical and well-controlled framework for elucidating flow transitions and coherent structures in rotating shear flows. Many practical devices can be idealized as a TC system comprising a rotating inner cylinder and a stationary outer cylinder, such as electric motors and turbine shafts. In such systems, the cylinder-surface geometry strongly influences the torque response and, consequently, the energy consumption and mechanical efficiency. This has motivated extensive efforts to design rough surfaces for torque reduction or enhancement, including V-shaped grooves, sandpaper roughness, and triangular obstacles. Against this background, identifying new roughness concepts and clarifying the mechanisms by which they modify the torque remain of both practical and fundamental interest. Drag reduction induced by dimple roughness has been investigated in a range of applications, including golf balls, plane Couette flow, and channel flow. The underlying mechanisms are generally attributed to local flow modifications induced by the dimples. However, the influence of dimple roughness on TC flow, and the associated mechanisms, remains unclear. In the present work, the effects of shallow dimple roughness on the torque and flow structures are investigated in a TC system with radius ratio η = 0.714 using direct numerical simulations (DNS). The considered conditions correspond to the classical TC regime rather than fully developed turbulence, spanning 400 ≤ Rei ≤ 3960. The aim is to provide physical insight that can inform the design of more energy-efficient rotating devices, such as electric motors and turbine shafts. Methodology The simulations are performed in a complete TC system with radius ratio η = 0.716 and aspect ratio Γ = 4, where the inner cylinder rotates about the z-axis and the outer cylinder is stationary. The analysis considers laminar and turbulent regimes for the present configuration, corresponding to Re = 400 and Re = 3960, respectively. The working fluid is assumed to be incompressible and Newtonian. The governing equations are the continuity and momentum equations. A second-order central-difference scheme is adopted for the convective terms in the momentum equation, while a third-order implicit Adams-Moulton scheme is applied for the time integration. The computational domain is discretized using unstructured meshes to accurately represent the dimple geometry. Direct numerical simulations are carried out with the in-house code FrontFlow/Red on the supercomputer Fugaku at the RIKEN Center for Computational Science, Japan, employing 28,800 CPU cores. For numerical stability, the Courant-Friedrichs-Lewy (CFL) number is maintained at approximately 0.3 in all simulations. The rotational motion of the inner cylinder is imposed using an arbitrary Lagrangian-Eulerian (ALE) method. No-slip boundary conditions are applied on the inner and outer cylinders, while free-slip boundary conditions are imposed on the upper and lower end-walls. Results A torque reduction of 6.8% is achieved with dimple roughness in the laminar regime, with the dimensionless angular velocity current decreasing from Nuω = 2.890 for the smooth case to Nuω = 2.693 for the dimpled case. Although the dimple roughness does not significantly alter the Taylor-vortex structure owing to weak momentum transport in the laminar regime, a pronounced reduction in skin friction is observed on the dimpled surface (Fig. 1), leading to a decrease in the friction-induced torque Tτ. In addition, compared with the smooth case, the dimpled surface produces an azimuthally asymmetric near-wall pressure field (Fig. 2). This pressure imbalance gives rise to a pressure-induced torque Tp, which counteracts the torque-reduction effect. The torque reduction in the laminar regime is primarily attributed to the decrease in Tτ. The dimples locally thicken the near-wall velocity boundary layer, thereby reducing the radial velocity gradient and the associated azimuthal shear stress, which results in a net reduction of Tτ. By contrast, the concave surface generates a pressure imbalance that produces Tp opposing torque reduction. Overall, the reduction in Tτ outweighs the increase in Tp, yielding a net torque reduction. In the turbulent regime, the dimple roughness leads to a torque enhancement of 11.2%, with Nuω increasing from Nuω = 7.505 for the smooth case to Nuω = 8.343 for the dimpled case. A marked change in the large-scale flow structure is observed (Fig. 3), with the number of Taylor vortices increasing from four to six. This transition introduces additional strong-interaction regions near the inner cylinder, where the flow between adjacent vortices impinges on the wall nearly perpendicularly. As in the laminar regime, the dimpled surface also exhibits reduced skin friction, contributing to a decrease in Tτ. Meanwhile, the pressure-induced torque Tp increases with rotation rate in the turbulent regime. The enhanced pressure imbalance is the dominant contributor to the torque enhancement in the turbulent regime. As shown in Fig. 4, the concave geometry generates local vortices near the leading and trailing edges of the dimples, introducing additional axial fluctuation that acts similarly to spanwise wall oscillations and tends to reduce skin friction in the streamwise direction. Consequently, Tτ decreases. However, with increasing rotation rate, the intensified oscillation impacts the original Taylor vortex structure, generating an extra interacting area above the inner cylinder wall. The difference between the low- and high-pressure regions associated with each dimple becomes stronger, resulting in a substantial increase in Tp. Finally, the increase in Tp outweighs the reduction in Tτ, leading to a net torque enhancement. Conclusions Direct numerical simulations are conducted to investigate the effects of dimple roughness in Taylor-Couette flow, with emphasis on laminar and turbulent regimes. The system response is characterized by the dimensionless angular velocity current Nuω and the associated flow structures. The results show a torque reduction of 6.8% in the laminar regime and a torque enhancement of 11.2% in the turbulent regime. The main conclusions are summarized as follows: 1.The torque reduction in the laminar regime is primarily attributed to the decrease in Tτ. The dimpled surface locally thickens the near-wall boundary layer, reducing the radial velocity gradient and thereby the friction-induced torque. Although a pressure-induced torque acts to offset this reduction, its contribution remains relatively weak in the laminar regime. 2.In the turbulent regime, the enhanced pressure imbalance is the dominant contributor to torque enhancement. Vortical structures attached to the dimples intensify axial fluctuations and promote a reduction in skin friction in the azimuthal direction, leading to a decrease in Tτ. However, the fluctuation modifies the flow structures and thereby introduces an extra interacting area, which produces more contribution in Tp. Consequently, the pressure-induced torque Tp increases more strongly and outweighs the reduction in Tτ, resulting in a net torque enhancement. Overall, this study elucidates the mechanisms by which dimple roughness modifies the torque in a Taylor-Couette system, providing guidance for torque control in rotating machinery such as electric motors and turbine shafts. These findings offer a reference for surface-shape design aimed at improving energy efficiency and mechanical performance, in line with industrial and environmental demands for reduced energy consumption.

ABSTRACT. This study investigates turbulent transition induced by Tollmien-Schlichting (TS) wave generated through receptivity. To simulate the target transition scenario, compressible linearized Navier-Stokes (CLNS) method and direct numerical simulation (DNS) are used. Unlike traditional stability analyses that rely on arbitrary initial amplitudes, the CLNS method captures leading-edge receptivity to freestream acoustic disturbances, providing physically determined upstream conditions that include both discrete eigenmodes and the continuous spectrum. These fluctuations are imposed at the DNS inlet to simulate nonlinear interactions and breakdown stage. Results demonstrate that the natural scenario, which considers receptivity stages, undergoes transition significantly earlier than the controlled scenario dominated solely by discrete modes, even with identical TS wave amplitudes. This highlights that incorporating receptivity is required for accurate transition prediction rather than considering only eigenfunctions of discrete modes.

ABSTRACT. Sustained coherent flow oscillations that occur at frequencies lower than that of turbulent eddies, Kelvin-Helmholtz instabilities, and von Kármán vortex shedding have been reported in a variety of situations, including flow over wings in transonic and incompressible regimes, spheres, discs, re-entry capsules, etc. Although these oscillations seem to have shared characteristics irrespective of the flow situation considered, such as large-amplitude dynamics variations in flow separation features and recirculation zone, the connections between them remain poorly understood. Exploring these links can aid in elucidating the physical mechanism that sustains these oscillations. Understanding the underlying mechanisms can be crucial for a variety of applications. such as in aviation, ballistics, and re-entry vehicles, as it can potentially aid in developing flow control strategies to mitigate these detrimental oscillations. Thus, to better understand the origins of these oscillations, the present study investigates the link between low-frequency oscillations (LFO) in various flow settings. Direct numerical simulation and large-eddy simulations of the flow over spheres, discs and crew-capsules are performed using the open-source, high-order, flow solver Xcompact3D. After ensuring grid and domain independence, the results are verified against previously reported simulation results. The coherent oscillatory features are analyzed using a spectral proper orthogonal decomposition (SPOD). These results are also compared with low-frequency oscillations observed in flow on airfoils at high angles of attack close to stall to establish further connections. The SPOD results show that for all cases considered, there are coherent oscillations with distinct peaks in the eigenvalue spectra at a Strouhal number (based on characteristic length of object and freestream velocity) of St ~ O(0.01), which are accompanied by high-frequency coherent oscillations at St ~ O(0.1) associated with vortex shedding. The low-frequency oscillations are found to have a topologically similar spatial structure, with the pressure in the near-wake being out of phase with that near the separation point, a feature that is also observed in flow over airfoils. Ongoing work is directed toward further exploring these connections using global linear instability approaches and elucidating the separation-related mechanism that gives rise to these oscillations, with the long-term objective of developing a unified mitigation strategy applicable to a broad class of flow-induced instabilities. Furthermore, by focusing on low to moderate Reynolds numbers, the present study enables a detailed examination of the baseline physics at significantly reduced computational cost, thereby establishing a robust foundation for future investigations extending to higher Reynolds number regimes.