International Journal for Numerical Methods in Fluids最新文献

{"title":"Exact Computation of the Color Function for Triangular Element Interfaces","authors":"Jieyun Pan,&nbsp;Désir-André Koffi Bi,&nbsp;Ahmed Basil Kottilingal,&nbsp;Serena Costanzo,&nbsp;Jiacai Lu,&nbsp;Yue Ling,&nbsp;Ruben Scardovelli,&nbsp;Grétar Tryggvason,&nbsp;Stéphane Zaleski","doi":"10.1002/fld.70086","DOIUrl":"https://doi.org/10.1002/fld.70086","url":null,"abstract":"<p>The calculation of the volume enclosed by curved surfaces discretized into triangular elements and a cube is of great importance in different domains, such as computer graphics and multiphase flow simulations. We propose a robust algorithm, the Front2VOF (F2V) algorithm, to address this problem. The F2V algorithm consists of two main steps. First, it identifies the polygons within the cube by segmenting the triangular elements on the surface, retaining only the portions inside the cube boundaries. Second, it computes the volume enclosed by these polygons in combination with the cube faces. To verify the proposed algorithm, we first compute the volume enclosed within a cubic cell for a range of synthetic configurations with known analytical solutions. We then apply the algorithm to initialize volume fraction fields on Cartesian meshes for complex interfaces and compare the results with those obtained using the existing <span>VOFI</span> library. The F2V results show excellent agreement with both the analytical solutions and the VOFI results, demonstrating the accuracy and robustness of the proposed approach. Finally, we evaluate the method for color function computation in multiphase flow simulations. The F2V method is compared with the conventional approach based on solving a Poisson equation, showcasing significantly improved computational efficiency, particularly on fine mesh resolutions.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 11","pages":"1181-1194"},"PeriodicalIF":2.1,"publicationDate":"2026-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70086","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assessment of a Single-Phase Dynamic-Boundary CFD Approach for Wave-Induced Unsteady Aerodynamics","authors":"J. B. Allen,&nbsp;C. M. Shelton,&nbsp;A. J. Schemmel,&nbsp;N. C. Prewitt,&nbsp;J. W. Foster","doi":"10.1002/fld.70089","DOIUrl":"https://doi.org/10.1002/fld.70089","url":null,"abstract":"<div>\u0000 \u0000 <p>This study presents a validated numerical framework for predicting unsteady aerodynamic loads induced by prescribed moving boundaries using a single-phase computational fluid dynamics (CFD) approach. Rather than explicitly resolving an air–water interface, wave-induced effects are represented through time-dependent deformation of a solid lower boundary within an incompressible air-only domain. The methodology is implemented in OpenFOAM using dynamic mesh motion and is evaluated for an airfoil operating in ground effect above mechanically generated waves. Numerical predictions are compared against experimental force measurements from the DARPA Wing Over Water campaign and against corresponding two-phase volume-of-fluid simulations. Results show that the single-phase dynamic-boundary approach accurately captures the dominant unsteady lift and drag trends, including frequency and phase behavior, while providing improved numerical robustness and substantially reduced computational cost. Although localized nonlinear effects and force amplitudes are attenuated under steep wave conditions, the framework offers a practical and scalable surrogate for fully coupled multiphase simulations. The study provides quantitative guidance on the applicability and limitations of dynamic-boundary single-phase CFD for wave-influenced aerodynamic flows, supporting its use in engineering analysis and parametric studies.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 11","pages":"1195-1211"},"PeriodicalIF":2.1,"publicationDate":"2026-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Development of 1D-2D Coupled Hp-Adaptive Discontinuous Galerkin Model for Nonlinear Shallow Water Equations With Wetting and Drying","authors":"Tsubasa Iwasaki,&nbsp;Tetsuya Shintani","doi":"10.1002/fld.70088","DOIUrl":"https://doi.org/10.1002/fld.70088","url":null,"abstract":"<div>\u0000 \u0000 <p>Nonlinear shallow-water modeling for tsunamis, river flooding, and storm surges faces persistent challenges in computational speed and numerical stability near wet/dry fronts. To address these issues, this study develops Systematic Grid, an object-oriented simulation framework that integrates 1D 2D coupling and hp-adaptive methods to accelerate computations while incorporating stabilization techniques for the Discontinuous Galerkin (DG) method. Systematic Grid provides a hierarchical structure consisting of Domains, Blocks, SubBlocks, and Elements. This organization allows flexible control of dimensions, polynomial orders, and spatial resolutions at each level. Object-oriented programming further allows consistent treatment of elements with different shapes and polynomial orders, naturally supporting hp-adaptive refinement on arbitrary grids. The paper first describes the design of Systematic Grid and the implementation of each numerical technique. It then introduces the stabilization methods and explains how they are applied near wet/dry fronts. Finally, the proposed framework is validated through the Carrier Greenspan problem, the dam-break flow in an L-shaped channel, and the Okushiri benchmark for the 1993 Hokkaido Southwest Offshore Earthquake tsunami. The results demonstrate clear improvements in both computational efficiency and numerical stability.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 11","pages":"1212-1231"},"PeriodicalIF":2.1,"publicationDate":"2026-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100455","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Employing the Moving Least-Squares Aided Finite Element Method to Study Heat Transfer Phenomenon in Closed-Cell Polymeric Foam","authors":"Mehdi Mostafaiyan,&nbsp;Sven Wiessner,&nbsp;Andreas Leuteritz","doi":"10.1002/fld.70090","DOIUrl":"https://doi.org/10.1002/fld.70090","url":null,"abstract":"<p>A new technique based on the finite element method (FEM) is introduced that couples the fluid flow and heat transfer processes within a gas-filled porous medium, such as closed-cell polymeric foam. For such an analysis the classic FEM relies on a mesh fitting the solid–fluid boundaries; however, the new approach requires a fixed background mesh independent of the foam morphology. We term the method the moving least-squares aided finite element method (MLS-FEM), as it employs moving least-squares interpolants to enhance the pressure, velocity, and temperature shape functions in the active elements or the elements intersected by the solid–fluid interface. The accuracy of the MLS-FEM for a single-void foam patch is assessed against a classical boundary-fitted FEM, showing that the field variables, such as velocity components and temperature, are in close agreement across different mesh resolutions. The comparison is then extended to multivoid patches, with similarly close agreement between the two approaches. Notably, the MLS-FEM reuses the same background mesh regardless of geometry, whereas the classical FEM requires remeshing whenever the foam morphology changes.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 11","pages":"1232-1243"},"PeriodicalIF":2.1,"publicationDate":"2026-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149100675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Edge-Based Discretizations on Triangulations in Any Dimension, With Special Attention to Four-Dimensional Space","authors":"Nicholas Tufillaro,&nbsp;David M. Williams,&nbsp;Hiroaki Nishikawa","doi":"10.1002/fld.70084","DOIUrl":"https://doi.org/10.1002/fld.70084","url":null,"abstract":"<p>Many time-dependent problems in the field of computational fluid dynamics (CFD) can be solved using <i>space-time</i> methods. However, such methods can encounter issues with computational cost and robustness. To address these issues, efficient, node-centered edge-based schemes are currently being developed. In these schemes, a median-dual tessellation of the space-time domain is constructed based on an initial triangulation. These methods are <i>node-centered</i> or <i>node-based</i>, as the primary components of the discretization are median-dual regions (polytopes) that surround the mesh nodes. These methods are extremely robust, as the median-dual regions will often maintain a positive volume and other good geometric properties, even in cases when some of the associated simplices have negative volumes, or other poor geometric properties. Unfortunately, it is not straightforward to construct median-dual regions or deduce their properties on triangulations for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 <mo>≥</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$$ dge 3 $$</annotation>\u0000 </semantics></math>. In this work, we provide the first rigorous definition of median-dual regions on triangulations in any number of dimensions. In addition, we introduce a new method for computing the hypervolume of a median-dual region in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>d</mi>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}^d $$</annotation>\u0000 </semantics></math>. Furthermore, we provide a new approach for computing the directed-hyperarea vectors for faces of a median-dual region in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>4</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {mathbb{R}}^4 $$</annotation>\u0000 </semantics></math>. These geometric properties are key for developing node-centered edge-based schemes in any number of dimensions. We conclude our work by analyzing the computational complexity of the edge-based schemes, and performing numerical experiments in two, three, and four dimensions. We successfully demonstrate their effectiveness by obtaining accurate solutions to several canonical problems.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 10","pages":"1143-1164"},"PeriodicalIF":2.1,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70084","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148862340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Monolithic Framework to Simulate Fluid-Structure Interaction Problems Using Geometric Volume-of-Fluid Method","authors":"Soham Prajapati,&nbsp;Ali Fakhreddine,&nbsp;Krishnan Mahesh","doi":"10.1002/fld.70082","DOIUrl":"https://doi.org/10.1002/fld.70082","url":null,"abstract":"<p>We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and viscous hyperelastic solids. A VOF-based one-continuum formulation is used to describe the unified momentum conservation equations with incompressibility constraints that are solved using the finite volume method (FVM). In the geometric VOF interface-capturing (IC) approach, the piecewise linear interface calculation (PLIC) method is used to reconstruct the interface, and the Lagrangian explicit (LE) method is used in the directionally split advection procedure. To model the hyperelastic behavior of the solid, we consider linear and nonlinear Mooney–Rivlin material models, where we use the left Cauchy–Green deformation tensor (<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$$ boldsymbol{B} $$</annotation>\u0000 </semantics></math>) to account for the solid deformation on an Eulerian grid and the fifth-order weighted essentially non-oscillatory (WENO-Z) finite difference reconstruction method is utilized to treat the advection terms involved in the transport equation of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>B</mi>\u0000 </mrow>\u0000 <annotation>$$ boldsymbol{B} $$</annotation>\u0000 </semantics></math>. Multiple benchmark problems and reversibility tests are considered to verify the accuracy of the approach. Furthermore, to demonstrate the capability of the solver to handle turbulent interactions, we perform direct numerical simulation (DNS) of turbulent channel flow with a deformable compliant bottom wall and a rigid top wall; our observations align well with previous experimental and numerical works. The detailed numerical experiments show that: (i) despite the discontinuity of the interface across the cell boundaries and stress discontinuity across the interface, a VOF/PLIC-based FSI framework can provide stable and accurate solutions that significantly minimizes numerical artifacts (e.g., flotsam and spurious currents) while maintaining a sharp interface. (ii) The accuracy of a VOF/PLIC-based FSI approach on coarse grids is comparable to the accuracy of a diffusive IC method-based FSI approach on much finer grids.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 10","pages":"1105-1125"},"PeriodicalIF":2.1,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70082","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148862534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subspace Acceleration for Efficient Nonlinear Water Wave Simulation","authors":"Rasmus Kleist Hørlyck Sørensen,&nbsp;Margherita Guido,&nbsp;Allan Peter Engsig-Karup,&nbsp;Daniel Kressner","doi":"10.1002/fld.70087","DOIUrl":"https://doi.org/10.1002/fld.70087","url":null,"abstract":"<p>Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier–Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a time-dependent discretized Poisson problem at every time step to enforce divergence free flow. This is crucial to ensure conservation of mass and requires solving long sequences of time-dependent linear systems typically using iterative methods, such as preconditioned Krylov subspace methods. In this work, we investigate new subspace acceleration techniques for improving initial guesses to reduce the number of iterations required by iterative solvers, with a focus on nonlinear wave propagation problems. We extend the original subspace acceleration method by incorporating the complete history of previous solutions through an exponentially weighted formulation. This approach eliminates the need for repeated sketching and orthonormalization, resulting in a more efficient and scalable strategy to generate better initial guesses. Our method is implemented within a high-order finite-difference framework using a method-of-lines formulation and a low-storage Runge–Kutta time integration scheme. We demonstrate that subspace acceleration significantly reduces the number of GMRES iterations when solving the Poisson equation in nonlinear water wave simulations. Performance is evaluated on two benchmark problems: nonlinear stream function wave propagation and harmonic wave generation over a submerged bar. In both cases, the new approach achieves substantial improvements in computational efficiency without compromising accuracy. Although demonstrated using high-order finite difference methods, the technique is discretization independent and broadly applicable to incompressible free-surface flow solvers.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 10","pages":"1165-1180"},"PeriodicalIF":2.1,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70087","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148862209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topology Optimization for Microfluidic Mixers by a Phase Field Method","authors":"Zongyuan Liu,&nbsp;Jiajie Li,&nbsp;Shengfeng Zhu","doi":"10.1002/fld.70083","DOIUrl":"https://doi.org/10.1002/fld.70083","url":null,"abstract":"<div>\u0000 \u0000 <p>We investigate multi-physical topology optimization for microfluidic mixers. Starting from the Ising model, we derive a thermodynamically consistent Ginzburg–Landau free energy functional that incorporates the objective functional as an effective external field, providing a physically interpretable framework for phase-field topology optimization. To eliminate fluid blockage in microfluidic mixers, we incorporate the coupled Navier–Stokes, convection–diffusion, and Poisson–Boltzmann equations. An Allen–Cahn type gradient flow method is proposed based on sensitivity analysis. The algorithm is validated for its computational effectiveness through numerical simulations of benchmark problems in 2D and 3D.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 10","pages":"1126-1142"},"PeriodicalIF":2.1,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148862204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lattice Boltzmann Simulation of Droplet Impact on an Oscillating Horizontal Surface","authors":"Qing Li,&nbsp;Juanyong Wang,&nbsp;Lei Wang,&nbsp;Zijin Zhu","doi":"10.1002/fld.70079","DOIUrl":"https://doi.org/10.1002/fld.70079","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this work, the droplet impact on a sinusoidally oscillating hydrophobic substrate is numerically simulated using the lattice Boltzmann method. We focus particularly on energy transfer and the maximum droplet spreading diameter (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {beta}_m $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) as functions of substrate oscillation parameters, the Weber number, and the wettability of the substrate. Our analysis shows that the maximum spreading diameter scales linearly with the tangential Weber number (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ W{e}_s $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), calculated from the substrate velocity amplitude. Notably, the spreading dynamics exhibit a nonmonotonic, resonance-like response, peaking when the spreading time coincides with half the oscillation period. Additionally, decreasing the contact angle strengthens interfacial adhesion to amplify horizontal migration, whereas superhydrophobic surfaces severely attenuate this tangential momentum exchange through inherent slip. Furthermore, the analysis of the normal Weber number (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ W{e}_n $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) uncovers a “forgetting” mechanism, whereby the droplet ultimately converges to a consistent dynamic response across different &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ W{e}_n $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; as the initial kinetic energy dissipates. The study further elucidates the distinct regulatory effects of amplitude and period: amplitude primarily shifts the overall &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 ","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 9","pages":"1017-1034"},"PeriodicalIF":2.1,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Physics-Informed Neural Networks for Modeling Near-Wall Steady Laminar Flows at High Reynolds Numbers","authors":"B. Y. Pang,&nbsp;Y. Xiao,&nbsp;L. M. Yang","doi":"10.1002/fld.70081","DOIUrl":"https://doi.org/10.1002/fld.70081","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, a multiscale, zonal-coupled physics-informed neural network (PINN) framework, termed BL-NS-PINNs, is proposed for accurately predicting steady laminar near-wall flow fields at high Reynolds numbers without requiring near-wall data. The framework ensures physical continuity across flow regions by solving the Blasius and Navier–Stokes equations in the inner and outer zones, respectively, while enforcing velocity consistency within the matching region. Numerical experiments demonstrate that BL-NS-PINNs significantly outperform conventional PINNs trained with data supervision, accurately capturing near-wall flow features and sharp gradients in high-Reynolds-number laminar boundary layers. The method is further extended to wedge flows with self-similar solutions, offering both a theoretical foundation and a practical pathway for integrating wall functions into data-driven boundary-layer modeling. Overall, BL-NS-PINNs effectively overcome the limitations of conventional PINNs in resolving sharp near-wall velocity gradients and show strong potential for efficient, high-fidelity modeling of high-Reynolds-number flows.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 9","pages":"1061-1082"},"PeriodicalIF":2.1,"publicationDate":"2026-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148667415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}