International Journal for Numerical Methods in Fluids最新文献

{"title":"A Novel Mesh-Free Approach for Solving Incompressible Fluid Flow Problems","authors":"Rajaa Fadil,&nbsp;Bouazza Braikat,&nbsp;Abdeljalil Tri","doi":"10.1002/fld.70057","DOIUrl":"https://doi.org/10.1002/fld.70057","url":null,"abstract":"<div>\u0000 \u0000 <p>In this study, we present a novel mesh-free approach for solving incompressible fluid flow problems, which is introduced here for the first time. Our approach solves the steady-state Navier–Stokes equations without requiring traditional mesh generation. For this purpose, we adopt a discrete framework in which variables are defined at specific points within the domain, thereby eliminating the need for numerical integration. The proposed approach combines a weighted least squares (WLS) approximation with a high-order continuation method (HOCM). This approach significantly enhances the accuracy of steady-state incompressible flow simulations, offering both improved precision and reduced computation time compared to classical methods. Our results indicate that this approach holds substantial potential for expanding practical applications across various engineering fields. In contrast to the coupling of the moving least squares (MLS) method with the HOCM, our approach avoids computing derivatives of the weight function within the influence domain, which reduces the computational cost and enhances accuracy. This original combination highlights the novelty of our work compared to research conducted in recent years. A comparison is presented between the results obtained using the HOCM with MLS approximation and those reported in the literature.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"598-612"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668251","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":"Polymer Stress-Tensor Calculation for a Laminar Submerged Viscoelastic Jet Flow Using Different Constitutive Models","authors":"Rafael de Lima Sterza,&nbsp;Leandro Franco de Souza,&nbsp;Marcio Teixeira de Mendonca,&nbsp;Analice Costacurta Brandi","doi":"10.1002/fld.70058","DOIUrl":"https://doi.org/10.1002/fld.70058","url":null,"abstract":"<p>Viscoelastic fluids, exhibiting both elastic and viscous properties, play a fundamental role in various industrial and biological applications. Accurate modeling of their rheological behavior requires constitutive equations that capture the complex interplay between these properties. The present study focuses on the analysis of incompressible, isothermal, two-dimensional, planar, laminar, submerged jet flow of viscoelastic fluids. A computational methodology is adopted to determine the polymer stress-tensor distribution for different viscoelastic models, including Oldroyd-B, UCM, Giesekus, Phan-Thien-Tanner (PTT), and finitely extensible nonlinear elastic (FENE). These models are chosen to represent a diverse range of viscoelastic behaviors. The Navier–Stokes equations, coupled with the appropriate constitutive model, are solved numerically. The proposed method allows one to access the distribution of the polymer stress-tensor components with very low computational cost. Results demonstrate the accuracy of the computational method for various models and their parameter values. The findings provide valuable insights into the fundamental behavior of viscoelastic jets and can serve as a foundation for subsequent linear and nonlinear stability investigations.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"628-643"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70058","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668618","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":"Data Assimilation of Compressible Flows With Discontinuities: Evaluating Algorithms on Sod's Shock Tube","authors":"Ayaboe K. Edoh,&nbsp;Eric J. West,&nbsp;Tomas Houba,&nbsp;Ramakanth Munipalli,&nbsp;Matthew E. Harvazinski,&nbsp;Wei Kang","doi":"10.1002/fld.70054","DOIUrl":"https://doi.org/10.1002/fld.70054","url":null,"abstract":"<div>\u0000 \u0000 <p>Data assimilation (DA) combines noisy observations with uncertain model predictions to obtain optimal state estimation. It has been used extensively in numerical weather prediction and is increasingly used in computational fluid dynamics. However, the application of DA to compressible flows with discontinuities such as shocks or detonation fronts is far less explored. In this paper, we examine three different DA algorithms applied to 1D, non-reacting, compressible flows: The particle filter (PF), the ensemble Kalman filter (EnKF), and 4D-Var. The Sod's shock tube problem is employed as a canonical test case. While the sequential DA methods (PF and EnKF) are able to successfully assimilate sparse pressure measurements, this comes at the risk of smearing sharp gradients due to reconstructing the state as an ensemble average. On the other hand, the 4D-Var method, applied in the context of a small parameter inverse problem, preserves sharp gradients within the resolution of the forward solver, but may require many iterations to converge to the truth. This study therefore provides assessments of sequential and variational DA methods in 1D shock tube problems and contributes towards applying DA to more complex shock-laden flows (e.g., in higher dimensions, or reacting flows).</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"644-672"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668432","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":"An Improved Curvature Estimation Method Based on Height Function and Volume Preserving Mean Curvature Motion","authors":"Cheng Liu,&nbsp;Ruoqing Gao,&nbsp;Peiqin Zhang,&nbsp;Changhong Hu","doi":"10.1002/fld.70060","DOIUrl":"https://doi.org/10.1002/fld.70060","url":null,"abstract":"<div>\u0000 \u0000 <p>We present an improved height function technique aimed at obtaining smooth curvature in three dimensions. The new approach is designed for estimating curvature from the volume of fluid (VOF) field. Motivated by the volume-preserved mean curvature (VPMC) motion, an iterative procedure is implemented to eliminate oscillations from the curvature field while simultaneously ensuring consistency with the VOF field. To validate the new method, the curvature of 2D and 3D drops is considered. Numerical tests demonstrate the efficient elimination of high-frequency errors in the local curvature, and the total volume enclosed by the interface is preserved. Considering the equilibrium of the static droplet problem, the spurious current is also effectively suppressed. The proposed method is further extended to an adaptive mesh and validated through the free oscillation of a 2D droplet. Finally, the accuracy and efficiency of the improved height function technique applied to 3D problems are confirmed through the simulation of a liquid droplet impact onto a deep liquid pool.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"673-687"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668694","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":"Numerical Analysis of Fluid–Structure Interaction in Open and Closed Saddle-Shaped Membrane Structures: A New Framework Based on Vortex Dynamics","authors":"Dong Li,&nbsp;Yi Qiu,&nbsp;Renyang Shen,&nbsp;Zhenxing Chen,&nbsp;Mingliang Liu,&nbsp;Feng Zhang","doi":"10.1002/fld.70059","DOIUrl":"https://doi.org/10.1002/fld.70059","url":null,"abstract":"<div>\u0000 \u0000 <p>The strong fluid–structure interaction (FSI) between the membrane structure and the surrounding airflow directly impacts the wind pressure distribution and structural stability, which are concerned with structural safety. This paper comparatively investigates the FSI of open and closed-type saddle-shaped membrane structures under wind loads, in terms of wind pressure distribution and flow field characteristics. First, a bidirectional FSI numerical simulation, integrated into this vortex dynamics-based framework, was implemented for the spatial membrane structure in laminar flows. The accuracy of the simulation was verified based on previous wind tunnel tests, from the perspective of both structural vibration and flow field. Subsequently, leveraging the framework's ability to track vortex evolution, a comparative analysis of wind pressure distribution and velocity trajectories was conducted for both configurations. Finally, the framework enabled a deep analysis of how vortex structures–their formation, development, and dissipation–influence structural vibration. The results indicate that the peak wind pressure coefficients of the open membrane structure at the leading edge under 0° and 90° wind directions reach 0.5 and 0.7, respectively. At a 45° wind direction, the flange area becomes a risk focus due to conical vortices. For closed membrane structures, the minimum average wind pressure coefficients under 0° and 90° wind directions were −0.52 and −1.0, respectively, with significant overall wind suction force. The open-type membrane structures exhibit both positive and negative pressure zones at all wind directions. Airflow separation results in wind pressure peaks at the leading edge of the windward side. Wind direction obviously affects the type of vortex structure, and the more sufficient vortex development would lead to increased trailing edge amplitude. Then, the local dynamic response of open-type membrane structures should be paid more attention. However, closed-type membrane structures experience upward lifting at all wind directions. The enhanced stiffness of the internal gas would reduce pulsations, and therefore the risk of structural overall instability should be considered as priorities.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"613-627"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668663","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":"POD-RBF Based Non-Intrusive Reduced Order Model for Multi-Physics Problems","authors":"Mainak Bhattacharyya,&nbsp;Slim Ben-Elechi,&nbsp;Delphine Brancherie,&nbsp;Piotr Breitkopf,&nbsp;Sadok Gaied","doi":"10.1002/fld.70064","DOIUrl":"https://doi.org/10.1002/fld.70064","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper essentially depicts a methodology to address computational frugality of multi-physics problem. Reduced-order modelling (ROM) is popular in engineering as it has the potential to gain CPU cost for simulations with different material parameters and/or different initial or boundary conditions. The basic idea in this article is to provide a nonintrusive setup for the ROM conducive for industrial problems using commercial software. The problem dealt here is a classical multiphase thermo-fluid problem, although the philosophy can be extended for other multi-physics problems. The first step is to decouple the involved physics, and thereafter a nonintrusive ROM is used through response surface method like neural networks to replace the full-order simulation of the most expensive physics. This essentially provides reduction in computational cost for the problem studied. The reduced order bases thus generated are also used to compute separate problems with altered parameters or loading conditions thereby eliminating the necessity of computations of full-order problems.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"688-706"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668711","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":"Impact of Uncertain Parameters on Navier–Stokes Equations With Heat Transfer via Polynomial Chaos Expansion","authors":"N. Nouaime,&nbsp;B. Després,&nbsp;M. A. Puscas,&nbsp;C. Fiorini","doi":"10.1002/fld.70052","DOIUrl":"https://doi.org/10.1002/fld.70052","url":null,"abstract":"<p>Performing sensitivity analysis in computational fluid dynamics is essential for assessing model robustness and reliability, since it determines how parameter variations or boundary conditions affect the simulation results. Specifically, this study focuses on the Navier–Stokes equations coupled with heat transfer, relevant to scenarios where temperature affects fluid flow behavior. Our sensitivity analysis is based on the Intrusive Polynomial Chaos Method (IPCM), which uses Probability Density Functions (PDFs) to describe stochastic variables. We extend previous work on uncertain initial or boundary conditions by focusing on input parameters such as viscosity and thermal diffusivity. We show that the sensitivity equations are well-posed and solve them numerically using the Finite Element Volume (FEV) method. The Rayleigh–Bénard convection test is used to validate the approach. This test is particularly relevant to applications in solar energy, materials processing, and energy storage, making it an excellent choice for demonstrating the effectiveness of our method.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"557-577"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70052","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668117","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":"A Gridless Method for Computing Interior Ballistic Flows With Moving Discrete Points","authors":"Shubham K. Vyas,&nbsp;Jayachandran T,&nbsp;Mathur Girijesh,&nbsp;Rajesh G","doi":"10.1002/fld.70056","DOIUrl":"https://doi.org/10.1002/fld.70056","url":null,"abstract":"<div>\u0000 \u0000 <p>This study presents a meshless computational framework for simulating unsteady fluid dynamics in interior ballistic applications. The proposed meshless method eliminates the need for grid generation and deformation by utilizing a cloud of dynamically moving points, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation. The key novelty of this work is integrating the meshless solver with a moving points system, which makes it highly suitable for ballistics applications involving complex geometries. Furthermore, the combustion process has been simplified, streamlining the simulation by avoiding the need for fully modeling propellant combustion, as required in multiphase solvers. The framework discretizes the unsteady axisymmetric Euler equations using local weighted least-squares approximations to calculate derivatives. Numerical fluxes are computed using a modified Harten, Lax, van Leer, Contact (HLLC) scheme, which is essential for achieving high accuracy and effectively capturing complex flow features. Temporal evolution is handled using the Explicit Strong Stability Preserving (ESSP) Runge–Kutta method, ensuring stability and accuracy under unsteady flow conditions. The method is applied to interior ballistic simulations, such as the motion of an M107–155 mm shell launched through an M185 cannon, achieving excellent agreement with experimental observations, particularly in predicting muzzle velocity and peak pressure. The simplified setup of this framework enables it to handle large grid deformations and complex geometries, and makes it an efficient, high-fidelity solution for dynamic flow problems in ballistics and aerospace, serving as a reliable predictive and assessment tool for interior ballistics studies. Further, the pressure wave analysis conducted within this framework provides valuable insights for optimizing shell design and propellant combustion characteristics, while also enhancing its role as a predictive tool for assessing shell integrity and mitigating resonance-induced structural risks in interior ballistics applications.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 5","pages":"578-597"},"PeriodicalIF":1.8,"publicationDate":"2026-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147668247","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":"Application of High-Order Direct Flux Reconstruction and Stiffness-Resilient Time Integration to Simulations of Idealized Atmospheric Flows","authors":"Stéphane Gaudreault,&nbsp;Christopher Subich,&nbsp;Shoyon Panday,&nbsp;Martin Charron,&nbsp;Vincent Magnoux,&nbsp;Valentin Dallerit,&nbsp;Mayya Tokman","doi":"10.1002/fld.70046","DOIUrl":"https://doi.org/10.1002/fld.70046","url":null,"abstract":"<p>High-order accurate discretizations in space and time are applied to the compressible Euler equations on the rotated cubed-sphere grid. The proposed methodology combines the Direct Flux Reconstruction (DFR) method for spatial discretization and stiffness-resilient exponential time integration for temporal evolution. The DFR method is quadrature-free and offers high-order accuracy, good conservation properties, and geometric flexibility. Stiffness-resilient exponential integrators allow for larger time steps than explicit methods while maintaining accuracy and stability. The governing equations are formulated using a space-time tensor formalism, allowing for a general representation in any curvilinear coordinate system. Discretization of these equations presents a number of challenges, including the numerical evaluation of geometric terms, pressure gradients, gravitational forcing, and aliasing errors. Stabilization techniques—such as filtering, numerically consistent calculation of Christoffel symbols, and vertical logarithmic reconstruction—are proposed to address these issues and compute physically plausible solutions. The numerical schemes are evaluated using a series of standard numerical tests.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"448-468"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147568086","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":"Elliptic Relaxation Strategies to Support Numerical Stability of Segregated Continuous Adjoint Flow Solvers","authors":"Niklas Kühl","doi":"10.1002/fld.70053","DOIUrl":"https://doi.org/10.1002/fld.70053","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper introduces a novel method for numerically stabilizing sequential continuous adjoint flow solvers utilizing an elliptic relaxation strategy. Unlike previous stabilization approaches, the proposed approach is formulated as a Partial Differential Equation (PDE) containing a single user-defined parameter, which analytical investigations reveal to represent the filter width of a probabilistic density function or Gaussian kernel. Key properties of the approach include smoothing features with redistribution capabilities while preserving integral properties. The technique targets explicit adjoint cross-coupling terms, such as the Adjoint Transpose Convection (ATC) term, which frequently causes numerical instabilities, especially on unstructured grids common in industrial applications. A trade-off is made by sacrificing sensitivity consistency to achieve enhanced numerical robustness. The method is validated on a two-phase, laminar, two-dimensional cylinder flow test case at a Reynolds number of &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;mtext&gt;Re&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;20&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {operatorname{Re}}_{mathrm{D}}=20 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and Froude number of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtext&gt;Fn&lt;/mtext&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;.&lt;/mo&gt;\u0000 &lt;mn&gt;75&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ mathrm{Fn}=0.75 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, focusing on minimizing resistance or maximizing lift. A range of homogeneous and inhomogeneous filter widths is evaluated. Subsequently, the relaxation method is employed to stabilize adjoint simulations during shape optimizations that aim at drag reduction of ship hulls. Two case studies are considered: A model-scale bulk carrier traveling at &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;mtext&gt;Re&lt;/mtext&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;7&lt;/mn&gt;\u0000 &lt;mo&gt;.&lt;/mo&gt;\u0000 &lt;mn&gt;246&lt;/mn&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;6&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"469-491"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147569833","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}