International Journal for Numerical Methods in Fluids最新文献

{"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}

{"title":"EVSS-Based Simulation Techniques for the Viscoelastic Fluids With Pure Polymer Melts Using Three-Field Approach","authors":"R. Ahmad,&nbsp;P. Zajac,&nbsp;S. Turek","doi":"10.1002/fld.70050","DOIUrl":"https://doi.org/10.1002/fld.70050","url":null,"abstract":"&lt;p&gt;To obtain the numerical solution of viscoelastic fluid simulations with pure polymer melts is a highly challenging task due to the lack of the solvent contribution to the viscosity in the standard viscoelastic formulation. The aim of this article is to present a mixed finite element method for solving the three-field Stokes flow with zero solvent viscosity using the elastic viscous stress splitting (EVSS) formulation. On one hand, the EVSS formulation helps to recover the velocity coupling back into the momentum equation by the application of the change of variables in the standard viscoelastic formulation. On the other hand, additional terms containing the second-order velocity derivatives appear in the convective part of the constitutive equation for stress. A common approach to address this issue is to expand the problem size to a four-field formulation by introducing the strain-rate tensor as an additional variable, which increases the computational cost. In contrast, our approach reformulates the convective term by explicitly taking into account the divergence-free nature of the velocity field and shifts the higher order derivatives to the test function in the weak formulation. This approach retains the problem as a three-field formulation, avoiding the need to treat the strain-rate tensor as an independent equation. As a result, it reduces the number of degrees of freedom and lowers the overall computational cost. The velocity, pressure and stress are discretized by the higher order stable FEM triplet &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;Q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;P&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Q&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;3&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ {Q}_2/{P}_1^{disc}/{Q}_3 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The proposed scheme is tested for Oldroyd-B, Giesekus, and exponential PTT models using both the decoupled and monolithic solution approaches. The numerical results are obtained on the 4:1 contr","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"492-509"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562393","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":"Investigation of Inducer Geometry Variations on Centrifugal Pump Hydraulic Performance: Numerical Approach","authors":"Davoud Pourabdollah,&nbsp;Peyman Sobhani,&nbsp;Amir F. Najafi","doi":"10.1002/fld.70049","DOIUrl":"https://doi.org/10.1002/fld.70049","url":null,"abstract":"<div>\u0000 \u0000 <p>Efficient suction performance and cavitation resistance are critical challenges in high-speed, low-pressure centrifugal pumps, and inducers, which are helical axial-flow components positioned upstream of pump impellers, play a pivotal role in addressing these challenges. This study evaluates the influence of inducer geometric parameters on impeller inlet pressure to identify configurations that enhance suction performance and reduce cavitation risk in centrifugal pumps. Experimentally validated three-dimensional numerical simulations were conducted to investigate the effects of hub-to-tip diameter ratio, blade angle, and blade number, which were systematically varied to examine their impact on pressure recovery and flow stability. Results show that decreasing the hub-to-tip ratio from 0.59 to 0.33 increased the average static pressure ratio at the impeller inlet from 1.12 to 1.38, corresponding to a 14%–23% improvement in suction performance. Increasing the blade angle from 15° to 30° enhanced local inlet pressure by 6%–30%, raising the pressure ratio from 1.10 to 1.43, while increasing the blade number from 2 to 4 yielded a 17%–23% pressure rise, with the pressure ratio increasing from 1.18 to 1.40. The optimal configuration with a hub-to-tip ratio of 0.33, blade angle of 30°, and four blades reduced the low-pressure region near the hub by approximately 28%, indicating improved cavitation resistance. Flow visualization using meridional streamlines and static pressure contours confirmed smoother acceleration and reduced recirculation for the optimized design. These findings provide quantitative insights into inducer geometry optimization and offer guidance for enhancing suction capability and designing high-performance centrifugal pumps.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"529-545"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562704","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 Investigation of the Impact of Heat Distribution on Fluid Flow for the Combination of Newtonian–Newtonian\u0000and Newtonian–Non-Newtonian Fluid","authors":"Arupjyoti Kakati,&nbsp;Saurabh Gupta,&nbsp;Mainak Basu,&nbsp;Arindam Bit","doi":"10.1002/fld.70055","DOIUrl":"https://doi.org/10.1002/fld.70055","url":null,"abstract":"<div>\u0000 \u0000 <p>Microchannels are used for thermal exchange because of their precise volume and higher heat dissipation capacity due to its surface to volume ratio. The thermal performance of microfluidic systems is greatly influenced by the dynamics of Newtonian and non-Newtonian fluid flows inside microchannels. In the current study, the regulation of temperature fluctuations within the working fluid is evaluated by executing the thermo-fluid coupling effects in micro-channels. For a combination of Newtonian–Newtonian and Newtonian–non-Newtonian influx fluid, the impact of flowing fluid on heat distributions with regards to micro-fins heat element sources within a microchannel was investigated numerically. Three micro-fins shape, viz., rectangular, triangular, and circular fin structures were used in the study. Rectangular fins had the largest as well as lowest heat transfer to the fluid flow for the combination of Newtonian–Newtonian fluids. It is also evaluated that for rectangular fins, the maximum <i>Nu</i> value obtained was 18.42 and the minimum <i>Nu</i> value obtained was 1.04. In addition, for triangular fins, the maximum <i>Nu</i> value obtained was 16.16 and the minimum <i>Nu</i> value obtained was 1.13. Finally, for circular fins, the maximum <i>Nu</i> value obtained was 9.82 and the minimum <i>Nu</i> value obtained was 1.22.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"546-556"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147563614","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":"Comparison of Surface Tension Models in the Navier–Stokes Equation Coupled With a Conservative Phase Field Model","authors":"Mingguang Shen,&nbsp;Ben Q. Li","doi":"10.1002/fld.70048","DOIUrl":"https://doi.org/10.1002/fld.70048","url":null,"abstract":"<div>\u0000 \u0000 <p>Surface tension matters in the simulation of two-phase flow. It is formulated mostly via the continuum surface force model or the surface-energy-based model. This paper compares the performance of three surface tension models, two based on the continuum surface force model and one on the other, in the Navier–Stokes equation coupled with the conservative Allen-Cahn/phase field model. The numerical model was solved using an explicit finite difference method on a half-staggered grid. A mesh independence study was conducted to select the appropriate mesh size. The surface tension models were compared in a couple of drop impacts, including a vigorous rebound and a weak rebound. It was found that the surface-energy-based model conserves mass the best. One of the continuum surface force models can capture fine structures like capillary waves on a drop impacting a solid surface. However, the continuum surface force models suffer from much more severe mass loss. Moreover, a theoretical analysis on mass conservation was conducted, and guidance for conserving mass was proposed.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"360-370"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565888","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":"Evaluation of Anisotropic Eddy-Viscosity Model Based on History Effect in Calculation of Pipe Swirling Flow Using OpenFOAM","authors":"Đorđe Novković,&nbsp;Jela Vorotović,&nbsp;Milan Lečić,&nbsp;Goran Vorotović","doi":"10.1002/fld.70047","DOIUrl":"https://doi.org/10.1002/fld.70047","url":null,"abstract":"<div>\u0000 \u0000 <p>Swirling flow refers to a type of fluid motion characterized by spatial rotational movement around the longitudinal axis. This flow pattern can occur in various environments, including natural phenomena such as tornadoes and whirlpools, as well as in engineering applications like combustion chambers and mixing tanks. Due to its ability to enhance mixing and increase heat transfer, swirling flow holds significant engineering importance. However, accurately simulating swirling flows is challenging. The flow is inherently three-dimensional and involves swirl decay, making numerical calculations complex. Among various computational approaches, Reynolds-averaged Navier–Stokes (RANS) turbulence modeling offers a good balance between accuracy and computational cost. Several types of turbulence models are available within the RANS framework to close the system of equations. In this study, we implement a new linear <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$$ k-varepsilon $$</annotation>\u0000 </semantics></math> turbulence model with anisotropic eddy viscosity in the OpenFOAM software. This model is formulated in cylindrical coordinates and incorporates the assumption of time non-locality in swirling flows, making it particularly suitable for such applications. To enable implementation in OpenFOAM, which is based on a Cartesian coordinate system, we developed a methodology for translating the model equations from cylindrical to Cartesian form. The model's performance was evaluated using a test case of swirling flow in a pipe. Numerical calculations were carried out using three existing turbulence models available in OpenFOAM, along with the newly implemented model. The effect of the time non-locality term on swirl decay prediction was also investigated by varying this term during computations. Additionally, a detailed analysis of how the viscous coefficients influence the velocity profiles distribution was conducted. The results demonstrate that the new model outperforms the existing models in terms of accurately predicting both velocity profiles and swirl decay.</p>\u0000 </div>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"433-447"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147567275","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":"Advection-Pressure Splitting Schemes Applied to a Non-Conservative 1D Blood Flow Model With Transport for Arteries and Veins","authors":"Alessandra Spilimbergo,&nbsp;Eleuterio F. Toro,&nbsp;Annunziato Siviglia,&nbsp;Lucas O. Müller","doi":"10.1002/fld.70026","DOIUrl":"https://doi.org/10.1002/fld.70026","url":null,"abstract":"<p>We introduce new first order, splitting-based numerical schemes for the non-conservative one-dimensional (1D) blood flow equations with a general constant momentum correction coefficient that describe blood flow, for different velocity profiles, in arteries and veins with discontinuous mechanical and geometrical properties. In this model an advection equation for a passive scalar transport is also considered. Our schemes are inspired by the original flux vector splitting approach of Toro and Vázquez-Cendón (2012) designed for the Euler equations. They also represent an improvement of the work proposed by Toro et al. (2024) regarding non-conservative blood flow models, which considered a tube law describing only arteries, a momentum correction coefficient equal to one, no passive scalar transport and included a smaller number of discontinuous mechanical and geometrical parameters. The considered framework separates advection terms and pressure terms, generating two different systems of PDEs: the advection system in conservative form, and the pressure system in non-conservative form, both of which have a very simple eigenstructure compared to that of the full system. Our schemes involve approximate Riemann solvers and present a modification of the path-conservative framework that renders unnecessary the use of a path. They are systematically assessed on a carefully designed suite of test problems with exact solution and compared with several existing mainstream methods. A detailed efficiency analysis is performed in order to showcase the advantages of the proposed methodology in comparison with standard approaches.</p>","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"398-432"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/fld.70026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147566286","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":"An Adaptive Meshless Method Based on the Residual-Based a Posteriori Error Estimation for Magnetohydrodynamics Problem at Very High Hartmann Number","authors":"Xiaohua Zhang,&nbsp;Ping Zhang","doi":"10.1002/fld.70044","DOIUrl":"https://doi.org/10.1002/fld.70044","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper presents an adaptive element-free Galerkin (EFG) method with streamline upwind Petrov-Galerkin (AEFG-SUPG) stabilization for solving steady magnetohydrodynamic (MHD) flows in insulated ducts with varying cross-sections at very high Hartmann number. The governing equations are first decoupled into convection-diffusion form via variable transformations, and discretized using the EFG method with SUPG (EFG-SUPG) stabilization to deal with numerical oscillations induced by strong convection dominance. To further improve accuracy and computational efficiency, an adaptive algorithm is developed, which incorporates a posteriori error estimation based on the background integration cell residual into the EFG-SUPG framework. This adaptive strategy enables node refinement in critical regions, remarkably reducing the total number of nodes compared to traditional uniform refinement methods. Four numerical cases involving square, circular, and arbitrary duct geometries with different magnetic field orientations are analyzed for Hartmann numbers &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ M $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; ranging from &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&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;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ 1{0}^2 $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&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;18&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ 1{0}^{18} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. The results highlight that the proposed method successfully resolves boundary layers and suppresses spurious oscillations even at &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&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;18&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$$ M=1{0}^{18} $$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Compared with existing adaptive meshless methods, it demonstrates superior computational efficiency and solution stability, showcasing its effectiveness in handling very high Hartmann num","PeriodicalId":50348,"journal":{"name":"International Journal for Numerical Methods in Fluids","volume":"98 4","pages":"371-397"},"PeriodicalIF":1.8,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147565887","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}