Many problems in fluid mechanics describe the change in the flow under the effect of electromagnetic forces. The present study explores the behaviour of an electric conducting, Newtonian fluid flow applying the magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) principles. The physical problems for such flows are formulated by the Navier–Stokes equations with the conservation of mass and energy equations, which constitute a coupled non-linear system of partial differential equations subject to analogous boundary conditions. The numerical solution of such physical problems is not a trivial task due to the electromagnetic forces which may cause severe disturbances in the flow field. In the present study, a numerical algorithm based on a finite volume method is developed for the solution of such problems. The basic characteristics of the method are, the set of equations is solved using a simultaneous direct approach, the discretization is achieved using the finite volume method, and the solution is attained solving an implicit non-linear system of algebraic equations with intense source terms created by the non-uniform magnetic field. For the validation of the overall algorithm, comparisons are made with previously published results concerning MHD and FHD flows. The advantages of the proposed methodology are that it is direct and the governing equations are not manipulated like other methods such as the stream function vorticity formulation. Moreover, it is relatively easily extended for the study of three-dimensional problems. This study examines the Hartmann flow and the fluid flow with FHD principles, that formulate MHD and FHD flows, respectively. The major component of the Hartmann flow is the Hartmann number, which increases in value the stronger the Lorentz forces are, thus the fluid decelerates. In the case of FHD fluid flow, the major finding is the creation of vortices close to the external magnetic field source, and the stronger the magnetic field of the source, the larger the vortices are.

Over the past decade, the integration of artificial neural networks (ANNs) has garnered significant interest, capitalizing on their ability to discern intricate patterns within data. Focused on enhancing computational efficiency, this article explores the application of ANNs in forecasting fluid-dynamics simulations, particularly for the benchmark problem of fluid flow in a two-dimensional (2D) channel. Leveraging a multilayer perceptron trained on finite volume method numerical data, for both interpolation and extrapolation estimations and various grid resolutions, our findings demonstrate the ANN's prowess as a swift and accurate surrogate for traditional numerical methods. Overall, the results of this work mark a pioneering step toward leveraging machine learning for modeling complex relationships in fluids phenomena, promising transformative advancements in computational fluid dynamics.

Symbolic Regression (SR) offers an interpretable alternative to conventional Machine-Learning (ML) approaches, which are often criticized as “black boxes”. In contrast to standard regression models that require a prescribed functional form, SR constructs expressions from a user-defined set of mathematical primitives, enabling the automated discovery of compact formulas that fit the data and reveal underlying physical relationships. In fluid mechanics, where understanding the underlying physics is as crucial as predictive accuracy, this study applies SR to model three-dimensional (3D) laminar flow in a rectangular channel, focusing on the axial velocity and pressure fields. Compact symbolic equations were derived from numerical simulation data, accurately reproducing the expected parabolic velocity profile and linear pressure drop, and showing excellent agreement with analytical solutions from the literature. To address the limitation that purely data-driven SR models may overlook domain-specific constraints, an innovative hybrid framework that integrates SR with Answer Set Programming (ASP) is also introduced. This integration combines the generative power of SR with the declarative reasoning capabilities of ASP, ensuring that derived equations remain both statistically accurate and physically plausible. The proposed SR/ASP methodology demonstrates the potential of combining data-driven and knowledge-representation approaches to enhance interpretability, reliability, and alignment with physical principles in fluid dynamics and related domains.

The development and progression of abdominal aortic aneurysms (AAA) are related to complex flow patterns and wall-shear-driven mechanobiological stimuli, yet the quantitative relationship between aneurysmal geometry and hemodynamics remains poorly defined. In this study, we conducted a comprehensive hemodynamic analysis of 74 patient-specific abdominal aortas, representing one of the largest Computational Fluid Dynamics (CFD) cohorts reported to date. A multiscale framework coupling 0D-1D systemic circulation models with 3D stabilized finite-element simulations is used to generate physiologically consistent boundary conditions and high-fidelity flow fields. From each model, we extract Time Averaged Wall Shear Stress (TAWSS), Oscillatory Shear Index (OSI), Relative Residence Time (RRT) and Local Normalized Helicity (LNH) indicators alongside an extended set of geometric descriptors characterizing diameter, curvature and torsion. This study provides a clear and comprehensive view of how aneurysm shape influences blood-flow behavior, supported by one of the largest systematically analyzed CFD datasets of AAAs to date. Our results show that specific geometric features reliably shape shear-stress patterns, suggesting that these geometry-driven flow signatures could serve as valuable biomarkers for patient-specific risk assessment. Together, these insights highlight the potential of incorporating detailed geometric descriptors into future models that aim to predict AAA growth and rupture.

The development of Abdominal Aortic Aneurysms (AAA) is related to complex flow patterns and wall-shear–driven mechanobiological stimuli, yet the quantitative relationship between aneurysmal geometry and hemodynamics remains poorly defined. In this study, we conduct a comprehensive hemodynamic analysis of 74 patient-specific abdominal aortas. A multiscale framework coupling zero-dimensional to one-dimensional (0D–1D) systemic circulation models with three-dimensional (3D) stabilized finite-element simulations is used to generate physiologically consistent boundary conditions and high-fidelity flow fields. From each model, we extract the Time Averaged Wall Shear Stress (TAWSS), Oscillatory Shear Index, Relative Residence Time (RRT), and Local Normalized Helicity indicators alongside an extended set of geometric descriptors characterizing diameter, curvature, and torsion. Our results reveal distinct and statistically significant geometry–hemodynamics relationships across the cohort, separately for the aneurysmal sac and the iliac regions. Large aneurysmal sacs exhibit elevated RRT values, enlarged recirculating zones, and reduced TAWSS. Surprisingly, the iliac arteries emerge as dominant contributors to disturbed hemodynamics, showing stronger geometric–hemodynamic correlations than the infrarenal aorta. These observations highlight previously underappreciated downstream effects of AAA morphology. This study provides a comprehensive view of how aneurysm shape influences blood-flow behavior, supported by one of the largest systematically analyzed Computational Fluid Dynamics datasets of AAAs to date. Our results show that specific geometric features reliably shape shear-stress patterns, suggesting that these geometry-driven flow signatures could serve as valuable biomarkers for patient-specific risk assessment. Together, these insights highlight the potential of incorporating detailed geometric descriptors into future models that aim to predict AAA growth and rupture.

Understanding and modeling the effect of magnetic fields on flows that present separation properties, such as those over a backward-facing step (BFS), is critical due to its role in metallurgical processes, nuclear reactor cooling, plasma confinement, and biomedical applications. This study examines the hydrodynamic and magnetohydrodynamic numerical solution of an electrically conducting fluid flow in a backward-facing step (BFS) geometry under the influence of an external, uniform magnetic field applied at an angle. The novelty of this work lies in employing an in-house finite-volume solver with a collocated grid configuration that directly applies a Newton–like method, in contrast to conventional iterative approaches. The computed hydrodynamic results are validated with experimental and numerical studies for an expansion ratio of two, while the MHD case is validated for Reynolds number $Re=380$ and Stuart number $N=0.1$. One of the most important findings is the reduction in the reattachment point and simultaneous increase in pressure as the magnetic field strength is amplified. The magnetic field angle with the greatest influence is observed at $\phi =\pi /2$, where the main recirculation vortex is substantially suppressed. These results not only clarify the role of magnetic field orientation in BFS flows but also lay the foundation for future investigations of three-dimensional configurations and coupled MHD–thermal applications.