Compositional convection is one of the primary physical processes responsible for redistributing solute during the solidification of crystal mushes from multicomponent melts, a phenomenon frequently encountered in geological fluid mechanics, in particular during the cooling of magma intrusions. The key factor controlling solidification is the rate of cooling through contact with the surroundings. In this study, we focus on understanding the interplay between the cooling history, compositional convection, and the growth of a crystal mush driven by local supercooling. We analyze a mathematical model that describes the growth of the mushy region cooled from below, bounded from above by a melt region of finite volume. The melt region is assumed to have a well-mixed composition as a result of compositional convection. Contrary to initial expectations, we found that increasing the rate of bottom cooling does not necessarily result in a thinner mush with a higher solid fraction. Instead, the response depends on the kinetic law governing the mush growth rate as a function of local supercooling. Our results contribute to the current open debate within the volcanological and petrological communities about the effects of compositional convection on magma crystallization.

Airfoil polynomials-based collocation approach to study time-varying fluid mechanism

Abstract In this study, we investigate the (2+1)-dimensional generalized Benjamin-Ono equation, a model relevant in fluid dynamics, nonlinear optics, and plasma physics. Our primary aim is to analyse the equation using Lie group theory and derive exact solutions that capture its dynamic behaviours. We first determine the Lie point symmetries of the equation and compute their commutator and adjoint representations. Using these symmetries, we perform reductions that facilitate the construction of closed-form solutions via different ansatz methods. These yield solutions expressed in diverse functional forms such as Jacobi elliptic, hyperbolic, rational, exponential, and trigonometric functions, which are central to nonlinear science and engineering applications. To aid interpretation, we present visual analyses of the solutions via 3D, 2D, and density plots. With appropriate parameter choices, these graphs illustrate wave behaviours. Finally, conserved vectors of the model are derived using Ibragimov’s theorem, offering insight into the system’s underlying conservation laws.

ABSTRACT The internal pressure fluctuations caused by vibration in oil‐immersed electrical equipment can initiate bubbles within narrow oil gaps, reducing the electrical strength of equipment and giving rise to the problem of abnormal gas production in oil‐immersed equipment. This study mainly investigates the dynamic characteristics of cavitation in insulating oil microgaps under varying vibration conditions. A microgap model with vibration is constructed based on fluid mechanics, the fluid pressure within the microgap is derived, and the maximum negative pressures caused by vibration under varying vibration conditions and geometric structures of the insulating oil microgap are analysed. Subsequently, combined with the theories of bubble dynamics, the dynamic processes of the bubble within the microgap during a single vibration cycle under varying vibration conditions are analysed, and the influence of vibration intensity and frequency on the dynamic characteristics of the bubble is also discussed. Finally, the bubbling phenomenon and cavitation processes within the microgap under varying vibration conditions are observed and analysed using an experimental platform of microgap vibration. A better understanding of the development process of cavitation within the microgap structure under vibration is achieved. Furthermore, this study also provides theoretical support for the insulation risk assessment of the microgap structure under vibration and the design optimisation of the internal structure of oil‐immersed electrical equipment.

Traditionally, the shallow-water equations have been formulated and developed within the Eulerian framework for studying shallow-water wave problems. In this paper, we present a Lagrangian-based approach based on Hamilton’s variational principle to derive an extended displacement shallow-water equation (EDSWE). Using elliptic functions, we obtain exact traveling wave solutions of the resulting EDSWE. The conditions for the formation of various wave types—including cnoidal waves, looped waves, and peaked waves—are systematically analyzed and summarized. The proposed displacement method, grounded in the Lagrangian description, provides an analytical framework for hydrodynamic problems and can be applied to symplectic formulations in fluid mechanics.

Staged multi-cluster fracturing in horizontal wells is a key technology for efficiently developing unconventional oil and gas reservoirs. Extreme Limited-Entry Fracturing (ELF) and Temporary Plugging Fracturing (TPF) are effective techniques to enhance the uniformity of fracture stimulation within a stage. However, in fractured reservoirs, the propagation morphology of multiple intra-stage fractures and fluid distribution patterns becomes significantly more complex under the influence of ELF and TPF. This complexity results in a lack of theoretical guidance for optimizing field operational parameters. This study establishes a competitive propagation model for multiple hydraulic fractures (HFs) within a stage under ELF and TPF conditions in fractured reservoirs based on the Displacement Discontinuity Method (DDM) and fluid mechanics theory. The accuracy of the model was verified by comparing it with laboratory experimental results and existing numerical simulation results. Using this model, the influence of ELF and TPF on intra-stage fracture propagation morphology and fluid partitioning was investigated. Results demonstrate that extremely limited-entry perforation and ball-sealer diversion effectively mitigate the additional flow resistance induced by both the stress shadow effect and the connection of natural fractures (NFs), thereby mitigating uneven fluid distribution and imbalanced fracture propagation among clusters. ELF artificially creates extremely high perforation friction by drastically reducing the number of perforations or the perforation diameter, thereby forcing the fracturing fluid to enter multiple perforation clusters relatively uniformly. Compared to the unlimited-entry scheme (16 perforations/cluster), the limited-entry scheme (5 perforations/cluster) yielded a 37.84% improvement in fluid distribution uniformity and reduced the coefficient of variation (CV) for fracture length and fluid intake by 54.28% and 44.16%, respectively. The essence of the TPF is non-uniform perforation distribution, which enables the perforation clusters with large fluid intake to obtain more temporary plugging balls (TPBs), so that their perforation friction can be increased and their fluid intake can be reduced, thereby diverting the fluid to the perforation clusters with small fluid intake. Deploying TPBs (50% of total perforations) at the mid-stage of fracturing (50% time) increased fluid distribution uniformity by 37.86% and reduced the CV of fracture length and fluid intake by 72.54% and 58.39%, respectively. This study provides methodological and modeling foundations for systematic optimization of balanced stimulation parameters in fractured reservoirs.

The purpose of this paper is to discuss the notion of conservation in hyperbolic systems and how one can formulate it at the discrete level depending on the representation of the solution on the mesh. Since it is impossible to have a fully general theory, we discuss several alternatives possibilities: cases where the solution is represented by average in volumes; cases where the mesh is staggerred (i.e. the components of the solution are not localized at the same places); cases where the solution is solely represented by point values; and an example where all the previous options are mixed. We show how each configuration can provide, or not, enough flexibility. Though the discussion could be adapted to any hyperbolic system endowed with an entropy, we focus on compressible fluid mechanics, it its Eulerian and Lagrangian formulations. On a given mesh, the unifying element is that we systematically express the update of conserved variables as [Formula: see text], where the functional [Formula: see text] depends on the value of [Formula: see text] at the current degree of freedom and its values from a set of degrees of freedom. This set defines the stencil of the scheme. From the stencil, one can naturally define a graph connecting the states that appears in [Formula: see text]. The notion of local conservation can be defined from this graph. We are aware of only two possible situations: either the graph is constructed from the faces of the mesh elements (or the dual mesh), or it is defined from the mesh itself. Two notions of local conservation then emerge: either we define a numerical flux, or we define a “residual” attached to elements and the degrees of freedom within the element. We show that this two notions are in a way equivalent, but the one with residual allows much more flexibility, especially if additional algebraic constraints must be satisfied. Examples of specific additional conservation constraints are provided to illustrate this flexibility. We also show that this notion of conservation gives a very clear framework for the design of schemes in the Lagrangian setting. In the ending section, we will provide a number of ongoing research avenues strongly related to the formulation discussed, and we highlight some open questions which will be explored in the future.

The flow around circular cylinders is a classic problem in fluid mechanics with significant implications for offshore engineering. While extensive numerical and experimental research has focused on the subcritical and critical Reynolds regimes, the supercritical and postcritical regimes remain challenging and relatively unexplored, primarily due to the complex nature of turbulence and the high computational requirements. In this study, we perform three-dimensional detached eddy simulations using the finite volume method in OpenFOAM v1906, employing Menter’s k-ω SST turbulence model, to systematically investigate the flow past an infinitely long smooth cylinder from the subcritical through the postcritical regimes. The numerical setup ensures accurate near-wall resolution and reliable representation of unsteady flow features. We present a detailed analysis of vortex shedding patterns, wake evolution, and statistical properties of lift and drag coefficients for selected Reynolds numbers representative of each regime. The simulation results are benchmarked against experimental data from the literature, demonstrating good agreement for Strouhal number and mean drag. Special emphasis is placed on the evolution of wake topology and force coefficients as the flow transitions from laminar to fully turbulent conditions. The findings contribute to the limited numerical literature on flow around circular cylinders across subcritical, critical, supercritical, and postcritical Reynolds number regimes, providing insights that are fundamentally relevant to the broader scope of understanding vortex shedding phenomena.

Driven by demands for energy efficiency, environmental protection and vehicle performance, aerodynamic optimization of automotive exterior shapes has become a core focus in the automotive industry. This review comprehensively summarizes its progress, methods and trends. It expounds basic aerodynamic characteristics, including fluid mechanics principles (Bernoulli's equation, boundary layer). main aerodynamic elements such as lift force, drag force, drag coefficient and their impacts on fuel economy. In aiming of handling stability and comfort. The paper outlines traditional methods such as streamline design evolution. Modern techno involves information technology such as CFD and Wind Tunnel simulation. Then development of algorithms makes new breakthrough. The new trends, by introducing advanced technologies like parametric modeling, machine learning and AI with neutral network(PINN, etc). Reviewing on evolution in fluid optimization tells future trends,challenges(EV design freedom, potential demands) and autonomous driving (sensor integration), as well as the need for multi-objective optimization. Continuous innovation in this field is essential to meet the industrys future requirements.

Quantifying differences between flow fields is a key challenge in fluid mechanics, particularly when evaluating the effectiveness of flow control or other problem parameters. Traditional vector metrics, such as the Euclidean distance, provide straightforward pointwise comparisons but can fail to distinguish distributional changes in flow fields. To address this limitation, we employ optimal transport (OT) theory, which is a mathematical framework built on probability and measure theory. By aligning Euclidean distances between flow fields in a latent space learned by an autoencoder with the corresponding OT geodesics, we seek to learn low-dimensional representations of flow fields that are interpretable from the perspective of unbalanced OT. As a demonstration, we utilise this OT-based analysis on separated flows past a NACA 0012 airfoil with periodic heat flux actuation near the leading edge. The cases considered are at a chord-based Reynolds number of 23 000 and a free-stream Mach number of 0.3 for two angles of attack (AoA) of $6^\circ$ and $9^\circ$ . For each angle of attack, we identify a two-dimensional embedding that succinctly captures the different effective regimes of flow responses and control performance, characterised by the degree of suppression of the separation bubble and secondary effects from laminarisation and trailing-edge separation. The interpretation of the latent representation was found to be consistent across the two AoA, suggesting that the OT-based latent encoding was capable of extracting physical relationships that are common across the different suites of cases. This study demonstrates the potential utility of optimal transport in the analysis and interpretation of complex flow fields.

Abstract Introduction Refractive-index-matched (RIM) silicone phantoms play a critical role in experimental biomedical fluid mechanics, enabling detailed investigations of complex flow phenomena in anatomically accurate geometries. However, providing transparent, patient-specific and non-compliant and compliant models for detailed experimental quantitative analysis of the flow field, i.e., with high-dimensional accuracy and minimal post-processing, remains a major challenge. Methods This work presents a scalable manufacturing workflow based on a wax-based lost-core casting technique. High-resolution wax printing enables the three-dimensional (3D) creation of both non-compliant and compliant silicone phantoms with smooth surfaces, fine structural details, and clean core removal. The method allows for modular assembly of large geometries, and it is demonstrated on three representative models, namely a patient-specific human airway model, a generic compliant bifurcation, and a compliant patient-specific thoracic aorta. Results Mechanical and geometric tests confirm that the compliant phantoms replicate physiologically relevant vessel properties, with a measured Young’s modulus of 1.71 MPa and wall thickness variations below 1%. The phantoms are integrated into flow circuits, and the velocity distribution in the phantoms is measured using volumetric 3D particle-tracking velocimetry (PTV) using the Shake-the-Box (STB) algorithm. Time-resolved measurements under steady and pulsatile inflow conditions reveal detailed flow structures and fluid–structure interactions in both non-compliant and compliant models. Conclusions The presented workflow enables reproducible, high-fidelity RIM phantoms for experimental studies of biomedical flows. Combined with advanced flow diagnostics, it provides a powerful platform for exploring pathophysiological mechanisms, validating simulations, and evaluating the performance of medical devices in realistic geometries.

In recent years, a novel decomposition of fluid motion has been proposed, which mathematically defines a type of fluid rigid rotation distinct from vorticity, termed the Liutex quantity. Since its introduction, Liutex has been successfully applied to describe fluid vortices and has emerged as an internationally recognized third-generation vortex identification method. This new motion decomposition undoubtedly leads to a revised description of rotational and deformational motions, thereby necessitating a new description of dynamics. Therefore, based on the Stokes assumption and the novel Liutex decomposition, this paper constructs a new constitutive equation and derives a new set of fluid dynamic equations. The research findings reveal two key insights: first, the new shear stress in the fluid is no longer symmetric; second, in addition to traditional forces such as body force, pressure, and viscous force, an additional force induced by Liutex-based rigid rotation is identified. Furthermore, the new dynamic framework encompasses traditional fluid dynamics, with the latter being a special case when Liutex equals the traditional vorticity. It is anticipated that the proposed equations will find significant applications in the study of fluid vortices and turbulence and will undoubtedly stimulate research interest in the field of fluid mechanics.

The main idea of this paper is to look into some novel exact wave solutions of the [Formula: see text]-dimensional Jimbo–Miwa equation (JME) that has a major role in the fields of fluid mechanics and physics. Based on the Hirota bilinear form (HBF) obtained by the Cole–Hopf transformation, the weight algorithm (WA) combined with the linear superposition theory (LST) is employed to develop the resonant multiple wave solutions (RMWSs). In addition, the multi-lump wave solutions are derived via adopting the homoclinic test approach. Finally, the complex N-soliton solutions (CNSSs) are also probed through the HBF. The graphical descriptions of the corresponding exact solutions are displayed to present the physical attributes by choosing the reasonable parameters. The findings in this paper are all new, which can help us make sense of the nonlinear dynamic behaviors of the considered equation better.

In the car industry, there is always the pursuit of enhancement in performance and fuel efficiency but underlying all these is one primary challenge and that is the minimization of aerodynamic drag. This drag directly influences fuel consumption and the general driving experience as it directly affects the interaction of this vehicle with the air during motion. Fluid mechanics interaction contributes to the development of the way the car body penetrates the air, and the optimization of the interaction with the air is one of the main concerns in the development of a car body design. Car designers understand that the less rounded the appearance the less resistance their cars have and therefore cars are more efficient. This is more than smooth curves, though; it is the way everything on the vehicle interacts with the air; the wheels and the mirrors and the way the back end is. With the pressure of lighter and fuel-efficient cars being taken by manufacturers, the relationship between weight loss and aero becomes increasingly more close. It is a natural fact that lighter cars experience a lower drag, but the problem is how to decrease the weight without losing aerodynamics and safety. In this paper, the author examines the extent to which the shape and structure of a car can be optimized to reduce the drag by examining the effects that minor adjustments to single components can cause. It also issues about the impact of weight reduction on the aerodynamics and general performance. With the changing technology of vehicles, it is not only the technical challenge of strike the balance between design, weight and air flow, but it has become the issue of progress.

The 2025 4th International Conference on Acoustics, Fluid Mechanics and Engineering (AFME 2025) was held from October 24 to 26, 2025, in Wuhan, China. The integration of acoustics and fluid mechanics is addressing scientific challenges and propelling technological innovations—spanning from environmental noise management and aerospace design to deep-sea exploration, energy equipment optimization, and biomedical engineering. This interdisciplinary domain not only tackles complex scientific problems but also embodies broad application prospects and far-reaching implications for the future. AFME 2025 and the papers compiled in this proceedings volume serve as a reflection of the cutting-edge trends. A total of 86 papers, having undergone a rigorous peer review process, were accepted for inclusion in this proceedings volume and systematically categorized into three thematic chapters based on their content and research directions: Chapter 1, “Acoustics and Vibration Characteristics”, focuses on the generation, propagation, and control of sound waves, as well as vibroacoustic coupling mechanisms. These works showcase the pivotal role of acoustics in achieving equipment noise reduction, environmental friendliness, and enhanced system reliability. Chapter 2, “Fluid Dynamics and Simulation”, is dedicated to unraveling the physical mechanisms of complex flows and developing advanced numerical simulation methods, highlighting the in-depth application of numerical algorithms and experimental techniques in complex flows. Chapter 3, “Engineering Applications and Multiphysics”, highlights the role of acoustics and fluid dynamics in real-world engineering challenges. It delineates the complete development chain—from fundamental principles and multiphysics coupling analysis to optimized design—serving national strategic needs and facilitating industrial technological upgrading. In retrospect, the plenary presentations and invited speeches at this conference, delivered with profound insights, presented breakthroughs across diverse research directions, including ship ice dynamics, flow and noise control of porous metal-based pump-jet propulsors, three-dimensional (3D) time-domain analysis for wave-elastic plate interactions, and advanced acoustic absorbers for flow-influenced applications. The oral and poster presentations, brimming with insights, vividly reflected the scholars’ perceptive thinking and innovative practices. All these insights and exchanges have been integrated into this proceedings volume. List of Committee Member is available in this PDF.

Abstract Magnetorheological dampers (MRDs) have become widely utilized for shock resistance and vibration mitigation due to their exceptional damping adjustability by magnetic control. However, researchers show that wide temperature range variations significantly affect their mechanical properties. As a typical system of coupled thermal-magnetic-fluid-solid multi-physical fields, the temperature factor complicates the coupling, making it hard to reveal its influence mechanism. Consequently, this study proposed a full-size, Multi-Physics field coupling simulation method considering the temperature effect for a single-outlet rod MRD with gas compensation to accurately characterize and predict its nonlinear mechanical properties at different temperatures. Firstly, the temperature and magneto-sensitive properties of magnetorheological fluids (MRF) are described based on the Bingham model. A thermo-magnetic-fluid-solid Multi-Physics coupling mathematical model is established by integrating theories with thermodynamics, electromagnetism, and fluid mechanics. Then, based on the above theoretical model, a Multi-physics field finite element simulation model is approved by the COMSOL platform to simulate the mechanical properties under different currents, velocities, and temperature conditions. Finally, tests are executed at temperatures ranging from -40℃ to 100℃ to verify mechanical performance under different working situations. The model's accuracy is validated, with an average FPRE of 5.4%, an average FRRMSE of 10.3%. This research provides an effective method for revealing the mechanism and predicting the damping force of MRD at different temperatures.

The detection and analysis of features in fluid flow are important tasks in fluid mechanics and flow visualization. One recent class of methods to approach this problem is to first compute objective optimal reference frames, relative to which the input vector field becomes as steady as possible. However, existing methods either optimize locally over a fixed neighborhood, which might not match the extent of interesting features well, or perform global optimization, which is costly. We propose a novel objective method for the computation of optimal reference frames that automatically adapts to the flow field locally, without having to choose neighborhoods a priori. We enable adaptivity by formulating this problem as a moving least squares approximation, through which we determine a continuous field of reference frames. To incorporate fluid features into the computation of the reference frame field, we introduce the use of a scalar guidance field into the moving least squares approximation. The guidance field determines a curved manifold on which a regularly sampled input vector field becomes a set of irregularly spaced samples, which then forms the input to the moving least squares approximation. Although the guidance field can be any scalar field, by using a field that corresponds to flow features the resulting reference frame field will adapt accordingly. We show that using an FTLE field as the guidance field results in a reference frame field that adapts better to local features in the flow than prior work. However, our moving least squares framework is formulated in a very general way, and therefore other types of guidance fields could be used in the future to adapt to local fluid features.

Secondary flow plays a pivotal role in flow separation within turbomachinery, impacting the performance of pump-jet propulsors through associated secondary flow losses. Past research has predominantly concentrated on water wing models, leading to limited insights into more intricate turbomachines. This study explores methods for extracting secondary flow characteristics in pump-jet propulsors through numerical simulations employing large eddy simulation, coupled with vortex identification techniques and analysis of velocity and pressure fields. Notable features of secondary flow include the tip leakage vortex and root shedding vortex, the latter exhibiting reverse flow and pronounced oscillations at the suction side's trailing edge. The distribution of driving forces and secondary flow intensity is evaluated using S3 flow surface theory, revealing a substantial influence of Coriolis forces at the blade root. This study proposes an innovative approach utilizing helical line techniques to form S3 approximate flow surfaces, facilitating thorough extraction of secondary flow characteristics at both blade tips and roots. This research fills existing gaps in the study of secondary flow phenomena in pump-jet propulsors, contributing valuable methodologies and a theoretical framework for evaluating secondary flow energy dynamics and related noise generation, thereby advancing the understanding of these critical elements in fluid mechanics and propulsion systems.

An artificial neural network (ANN) model has been developed to investigate the flow and thermal characteristics of aqueous humor (AH) within the anterior chamber (AC) of the human eye. The impact of convective heat transfer coefficients (CHTC) and thermal conductivity (TC) on intraocular fluid velocity and temperature distributions, plays a critical role in regulating ocular function and preserving overall eye health. An ANN is trained on data derived from modified Navier–Stokes equations formulated using a lubrication theory, incorporating convective and no-slip boundary conditions at the corneal surface. The model produced mathematical formulations for profile of temperature, velocity, and stream function, providing a close relation with analytical expectations. Graphical analysis highlights the ANN's ability to capture variations in AH velocity and temperature distribution with changing TC and CHTC. To ensure the reliability of our results, we validated the ANN model predictions against established experimental data and numerical simulations. Our findings align well with previous simulations, enhancing the understanding of ocular fluid mechanics and health implications.

When simulating three-dimensional flows interacting with deformable and elastic obstacles, current methods often encounter complexities in the governing equations and challenges in numerical implementation. In this work, we introduce a novel numerical formulation for simulating incompressible viscous flows at low Reynolds numbers in the presence of deformable interfaces. Our method employs a vorticity-stream vector formulation that significantly simplifies the fluid solver, transforming it into a set of coupled Poisson problems. The body–fluid interface is modeled using a phase field, allowing for the incorporation of various free-energy models to account for membrane bending and surface tension. In contrast to existing three-dimensional approaches, such as lattice Boltzmann methods or boundary-integral techniques, our formulation is lightweight and grounded in classical fluid mechanics principles, making it implementable with standard finite-difference techniques. We demonstrate the capabilities of our method by simulating the evolution of a single vesicle or droplet in Newtonian Poiseuille and Couette flows under different free-energy models, successfully recovering canonical axisymmetric shapes and stress profiles. Although this work primarily focuses on single-body dynamics in Newtonian suspending fluids, the framework can be extended to include body forces, inertial effects, and viscoelastic media.