Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (1,628)

Search Parameters:
Keywords = Stokes equation

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
21 pages, 7899 KB  
Article
Multi-Objective Topology Optimization of Intravascular Ultrasound Catheters Under Coupled Acoustic–Fluid–Structure Interactions
by Zhenzhang Liu, Yanping Feng and Dachang Zhu
Mathematics 2026, 14(13), 2254; https://doi.org/10.3390/math14132254 (registering DOI) - 24 Jun 2026
Abstract
The design of intravascular ultrasound (IVUS) catheters involves inherently coupled acoustic, hemodynamic, and structural requirements. Existing design strategies, which often rely on empirical geometric refinement or single-physics optimization, are limited in their ability to simultaneously ensure acoustic transmission efficiency, flow compatibility, and mechanical [...] Read more.
The design of intravascular ultrasound (IVUS) catheters involves inherently coupled acoustic, hemodynamic, and structural requirements. Existing design strategies, which often rely on empirical geometric refinement or single-physics optimization, are limited in their ability to simultaneously ensure acoustic transmission efficiency, flow compatibility, and mechanical reliability. A multiphysics topology optimization method for the integrated design of IVUS catheters under acoustic–fluid–structure interactions is proposed in this paper. A density-based design variable is introduced to characterize the material distribution within the design domain, and consistent interpolation schemes are employed to relate this variable to the effective acoustic properties in the Helmholtz equation, the Brinkman penalization coefficient in the incompressible Navier–Stokes equations, and the elastic stiffness tensor in the structural equilibrium equation. The optimization problem is formulated as a normalized multi-objective minimization of acoustic transmission loss, flow resistance, and structural compliance, subject to constraints on material volume, received acoustic energy, wall shear stress, and structural displacement. Density filtering and smooth Heaviside projection are incorporated to regularize the design field and promote well-defined material boundaries. An adjoint sensitivity formulation is further developed to enable efficient gradient evaluation for the coupled system. Compared with the initial design, the average acoustic transmission efficiency has increased by 59.01%, the shear stress has decreased by 53.87%, and the stiffness matching rate has reached 98.27%. The objective function converged after 35 iterations, demonstrating the numerical stability of the proposed acoustic–fluid–structure topology optimization framework. Full article
18 pages, 4457 KB  
Article
Engineering Design of Stepped Hull for Planing Vessels Using CFD-Based Evaluation
by Samuel, Serliana Yulianti, Muhammad Iqbal, Davis Rian Kusuma, Ari Wibawa Santosa, Good Rindo, Andi Trimulyono and Ahmad Fitriadhy
Designs 2026, 10(4), 66; https://doi.org/10.3390/designs10040066 (registering DOI) - 23 Jun 2026
Viewed by 1
Abstract
The growing demand for high-speed marine transportation requires continuous improvement in ship design to achieve higher hydrodynamic efficiency. From an engineering design perspective, hull form modification is a key approach to optimizing the performance of planing vessels, particularly through the implementation of stepped [...] Read more.
The growing demand for high-speed marine transportation requires continuous improvement in ship design to achieve higher hydrodynamic efficiency. From an engineering design perspective, hull form modification is a key approach to optimizing the performance of planing vessels, particularly through the implementation of stepped hull configurations. This study aims to investigate the effects of step geometry and step position on the resistance and trim characteristics of a planing hull based on Taunton et al.’s Model C, with the objective of improving vessel efficiency. The design methodology integrates hull geometry modification, parametric variation in step position and step height, and numerical performance assessment. In this research, the governing equations are solved using the Reynolds-Averaged Navier–Stokes (RANS) framework with the Finite Volume Method (FVM) as the discretization technique. The turbulence model used is k-ω SST, while the interaction between water and air phases is represented using the Volume of Fluid (VOF) method. From a design performance perspective, the results demonstrate that stepped hull geometry significantly influences resistance and trim characteristics. The optimal design configurations achieved a resistance reduction of up to 17.93% and a trim of 1.53° was achieved with a stepped position of 430 mm from the transom and a stepped height of 25 mm (Model A3) at Fr 2.28. Meanwhile, a resistance reduction of 15.49% and a trim of 1.46° were observed for a stepped position of 860 mm from the transom and a stepped height of 25 mm (Model B3) at Fr 2.72. These findings highlight the importance of step geometry and placement as key design variables in improving planing hull performance. This study demonstrates that CFD-based evaluation can effectively support engineering design decisions for stepped hull optimization, providing a systematic approach for improving hydrodynamic efficiency in high-speed vessel design. Full article
(This article belongs to the Topic Vehicle Dynamics and Control, 2nd Edition)
Show Figures

Graphical abstract

32 pages, 8597 KB  
Review
Intelligent Digital Rock Physics: Advances and Perspectives from Imaging Reconstruction to Pore-Scale Multiphase Flow Simulation
by Xue Li, Lin Zhu, Feng Gao, Xin Liang and Zhengzheng Cao
Appl. Sci. 2026, 16(12), 6118; https://doi.org/10.3390/app16126118 - 17 Jun 2026
Viewed by 234
Abstract
In characterizing unconventional reservoirs, conventional Digital Rock Physics (DRP) has long been constrained by three fundamental bottlenecks: the trade-off between imaging resolution and field of view, challenges in reconstructing multiscale pore topology, and the prohibitive computational cost of direct numerical simulation (DNS) at [...] Read more.
In characterizing unconventional reservoirs, conventional Digital Rock Physics (DRP) has long been constrained by three fundamental bottlenecks: the trade-off between imaging resolution and field of view, challenges in reconstructing multiscale pore topology, and the prohibitive computational cost of direct numerical simulation (DNS) at the pore scale. The deep integration of artificial intelligence and rock physics has given rise to a new paradigm—Intelligent Digital Rock Physics (IDRP). This paper provides a systematic review of the evolutionary trajectory of IDRP, with a focus on how machine learning is reshaping the end-to-end workflow from imaging and segmentation to reconstruction and simulation. First, we survey image super-resolution and 3D pore structure generation techniques based on convolutional neural networks (CNNs), generative adversarial networks (GANs), and diffusion models, elucidating their mechanisms for surpassing optical diffraction limits and incorporating macroscopic petrophysical constraints. Second, we outline algorithmic strategies for fusing multi-source heterogeneous data (e.g., Micro-CT and SEM) and representing dual-porosity or multi-continuum systems. Third, we critically examine the application of machine learning surrogates in single- and multiphase flow prediction, highlighting how physics-informed machine learning (PIML) and reinforcement learning (RL)—by embedding governing equations such as Navier–Stokes or Muskat–Leverett into loss functions—achieve both computational acceleration and physical consistency. We further identify key limitations of current IDRP approaches, including insufficient validation of generated topological realism, narrow generalization across lithologies, inadequate representation of dynamic wettability, and limited model interpretability. Finally, we propose a forward-looking roadmap centered on multimodal foundation models for rocks, coupled with neural operators and uncertainty quantification frameworks, emphasizing the critical pathways for translating IDRP into engineering digital twins for unconventional hydrocarbon development, coalbed methane production enhancement, Enhanced Geothermal Systems, and geological CO2 storage. This review offers a comprehensive reference for researchers at the intersection of geophysics, rock mechanics, and artificial intelligence. Full article
(This article belongs to the Section Civil Engineering)
Show Figures

Figure 1

21 pages, 11135 KB  
Article
Performance Research of a Thermal-Transpiration-Effect-Based Circulating-Flow Gas Separator Applied to CH4-H2 Mixture Separation at Slip Flow Regime
by Dasen Yang, Wei Lu and Qihang Jin
Energies 2026, 19(12), 2831; https://doi.org/10.3390/en19122831 - 13 Jun 2026
Viewed by 218
Abstract
To address hydrogen separation from hydrogen-blended natural gas, this work develops a mathematical model for a novel thermal-transpiration-effect-based circulating-flow gas separator according to the Navier–Stokes equations, following the joint modification with velocity-slip and temperature-jump boundary conditions, and a binary gas diffusion model derived [...] Read more.
To address hydrogen separation from hydrogen-blended natural gas, this work develops a mathematical model for a novel thermal-transpiration-effect-based circulating-flow gas separator according to the Navier–Stokes equations, following the joint modification with velocity-slip and temperature-jump boundary conditions, and a binary gas diffusion model derived from the Maxwell–Stefan equations. The model is then used to investigate the component transport and flow of a CH4-H2 mixture at the slip flow regime. The average hydrogen mole fraction in the component enrichment zone increases monotonically as the temperature difference increases, reaching 0.429 at a hot channel temperature of 400 K. An optimum inlet gas velocity of 0.93 m/s is identified to achieve the maximum average hydrogen mole fraction in the enrichment zone. In addition, decreasing the microchannel diameter enhances the hydrogen enrichment performance, with the average hydrogen mole fraction reaching 0.578 at a microchannel diameter of 1 μm whereas increasing the microchannel diameter improves the product gas flow rate, indicating a trade-off between separation performance and processing capacity. These insights provide guidance for understanding the component transport mechanism and for the preliminary design of this type of gas separator for hydrogen separation applications. Full article
(This article belongs to the Section A5: Hydrogen Energy)
Show Figures

Figure 1

19 pages, 3735 KB  
Article
Rheological Transformation of Waxy Crude Oil During Transition to a Viscoplastic State
by Uzak Zhapbasbayev, Timur Bekibayev, Gaukhar Ramazanova and Olzhas Kenzhaliev
Appl. Sci. 2026, 16(12), 5999; https://doi.org/10.3390/app16125999 - 13 Jun 2026
Viewed by 113
Abstract
This study investigates non-isothermal laminar flow of waxy crude oil in a pipe. Due to heat exchange with the surroundings, the flow cools along the pipe length, resulting in a gradual transformation of the oil rheology from Newtonian to viscoplastic behavior. The mathematical [...] Read more.
This study investigates non-isothermal laminar flow of waxy crude oil in a pipe. Due to heat exchange with the surroundings, the flow cools along the pipe length, resulting in a gradual transformation of the oil rheology from Newtonian to viscoplastic behavior. The mathematical model is based on the generalized Navier–Stokes equations coupled with the Shvedov–Bingham rheological model and the effective viscosity approach. The governing equations were solved numerically using the control volume method in the velocity–pressure formulation. The numerical simulations produced velocity, temperature, and effective viscosity fields, as well as pressure-drop data characterizing the rheological state of the waxy crude oil throughout the pipe flow domain. It was established that, in the central region of the inlet flow, the oil retains Newtonian behavior, whereas viscoplastic behavior begins to develop near the pipe wall. Further downstream, the flow progressively transforms into a viscoplastic state over the entire pipe cross-section, accompanied by the formation of stagnant near-wall regions and a plug-flow core. Full article
Show Figures

Figure 1

19 pages, 26846 KB  
Article
Numerical Investigation of Stall Flutter of a Pitching Airfoil at Low Reynolds Number
by Maria Adele Cecchini, Giulio Soldati, Peter Jordan and Sergio Pirozzoli
Fluids 2026, 11(6), 149; https://doi.org/10.3390/fluids11060149 - 11 Jun 2026
Viewed by 156
Abstract
The present work investigates fluid–structure instabilities and flow-induced oscillations of a pitching NACA0012 airfoil through numerical simulations. The flow is modeled using the compressible Navier–Stokes equations in a non-inertial rotating reference frame, while the structural dynamics are represented by a torsional spring–mass–damper system. [...] Read more.
The present work investigates fluid–structure instabilities and flow-induced oscillations of a pitching NACA0012 airfoil through numerical simulations. The flow is modeled using the compressible Navier–Stokes equations in a non-inertial rotating reference frame, while the structural dynamics are represented by a torsional spring–mass–damper system. The analysis focuses on the effects of reduced velocity, equilibrium angle of attack, and elastic axis position on the aeroelastic behavior at low Reynolds number (Re=1000). Particular attention is devoted to characterizing the transition from vortex-shedding-dominated oscillations to fully developed limit-cycle oscillations and to assessing its sensitivity to aerodynamic and structural parameters. The results show a transition from steady flow to vortex shedding and, at higher reduced velocities, to limit-cycle oscillations. Increasing the equilibrium angle of attack promotes an earlier onset of instability and stronger aerodynamic forcing, while moving the elastic axis downstream has a similar destabilizing effect due to the larger aerodynamic moment arm (up to approximately 20% reduction of the critical reduced velocity). The nature of the transition is found to depend strongly on the equilibrium angle of attack, with distinct behaviors observed at low and high incidence. Frequency analysis highlights the progressive coupling between fluid and structural dynamics: vortex shedding dominates in the weakly coupled regime, whereas the structural frequency governs the response in the limit-cycle regime. The study provides a consistent description of the mechanisms driving flow-induced oscillations and of the parameters controlling aeroelastic stability. Full article
(This article belongs to the Special Issue Industrial CFD and Fluid Modelling in Engineering, 4th Edition)
Show Figures

Figure 1

13 pages, 1399 KB  
Article
Mathematical Modeling of Fluid Flow and Heat Transfer in the Laminar Entrance Region of a Cylindrical Pipe
by Ismatulla Khujaev, Khusniddin Mamadaliev, Muzaffar Hamdamov, Shohjaxon Ravshanov, Makhbuba Boborakhimova, Oybek Begimov and Shokhrukh Chulliyev
Fluids 2026, 11(6), 140; https://doi.org/10.3390/fluids11060140 - 4 Jun 2026
Viewed by 252
Abstract
This study conducted a numerical simulation of laminar flow within a cylindrical pipe using a semi-implicit method. The full Navier–Stokes equations in cylindrical coordinates were solved, with modifications to the SIMPLE algorithm to handle pressure-linked equations. We evaluated three key thermophysical parameters—dynamic viscosity, [...] Read more.
This study conducted a numerical simulation of laminar flow within a cylindrical pipe using a semi-implicit method. The full Navier–Stokes equations in cylindrical coordinates were solved, with modifications to the SIMPLE algorithm to handle pressure-linked equations. We evaluated three key thermophysical parameters—dynamic viscosity, specific heat capacity, and thermal conductivity—under both constant and variable conditions in the entrance region. Due to the process’s two-dimensional, time-dependent nature, third-kind boundary conditions were used to accurately model the effects of ambient temperature, external wind, and the pipe’s geometric and physical features. From the numerical results, we analyzed the velocity field, pressure distribution, surface friction coefficient, and temperature distribution at various pipe cross-sections. These findings are of practical and scientific importance: they offer insights into the hydrodynamics and thermal behavior of the internal flow and enhance understanding of fluid flow and heat transfer, improving predictive models. This advancement supports better design and operational control in pipeline systems. Full article
(This article belongs to the Topic Advanced Heat and Mass Transfer Technologies, 2nd Edition)
Show Figures

Figure 1

16 pages, 4598 KB  
Article
Comparing Methods of Deforming and Overlapping Meshes to Simulate the Motion of Bodies on a Free Surface
by Andrey Kozelkov, Andrey Kurkin, Kseniya Plygunova, Vadim Kurulin and Vitaliy Gerasimov
Fluids 2026, 11(6), 138; https://doi.org/10.3390/fluids11060138 - 31 May 2026
Viewed by 179
Abstract
Two methods of accounting for the motion of the bodies—the deforming mesh method and the method of overlapping meshes (or overset mesh method)—are compared using problems with floating bodies, which are typical for the shipbuilding industry. Three problems are considered: oscillation of the [...] Read more.
Two methods of accounting for the motion of the bodies—the deforming mesh method and the method of overlapping meshes (or overset mesh method)—are compared using problems with floating bodies, which are typical for the shipbuilding industry. Three problems are considered: oscillation of the cylinder on the water surface, movement of the box under the influence of waves, and heaving and pitching of the ship model in head waves. Numerical computations are carried out in the LOGOS software package, the simulation methodology used is based on the solution of a system of Reynolds-averaged Navier-Stokes equations, and the Volume of fluid (VOF) method to take into account the free surface. In all problems, the characteristics of the movement of bodies are evaluated; the resistance force of the ship model is also determined in the third problem; control values obtained using two methods of accounting for moving bodies are compared with the available experimental data. The results of numerical simulation have shown that both methods predict body movement parameters well; the accuracy in determining the resistance force in the task of streamlining the ship’s hull is also comparable: the difference between the maximum deviations of the resistance coefficient in the computations with deformation and overlapping computation meshes is 0.5%. In the case of computations of the three-dimensional problem, the time spent when using the mesh-deformation method turned out to be 10% more; therefore, the method of overlapping meshes can be considered more optimal when solving such shipbuilding tasks as self-propelled tests and streamlining the ship’s hull with and without wind and wave loads. Full article
Show Figures

Figure 1

23 pages, 11660 KB  
Article
Influence of Dam Surface Flood Discharge Patterns on Navigation Flow Conditions in the Downstream Approaching Channel: A Case Study of the Xiangjiaba Hydraulic Project, China
by Xiting Zhang, Boyu Chen, Zhenyu Zhong, Ye Zhao and Qin Jiang
Water 2026, 18(11), 1329; https://doi.org/10.3390/w18111329 - 30 May 2026
Viewed by 352
Abstract
Flood discharge from the dam surface and tailwater discharge from the power station directly affect the hydrodynamic processes in the downstream river channel as well as at the entrance area of approaching channel, which are closely related to the navigation stability and safety [...] Read more.
Flood discharge from the dam surface and tailwater discharge from the power station directly affect the hydrodynamic processes in the downstream river channel as well as at the entrance area of approaching channel, which are closely related to the navigation stability and safety of vessels entering or leaving the ship lock. To investigate the influence of different dam flood discharge operational scenarios on the hydrodynamic characteristics at the entrance of the downstream ship lock approach channel, a three-dimensional nested coupled CFD model is established for free surface flows with strong nonlinearity in the stilling basin and unsteady turbulent flows in the downstream channel of the Xiangjiaba Hydraulic Project. The model adopts the Reynolds-Averaged Navier–Stokes (RANS) equations for unsteady flows, combined with the Realizable k-ε turbulence model as well as the VOF free surface tracking method for stilling basin flow and the standard k-ε turbulence model for downstream river flow, respectively. Numerical investigations are conducted to clarify characteristics of river flows associated with the discharged flood from dam surface and tailwater from power stations under different flood discharge patterns. The results show that the balanced discharge scenario involving the combined operation of releasing the flood through the crest and middle outlets of both left and right stilling basins can significantly reduce flow velocity and water level fluctuations near the entrance of the approach channel. Optimizing flood discharge scheduling can effectively improve flow conditions at the entrance area, which is beneficial to enhancing navigation safety for ships. Full article
(This article belongs to the Section Hydraulics and Hydrodynamics)
Show Figures

Figure 1

22 pages, 21774 KB  
Article
Thrust Characteristics of a Ducted Fan of a Quadcopter in Various Flight Modes
by Pavel Bulat and Pavel Chernyshov
Fluids 2026, 11(6), 135; https://doi.org/10.3390/fluids11060135 - 29 May 2026
Viewed by 167
Abstract
Ducted fans are widely used in vehicles with a high engine power per unit swept area, including hovercraft propulsors and vertical take-off aircraft. Computational fluid dynamics (CFD) is a powerful tool for selecting the aerodynamic configuration of new aircraft and engines and for [...] Read more.
Ducted fans are widely used in vehicles with a high engine power per unit swept area, including hovercraft propulsors and vertical take-off aircraft. Computational fluid dynamics (CFD) is a powerful tool for selecting the aerodynamic configuration of new aircraft and engines and for determining their optimal operating conditions. The full Navier–Stokes equations, closed by the Shear Stress Transport (SST) and Spalart-Allmaras (SA) turbulence models, are used to simulate airflow induced by the rotating blades of quadcopter ducted-fan propulsors. Thrust characteristics of the ducted fan are analyzed based on numerical simulations in different flight modes, such as hovering and oblique inflow. Tip clearance and inner-wall effects on thrust and power are reported. For the studied four-blade ducted fan, varying the blade angle of attack from 16 to 32 raises the thrust coefficient from 0.27 to 0.84 and the power coefficient from 0.18 to 0.50. At a constant shaft power of 3750 W, the optimal relative tip clearance for moderately loaded blades is 1.5% (16 angle). For heavily loaded blades (32 angle), maximum thrust occurs at zero clearance. However, even at 0.8% clearance, losses are less than 0.1% compared to the closed-tip configuration. For technological reasons, a small clearance is generally preferred. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics Applied to Transport Phenomena)
Show Figures

Figure 1

22 pages, 4612 KB  
Article
Hydrodynamic Characteristics of Seepage Beneath Underwater Structures Under Complex Geological and Geometric Boundaries
by Meng Zhu, Jun Hu, Yanan Zhang and Enjin Zhao
J. Mar. Sci. Eng. 2026, 14(11), 1008; https://doi.org/10.3390/jmse14111008 - 29 May 2026
Viewed by 279
Abstract
The spatiotemporal evolution of seepage fields and the associated hydrodynamic risk of subsequent internal erosion pose a critical threat to the structural integrity of marine and hydraulic infrastructure. To quantify these complex fluid–solid interactions, this study develops a high-fidelity numerical model—coupling the Navier–Stokes [...] Read more.
The spatiotemporal evolution of seepage fields and the associated hydrodynamic risk of subsequent internal erosion pose a critical threat to the structural integrity of marine and hydraulic infrastructure. To quantify these complex fluid–solid interactions, this study develops a high-fidelity numerical model—coupling the Navier–Stokes equations with the Darcy–Forchheimer resistance model and the Volume of Fluid (VOF) method—to investigate transient hydrodynamics within porous foundations under complex geometric and geological boundary conditions. Parametric analyses reveal that spatial porosity distribution fundamentally dictates the system’s seepage capacity; notably, relocating a highly permeable stratum to the shallow sub-surface eliminates upper hydraulic bottlenecks and significantly escalates total volumetric discharge. Furthermore, the study systematically evaluates the hydrodynamic efficacy of multi-dimensional seepage control structures. Results demonstrate that while increasing the vertical depth of a cutoff wall is highly efficient in restricting bulk volumetric flux, it inadvertently induces intense localized streamline convergence and flow acceleration at the structural tip. Conversely, lateral expansion of the wall base, though yielding only a moderate reduction in total seepage, successfully diffuses this concentrated flow and substantially attenuates peak pore fluid velocities. Ultimately, a combined design paradigm is proposed for practical coastal engineering applications: prioritizing vertical penetration to optimize bulk seepage reduction, concurrently integrated with moderate lateral base expansion to redistribute concentrated hydrodynamic shear stresses, thereby minimizing the hydrodynamic potential for localized piping and ensuring long-term stability against seepage-induced degradation. Full article
Show Figures

Figure 1

18 pages, 3652 KB  
Article
Synchronization of Low-Frequency Thermoacoustic Oscillation in Can-Annular Combustor via Compressor Combustion Casing
by Yichen Wang, Guojun Sun, Zhiqian Liu, Yupeng Qin, Jiefeng Geng, Jikang Wang, Guogang Shu and Xuan Lv
Energies 2026, 19(11), 2552; https://doi.org/10.3390/en19112552 - 26 May 2026
Viewed by 459
Abstract
Thermoacoustic instability remains an important challenge in gas turbines. In can-annular combustors, cross-talk effects can lead to complex collective dynamics. This paper investigates the in-phase synchronization of low-frequency thermoacoustic oscillations in a can-annular combustor, focusing on the upstream cross-talk mechanism mediated by the [...] Read more.
Thermoacoustic instability remains an important challenge in gas turbines. In can-annular combustors, cross-talk effects can lead to complex collective dynamics. This paper investigates the in-phase synchronization of low-frequency thermoacoustic oscillations in a can-annular combustor, focusing on the upstream cross-talk mechanism mediated by the compressor combustion casing. Dynamic pressure data from the full-scale engine reveal a transition from independent, low-amplitude pressure dynamics to a state of high-amplitude, in-phase synchronized oscillation in the combustor system. To quantify the upstream cross-talk effect, the multi-port acoustic scattering matrix of the casing is computed by solving the Helmholtz equation based on a mean-flow field obtained from Reynolds-Averaged Navier–Stokes simulations. Analysis of the matrix shows that the casing provides a coupling path between cans, with strength and phase being insensitive to the relative azimuthal position of the cans. Based on this physical insight, a star-network model of coupled Van der Pol oscillators is developed. The model, with parameters identified from experimental data and inferred from the scattering matrix, successfully reproduces the synchronization phenomenon observed in the experiment. A subsequent parametric study based on the validated model shows that in-phase synchronization occurs within periodic windows of the time delay and that the range of these windows expands with increasing coupling strengths. For τ=0.1T, 0.85T and 1.1T, synchronization is achieved with moderate coupling strengths. For τ=0.35T and 0.6T, the interaction between the two coupling mechanisms suppresses synchronization even at strong coupling strengths. This study shows that the upstream cross-talk effect is an important mechanism for in-phase synchronization and provides a validated, physics-based model for analyzing and predicting the collective thermoacoustic behavior of can-annular combustors. Full article
Show Figures

Figure 1

22 pages, 4763 KB  
Article
Determination of Added-Mass Coefficients in Eccentrically Confined Square Cylinders Using Deforming-Mesh and Immersed-Boundary Methods
by Bruno Oettinger-Barrientos, Armando Blanco-Alvarez and Gonzalo Tampier
Appl. Sci. 2026, 16(11), 5239; https://doi.org/10.3390/app16115239 - 23 May 2026
Viewed by 173
Abstract
Accurate prediction of hydrodynamic forces on confined oscillating structures is essential in applications related to nuclear engineering, energy systems, offshore devices, and mechanical components subjected to flow-induced vibrations. In this work, two computational fluid dynamics (CFD) methodologies implemented in ANSYS CFX are compared [...] Read more.
Accurate prediction of hydrodynamic forces on confined oscillating structures is essential in applications related to nuclear engineering, energy systems, offshore devices, and mechanical components subjected to flow-induced vibrations. In this work, two computational fluid dynamics (CFD) methodologies implemented in ANSYS CFX are compared to determine the added-mass coefficients for a square cross-section cylinder confined within a square container: a deforming-mesh method (DMM) and an immersed-boundary method (IBM). Unlike previous studies restricted either to concentric square cylinders or to eccentric configurations treated with potential flow, the present study addresses eccentric confined configurations by solving the incompressible Navier–Stokes equations and focuses primarily on the prediction of added mass under strong confinement. Horizontal, vertical, and combined eccentric displacements are analyzed in detail. Mesh-independence, domain-size sensitivity, and temporal-convergence analyses are performed. Results show that both methods provide closely matching added-mass predictions over a wide range of eccentricities, with relative differences typically below 1% for moderate eccentricities, although discrepancies increase under extreme confinement. Relative to the concentric configuration, the added-mass coefficient increases by about 44% for the most eccentric vertical case and by about 87% for the most eccentric corner-approach case. Force decomposition and pressure-field analysis show that this increase is governed primarily by pressure-induced inertial effects, whereas viscous shear plays a secondary role under the conditions considered. From a practical standpoint, the immersed-boundary method reduced the computational time by approximately 92% in the most demanding case. Full article
(This article belongs to the Special Issue Mathematical and Numerical Methods in Fluid Engineering)
Show Figures

Figure 1

39 pages, 909 KB  
Article
Projective Solutions Methods Automatically Satisfying the Stokes, Oseen and Brinkman Equations
by Chein-Shan Liu, Tai-Wen Hsu and Chia-Cheng Tsai
Mathematics 2026, 14(10), 1783; https://doi.org/10.3390/math14101783 - 21 May 2026
Viewed by 199
Abstract
The new projective solutions methods (PSMs) for solving the Stokes, Oseen, and Brinkman flow problems are presented in this paper. They automatically satisfy the governing equations and are therefore Trefftz-type methods. Utilizing the third-order formulation and three-dimensional analytic functions, we derive a meshless [...] Read more.
The new projective solutions methods (PSMs) for solving the Stokes, Oseen, and Brinkman flow problems are presented in this paper. They automatically satisfy the governing equations and are therefore Trefftz-type methods. Utilizing the third-order formulation and three-dimensional analytic functions, we derive a meshless Trefftz-type method to solve three-dimensional Stokes flow problems. The Oseen and Brinkman equations are transformed into four coupled third-order/first-order partial differential equations. The projective-type particular solution (PTPS) is obtained via a projective function in terms of the projective variable; the third-order ordinary differential equations (ODEs) with constant coefficients are derived to determine the projective functions. The Trefftz-type PSM is extremely accurate, because the governing equations (including the incompressibility condition) are implemented automatically. For the Brinkman equations, the general solutions of velocity and pressure are presented by using the Helmholtz function and a harmonic function, whose corresponding Trefftz-type numerical method is developed. Upon comparison with the method of fundamental solutions (MFS), the new methods exhibit some advantages, including lower condition numbers, faster convergence, and better accuracy. We also apply the Trefftz-type PSM to solve the exterior problem of the Stokes equations, where the velocity tends to zero at infinity. Full article
(This article belongs to the Section E: Applied Mathematics)
Show Figures

Figure 1

18 pages, 24885 KB  
Article
Numerical Simulation Study of a Triangular Numerical Wave Tank
by Juncheng Ruan, Ji Huang, Jiewei Liao, Bo Hu and Yulin Wang
J. Mar. Sci. Eng. 2026, 14(10), 960; https://doi.org/10.3390/jmse14100960 - 21 May 2026
Viewed by 261
Abstract
This study establishes a triangular numerical wave tank based on the viscous incompressible Navier–Stokes equations. The model is implemented in STAR-CCM+, employing the Reynolds-Averaged Navier–Stokes equations and the Volume of Fluid method, combined with velocity boundary wave-making and momentum source wave-making techniques for [...] Read more.
This study establishes a triangular numerical wave tank based on the viscous incompressible Navier–Stokes equations. The model is implemented in STAR-CCM+, employing the Reynolds-Averaged Navier–Stokes equations and the Volume of Fluid method, combined with velocity boundary wave-making and momentum source wave-making techniques for wave generation. On this basis, systematic numerical simulations of oblique and head-on waves were conducted, along with simulation studies of wave interactions with both fixed and floating circular cylinders. The accuracy and reliability of the model were validated by comparing simulation results with theoretical solutions and existing literature data. The results demonstrate that the performance of this triangular wave tank is not affected by the wave incident direction. It can stably generate high-quality oblique and head-on waves, making it suitable for numerical simulation studies of wave–structure interactions. Full article
(This article belongs to the Section Ocean Engineering)
Show Figures

Figure 1

Back to TopTop