Search Results (396)

This paper presents a mathematical model to investigate how waves and currents interact with a flexible perforated floating membrane in finite water depth within the framework of linear wave theory. The perforated flexible membrane is modeled based on Darcy’s law and the one-dimensional string equation. The complex dispersion relation in the presence of current velocity is derived from the Green’s function technique using a fundamental source potential solution. The dispersion curve is analyzed by comparing the phase and group velocities for different water depths. Further, a physical model associated with the effect of current on a moored finite floating perforated flexible membrane integrated with a vertical wall is formulated. Then, the theoretical solution of a physical boundary value problem near a vertical rigid wall is obtained using the matching technique and the roots of the dispersion relation derived from the Green’s function technique. Numerical simulations are provided to verify the convergence of the series solution and the accuracy of the obtained analytical findings are evaluated against previously published analytical and experimental datasets. Further, several numerical results on the membrane deflection, hydrodynamic coefficients, and horizontal force on the wall for various structural parameters, mooring stiffness, and current velocities are analyzed. It is observed that the present analysis with this perforated membrane breakwater will be helpful to coastal and marine engineers to understand the influence of current velocity. Full article

Shale gas reservoirs are characterized by low permeability, nanoscale pore structures, and complex fracture networks. Multistage fractured horizontal wells are an important technology for commercial shale gas development. However, many shale gas productivity models primarily emphasize gas transport within the reservoir and fracture system, while pressure variations caused by frictional losses along the horizontal wellbore are often simplified or treated separately. To address this issue, this study develops a fully coupled multiscale dual-porosity numerical model that integrates the shale matrix, hydraulic fractures, and horizontal wellbore within a unified simulation framework. The model incorporates key physical mechanisms governing shale gas transport, including Knudsen diffusion, Langmuir adsorption–desorption, stress sensitivity, and non-Darcy flow in fractures. Meanwhile, the Darcy–Weisbach equation is introduced to describe wellbore frictional pressure losses. The reliability of the proposed model is validated through history matching with field production data from the Changning shale gas reservoir. The results demonstrate that neglecting wellbore friction losses leads to a 30–50% overestimation of horizontal well productivity, indicating that wellbore friction has a significant impact on fracture flow distribution and productivity prediction. Furthermore, an exponent factor r is introduced to characterize and evaluate non-uniform fracture placement patterns. The results show that toe-dense fracture placement can increase cumulative gas production by approximately 37.8% compared with uniform fracture placement when r = 1.10, which yields the highest cumulative gas production among the tested cases. However, the additional production benefit becomes substantially smaller after the initial increase and remains relatively stable as r further increases. This study improves the understanding of friction-induced heel-to-toe effects and provides an effective numerical approach for productivity prediction and fracture placement design in shale gas horizontal wells. Full article

This work examines a new methodology for the nonlinear electrohydrodynamic interfacial stability of dielectric viscoelastic liquids to enhance the predictive accuracy of microfluidic and biological applications. It tackles the intricacies of nonlinear coupled dynamics, encompassing interfacial deformation and viscoelastic stress influences. This study examines nonlinear stability, as linear stability has previously been thoroughly scrutinized. The interacting fluids are distinguished by differences in density, dielectric permittivity, permeability, viscoelastic parameters, surface tension, and their dynamic response at the perturbed interface. To simplify the mathematical organization, viscous potential flow theory is adopted. Further reduction is achieved by coupling linearized governing partial differential equations with the applicable nonlinear interfacial boundary conditions. This formulation leads to a nonlinear Mathieu oscillator, which governs the evolution of interface displacement. By adopting a non-perturbative approach, the achieved nonlinear ordinary differential equation is transformed into an equivalent linear one. Numerical solutions to the derived stability conditions reveal that the fundamental stability behavior remains qualitatively identical to both the real and complex coefficients associated with nonlinear characteristic equations describing the movement of interfacial displacement. The findings demonstrate that the Darcy number negatively influences the stability region, whereas kinematic viscosities, the Weber number, and Ohnesorge number facilitate the system’s stabilizing impact. Full article

Accurate prediction of coupled heat-transfer and fluid-flow phenomena is essential for the thermal design, performance assessment, and optimization of heat exchangers (HXs). Among key HXs, concentric tube heat exchangers (CTHXs) are widely used in thermal energy systems, where their performance is governed by the coupled interaction of fluid flow and heat transfer. Although computational fluid dynamics (CFD) provides detailed insights into these transport phenomena, its high computational cost limits its applicability in design optimization and real-time monitoring applications. To overcome this limitation, the present study proposes a physics-guided neural network (PGNN) for the accurate and efficient prediction of CTHX thermo-hydraulic performance, including the overall heat-transfer coefficient (U) and the pressure drops of the cold (ΔP_c) and hot (ΔP_h) streams. The PGNN introduces correlation-based physical guidance through established Nusselt number, overall thermal-resistance, and Darcy–Weisbach pressure-drop relations. Accordingly, the proposed framework is a correlation-guided PGNN rather than a residual-based physics-informed model, because the local conservation-equation residuals are not explicitly enforced during training. For comparison, a standard artificial neural network (ANN) with the same architecture and input parameters was also developed. Both models were trained on a dataset generated from 1575 CFD simulations covering a wide range of operating and geometric conditions, including the Reynolds and Prandtl numbers of both fluids, inner and outer tube diameters, and inlet temperatures. A comprehensive error analysis demonstrates the superior predictive capability of the PGNN over the ANN under various flow and geometric conditions. On the unseen test dataset, the PGNN achieved mean absolute percentage errors of 2.03%, 1.09%, and 1.11% for predicting U, ΔP_c, and ΔP_h, respectively. The proposed PGNN therefore provides a reliable, high-fidelity, and computationally efficient alternative to CFD, supporting the analysis, optimization, and operation of thermal energy systems. Full article

This paper investigates the relaxation filtration of a suspension through a radial filter surface under conditions of constant flow velocity. A mathematical model for relaxation cake growth is formulated based on the liquid-phase continuity equation, Darcy’s relaxation law, and constitutive relations for both compressive and liquid pressures. The resulting governing equation is a nonlinear partial differential equation for the compressive pressure, complemented by a Stefan condition that characterizes the motion of the cake–slurry interface. The moving-boundary problem is solved numerically using a finite difference method employing a coordinate-based front-tracking technique combined with iterative procedures. The numerical results demonstrate the influence of relaxation effects on cake formation. Increasing the relaxation time slows the compaction process, thereby maintaining higher porosity and promoting accelerated growth of the cake layer thickness. Full article

Hydrological processes in dryland urban lakes are jointly shaped by landscape pattern dynamics and water resource scarcity, yet the spatial correspondence between landscape fragmentation and lake ecological water demand remains poorly understood. This study took Yuehai Lake, a typical dryland urban lake in Northwest China, as a case study. Landscape pattern analysis was integrated with a water balance model to quantify ecological water demand and its spatial correspondence with landscape metrics. The model coupled the Penman–Monteith equation, a depth-modified evaporation model, and a Darcy’s Law-based zonal seepage calculation. Results showed that: (1) the landscape structure remained highly stable over 2014–2022, with the Aggregation Index ranging from 95.07% to 95.28% and the Largest Patch Index from 90.20% to 90.70%; (2) the annual ecological water demand for maintaining ecosystem integrity was estimated at 2036.97 × 10⁴ m³, comprising inherent lake water volume of 1138.02 × 10⁴ m³ (55.9%), evapotranspiration of 659.72 × 10⁴ m³ (32.4%), and lakebed seepage of 239.23 × 10⁴ m³ (11.7%); and (3) evapotranspiration was concentrated between May and August, accounting for 80.5% of annual losses, with water surface evaporation dominating the flux at 91.5%. These findings suggest a spatial correspondence between landscape metrics and ecological water demand components, providing quantitative support for differentiated water supplementation strategies in dryland urban lakes. Full article

Aqueous humor (AH) is a watery fluid continuously circulating through the posterior and anterior chambers of the human eye and is essential to maintain a healthy intraocular pressure in the eyeball and keep the eye clean from waste products of metabolism and external agents. This paper presents a stationary compartment model of AH dynamics consisting of three integrated modules (M): M1 for AH production, M2 for AH passive flow and M3 for AH drainage. M1 is a zero-dimensional (0D) reduction of the velocity-extended Poisson-Nernst-Planck model and simulates solute transfer and fluid movement across the cellular structure of the ciliary epithelium (CE). M2 is the electric equivalent representation of Poiseuille flow across the series of two linear hydraulic resistors. M3 is a 0D reduction of the Darcy equations for a porous medium and simulates AH flow across the parallel between a nonlinear and a linear resistor. Compared to existing compartment approaches, the present model integrates at the macroscopic scale the multi-physical description of the human eye at the cellular scale. Numerical simulations suggest that (1) sodium channels in the CE are essential for maintaining proper AH dynamics; and (2) increased episcleral vein pressure reduces AH drainage, potentially explaining the development of secondary open-angle glaucoma. These insights advance the understanding of the mechanisms regulating AH dynamics and offer new perspectives for patient-specific therapies. Full article

This paper presents a comprehensive numerical modeling of nonlinear groundwater flow in a synthetic heterogeneous four-layer porous medium. Multilayered aquifer systems present significant modeling challenges due to nonlinear filtration and interlayer exchange processes. The mathematical model consists of four coupled nonlinear parabolic partial differential equations, where the nonlinearity arises from the dependence of hydraulic conductivity on hydraulic head. Vertical exchange between layers is described by Darcy’s law through separating aquicludes. The system is solved using a fully implicit finite-difference scheme by employing an alternating-direction implicit approach, resulting in a block-tridiagonal system of equations. The model is verified using analytical solutions and mass conservation tests. Application to a synthetic aquifer system demonstrates the model’s ability to reproduce complex transient behavior, including delayed response of upper layers to pumping and asymmetry of water-level drawdown cones due to nonlinear conductivity. The model’s greatest sensitivity is observed to the conductivity of the pumped layer and the vertical conductivity of the separating layers. The proposed approach represents a robust tool for groundwater management in structurally complex geological settings. Full article

This study investigates the low-Reynolds-number rotation of two eccentric spheres within an incompressible fluid that accounts for both micro-rotational effects and the presence of a porous medium. The region between the spheres contains a rigid, stationary skeleton, and we model the resulting flow using the Brinkman-extended Darcy approach. We derive the governing field equations, which account for the resistance to rotation through specific fluid viscosity parameters, while also incorporating surface slip effects on the interior sphere. The system of equations is solved using a semi-analytical boundary collocation method, where the fluid motion is expressed through a series of mathematical expansions satisfied at discrete points along the spherical boundaries. Our numerical results demonstrate that the hydrodynamic torque exerted on the spheres is highly sensitive to the porous environment. Specifically, increasing the permeability of the medium from $0.001$ to $0.5$ results in a substantial torque increase of approximately $210\%$. Additionally, the fluid’s resistance to micro-rotation acts as a torque-enhancing factor, with a variation in viscosity parameters from $0.02$ to $0.45$ inducing a $5.25\%$ increase in torque under conditions of high eccentricity. These findings were validated against established benchmarks for standard fluids in non-porous media, showing excellent agreement. Full article

Fourier Neural Operators have become a central tool for learning solution operators of partial differential equations, but their spectral layers remain entirely classical and rely on digital Fourier processing. In this work, we introduce the Continuous-Variable Quantum Fourier Neural Operator (CV-QFNO), a Gaussian photonic formulation of the FNO spectral layer. The proposed architecture maps the essential operations of Fourier-domain operator learning, Fourier transformation, mode selection, and channel mixing, onto native continuous-variable optical primitives. In this way, the CV-QFNO provides a photonic quantum analogue of the truncated spectral mechanism underlying the classical FNO, while avoiding the compilation overhead and spectral mismatch that arise in qubit-based Quantum FNO constructions. We extended the framework to both one- and two-dimensional operator learning and validated it on standard PDE benchmarks, including Burgers’ equation, heat equation, Navier–Stokes dynamics, and Darcy flow. The results show that the proposed model preserves the predictive accuracy, resolution generalisation, and spectral inductive bias of Fourier neural operators while using structurally constrained photonic parameterisation. Since all the experiments were performed as classical simulations, the contribution should be understood as an architectural and algorithmic blueprint for photonic neural operators rather than as a demonstration of quantum computational advantage. Full article

Fractured coal in the residual-strength stage is a primary medium for gas migration and drainage in deep mining areas. To investigate the hydro–mechanical seepage response of post-peak fractured coal under constant-pressure-difference conditions, triaxial CO₂ seepage tests were conducted on coal specimens collected from the Xinyuan Coal Mine. A Weibull-based damage constitutive model was established to characterize the confining-pressure-induced hysteresis in the damage-evolution path. The flow-rate evolution and Reynolds number analysis indicated that gas flow remained within the linear Darcy regime. A controlled-variable analysis was used to examine the competing effects governing permeability evolution. Mechanical compaction induced an exponential decrease in permeability, whereas the decrease in permeability with increasing pore pressure was interpreted, within the proposed model framework, as the combined effect of possible adsorption-induced matrix swelling and weakened gas slippage. To address the limitations of conventional constant-slip-factor models, a pressure-dependent slip modulation coefficient was introduced into a composite permeability equation incorporating effective stress, adsorption-related deformation, and dynamic gas slippage. Global nonlinear fitting yielded R² = 0.97 and an RMSE of 0.1909, with the residuals generally distributed around zero, supporting the fitting reliability of the model within the investigated stress–pressure range. Response-surface analysis identified mechanical compaction as the dominant controlling mechanism, while adsorption-related deformation and gas slippage acted as secondary correction mechanisms. The proposed framework provides a quantitative basis for distinguishing the mechanical and fluid-related effects governing permeability evolution in post-peak fractured coal. Full article

Fourier Neural Operators (FNOs) exhibit mode saturation on high-contrast inhomogeneous media, and recent multi-scale extensions (MscaleFNO) further worsen out-of-distribution (OOD) generalization. We introduce the Helmholtz Neural Operator (HNO), a physics-informed, FFT-free branch–trunk operator in the DeepONet family, with a hybrid SIREN+learnable-Fourier trunk and a dual-path rank-32 hypernetwork branch, with bounded multiplicative gating on per-mode coefficients. At a matched parameter count (∼1.05 M, five seeds), HNO achieves a 2.6× lower OOD generalization gap than FNO (19.6% vs. 50.6%, $p=1.7\times {10}^{-3}$, Cohen’s $d=5.1$), 5.1× lower than vanilla DeepONet (19.6% vs. 99.9%, $p=8.2\times {10}^{-3}$), and 6.0× lower than MscaleFNO (19.6% vs. 117.4%, $p=2.4\times {10}^{-6}$); MscaleFNO’s deficit grows at 4.2× more parameters, ruling out capacity starvation. HNO is 4.6×/16.4× faster than FNO/MscaleFNO and 64×–245× faster than multi-threaded FD-PML (MKL PARDISO, 12 cores; 183×–698× vs. single-thread scipy.spsolve), making it suitable as a forward surrogate inside many-query workflows. Absolute accuracy on extreme-contrast (15:1) OOD samples is limited (relative $L^2\approx 1$), so HNO is positioned as a many-query surrogate or warm start for refinement loops, not a stand-alone replacement for direct solvers. A scope limitation is that HNO underperforms FNO on elliptic Darcy Flow, confirming specialization for hyperbolic/wave equations rather than universal operator learning. Full article

Mass transfer is central to food processing but remains difficult to quantify because food materials are heterogeneous, multiphase, porous, biologically structured, and dynamically changing. Under these conditions, experiments alone cannot fully capture the spatiotemporal complexity of transport behavior, making modeling and simulation essential for mechanism interpretation, process prediction, and engineering optimization. Existing reviews mainly address specific operations or numerical methods, with limited synthesis of governing equations, simulation workflows, application implementation, and practical applicability. This review examines food mass transfer by linking coupled momentum, heat, and mass transfer laws with governing equation selection, simulation workflow, and representative food processing applications. Governing formulations for Fickian diffusion, conservation-based transport, heat–mass coupling, multicomponent transfer, Darcy-type porous-medium flow, and related model extensions are summarized, together with their assumptions, geometric applicability, and dimensionless criteria. A unified simulation workflow is then organized, covering transport type identification, governing equation and physical model selection, geometric representation, parameter determination, initial and boundary condition specifications, numerical method and simulation tool selection, numerical implementation, validation, and transferability assessment. Representative applications are discussed for drying, heat–mass coupled processes, multicomponent transfer, transport in porous foods, and redistribution in multi-ingredient or multilayer foods. Overall, future progress requires more integrated, structure-aware, experimentally validated, transferable, and application-oriented simulation frameworks. Full article

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

Capillary imbibition is the process by which liquids are absorbed into porous materials as a result of capillary pressure differences at the pore scale. Accurate characterization of imbibition dynamics, particularly in the presence of gravitational potential, is essential for understanding fluid transport in diverse systems such as soil, fractured rocks, filtration media, and plant roots. This study presents systematic imbibition experiments using filter papers with pore sizes of 2.5 µm, 11 µm, and 20 µm, each inclined at 80° to quantify the influence of gravitational potential on imbibition behavior. For horizontally positioned samples, the imbibition front propagated radially and symmetrically, exhibiting a power law dependence on time. The measured temporal exponents ranged from 0.386 to 0.403, consistently lower than the theoretical value of 1/2 predicted by the Lucas–Washburn law. With increasing permeability, the temporal exponent approached the Washburn limit, indicating a marked dependence of imbibition dynamics on pore structure. For the inclined configuration at an 80° angle, the imbibition fronts remained nearly circular but exhibited a pronounced displacement of the front center toward gravity. This displacement increased with permeability, from approximately 0.497 cm for the 11 µm filter paper to 3545 cm for the 20 µm filter paper, highlighting the combined effects of permeability and gravitational potential on fluid movement. Furthermore, the advance of the imbibition front was significantly slower in the smallest pores (2.5 µm) compared to the larger ones. Experimental results were evaluated against a theoretical model proposed by Medina, demonstrating moderate quantitative agreement at early times, when gravitational potential effects are less significant. These findings confirm that both the temporal scaling exponent and the spatial evolution of the imbibition front are governed by the porous medium’s permeability and inclination angle, providing experimental evidence of deviations from ideal Washburn behavior in real porous systems. Full article