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Keywords = surface integral equation method

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24 pages, 2567 KB  
Article
Theoretical Study on Pipeline Settlement Induced by Excavation of Ultra-Shallow Buried Pilot Tunnels Based on Stochastic Media and Elastic Foundation Beams
by Caijun Liu, Yang Yang, Pu Jiang, Xing Gao, Yupeng Shen and Peng Jing
Appl. Sci. 2026, 16(2), 590; https://doi.org/10.3390/app16020590 - 6 Jan 2026
Abstract
Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in [...] Read more.
Excavation of ultra-shallow pilot tunnels triggers surface settlement and endangers surrounding pipelines. The discontinuous settlement curve from traditional stochastic medium theory cannot be directly integrated into the foundation beam model, limiting pipeline deformation prediction accuracy. The key novelty of this study lies in proposing an improved coupled method tailored to ultra-shallow burial conditions: converting the discontinuous settlement solution into a continuous analytical one via polynomial fitting, embedding it into the Winkler elastic foundation beam model, and realizing pipeline settlement prediction by solving the deflection curve differential equation with the initial parameter method and boundary conditions. Four core factors affecting pipeline deformation are identified, with pilot tunnel size as the key. Shallower depth (especially 5.5 m) intensifies stratum disturbance; pipeline parameters (diameter, wall thickness, elastic modulus) significantly impact bending moment, while stratum elastic modulus has little effect on settlement. Verified by the Xueyuannanlu Station project of Beijing Rail Transit Line 13, theoretical and measured settlement trends are highly consistent, with core indicators meeting safety requirements (max theoretical/measured settlement: −10.9 mm/−8.6 mm < 30 mm; max rotation angle: −0.066° < 0.340°). Errors (max 5.1 mm) concentrate at the pipeline edge, and conservative theoretical values satisfy engineering safety evaluation demands. Full article
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14 pages, 5928 KB  
Article
Predictors of Clinical Success in Resin Infiltration for MIH Opacities
by María Dolores Casaña-Ruiz, Mª Angeles Velló-Ribes and Montserrat Catalá-Pizarro
J. Clin. Med. 2026, 15(1), 124; https://doi.org/10.3390/jcm15010124 - 24 Dec 2025
Viewed by 168
Abstract
Background/Objectives: Enamel defects in molar-incisor hypomineralization (MIH) have a multifactorial etiology involving environmental, systemic, and genetic factors. These alterations represent an aesthetic and emotional challenge, especially in anterior teeth. Resin infiltration has emerged as a minimally invasive treatment for MIH opacities, though [...] Read more.
Background/Objectives: Enamel defects in molar-incisor hypomineralization (MIH) have a multifactorial etiology involving environmental, systemic, and genetic factors. These alterations represent an aesthetic and emotional challenge, especially in anterior teeth. Resin infiltration has emerged as a minimally invasive treatment for MIH opacities, though outcome predictability remains limited. This study aims to analyze the baseline characteristics of MIH enamel defects and identify specific patterns that may predict clinical outcomes. Methods: This was a single-arm, prospective, observational clinical study with a six-month follow-up, with a total of 101 MIH-affected teeth treated with Icon® resin infiltration. Opacities were analyzed using CIELAB color parameters (Lab*), including luminance, lesion extent, affected tooth type, opacity location, and patient age. Treatment success was assessed using simple linear regression models with generalized estimating equations, which were based on different covariates. Clinical success was defined as the combined achievement of a significant reduction in ΔE, a decrease in L* indicating reduced opacity brightness, and a reduction in the relative surface area of the lesion at six months. Results: White opacities showed greater reduction after infiltration than yellow and brown ones (p < 0.029). Larger lesions exhibited greater improvement (p < 0.007). Canines and lateral incisors achieved better masking (p < 0.001), and incisal opacities had superior outcomes (p < 0.019). Additionally, younger patients experienced a greater reduction (p < 0.026). Conclusions: Resin infiltration enhances the esthetics of anterior teeth with MIH in pediatric patients. While no single predictive pattern was identified, white opacities achieved greater luminance reduction and better integration with sound enamel. Factors such as age, tooth type, opacity location, lesion extent, and color significantly influence treatment effectiveness and esthetic perception. Full article
(This article belongs to the Section Dentistry, Oral Surgery and Oral Medicine)
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12 pages, 3507 KB  
Article
Characteristics and Impact of Fouling from Copper Production on the Operation of a Waste Heat Recovery Boiler
by Roksana Urbaniak, Beata Hadała and Marcin Kacperski
Energies 2026, 19(1), 31; https://doi.org/10.3390/en19010031 - 20 Dec 2025
Viewed by 198
Abstract
The paper focuses on the characteristics of fouling from copper production on the tube surface in a waste heat recovery boiler during the transfer of heat from the flash furnace process gas. The likely mechanism of deposit formation on the tubes is described, [...] Read more.
The paper focuses on the characteristics of fouling from copper production on the tube surface in a waste heat recovery boiler during the transfer of heat from the flash furnace process gas. The likely mechanism of deposit formation on the tubes is described, and the morphology and chemical composition of the bound deposit taken from the radiation zone of the waste heat recovery boiler are reviewed. In addition, the impact of the presence of bound and loose deposits on the tube’s surface on the increase in the deposit surface temperature and the decrease in the heat transferred at the inner side of the tube is evaluated. Changes in the chemical, mineralogical, and phase constitutions along the thickness of the build-up were established on the basis of XRF, SEM, and XRD quantitative analyses. The heat exchanger tube temperature distribution was computed with the finite element method using an axi-symmetrical solution of the heat conductivity equation. Computing was carried out for a clean tube surface as well as for a case with loose and bound deposits present on the surface, with thicknesses of 0.5 cm, 1 cm, and 2 cm. The boundary conditions at the deposit side varied. For loose deposits with a thickness of 0.5 cm, the decline in the heat transferred was similar to the values obtained for a bound deposit with a thickness of 2 cm. It was established that, for a deposit with a thickness of 20 mm, there was an approximately 80% decline in the energy transferred by the walls compared to the clean tube surface. This study represents a novel approach by integrating mineralogical and phase analyses with finite element modelling to comprehensively assess the impact of both bound and loose deposits on heat transfer efficiency in waste heat recovery boilers from copper production. Full article
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23 pages, 2412 KB  
Article
Fixed-Time Preset Performance Sliding Mode Control for Underwater Manipulators Considering Input Saturation
by Ran Wang, Weiquan Huang, Zixuan Li, Yanjie Song and He Wang
J. Mar. Sci. Eng. 2026, 14(1), 11; https://doi.org/10.3390/jmse14010011 - 19 Dec 2025
Viewed by 205
Abstract
This paper addresses the trajectory tracking problem for a six-degree-of-freedom (6-DOF) underwater manipulator subject to complex disturbances and input saturation. It proposes a fixed-time preset performance sliding mode control method considering input saturation (FT-PP-SMC-IS), aiming to achieve rapid and stable tracking performance under [...] Read more.
This paper addresses the trajectory tracking problem for a six-degree-of-freedom (6-DOF) underwater manipulator subject to complex disturbances and input saturation. It proposes a fixed-time preset performance sliding mode control method considering input saturation (FT-PP-SMC-IS), aiming to achieve rapid and stable tracking performance under these constraints. Firstly, to improve modeling accuracy, the Newton–Euler method and Morison’s equation are integrated to establish a more precise dynamic model of the underwater manipulator. Secondly, to balance dynamic and steady-state performance, a preset performance function is designed to constrain the tracking error boundaries. Based on dual-limit homogeneous theory, a fixed-time sliding mode surface is constructed, significantly enhancing the convergence speed and fixed-time stability. Furthermore, to suppress the effects of input saturation, a fixed-time auxiliary system is designed to compensate in real-time for deviations caused by actuator saturation. By separately constructing the sliding mode reaching law and equivalent control law, global fixed-time convergence of the system states is ensured. Based on Lyapunov stability theory, the fixed-time stability of the closed-loop system is rigorously proven. Finally, comparative simulation experiments verify the effectiveness and superiority of the proposed method. Full article
(This article belongs to the Section Ocean Engineering)
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23 pages, 10338 KB  
Article
Numerical Analysis of the Three-Dimensional Interaction Between Nanosecond-Pulsed Actuation and Pulsed H2 Jets in Supersonic Crossflow
by Keyu Li, Jiangfeng Wang and Yuxuan Gu
Aerospace 2025, 12(12), 1113; https://doi.org/10.3390/aerospace12121113 - 17 Dec 2025
Viewed by 168
Abstract
A combined flow control method, integrating nanosecond pulsed surface dielectric barrier discharge (NS-SDBD) with pulsed jets, is proposed to address the challenge of low mixing efficiency in supersonic combustion. Numerical validation and mechanism analysis were conducted by solving the three-dimensional unsteady Reynolds-averaged Navier–Stokes [...] Read more.
A combined flow control method, integrating nanosecond pulsed surface dielectric barrier discharge (NS-SDBD) with pulsed jets, is proposed to address the challenge of low mixing efficiency in supersonic combustion. Numerical validation and mechanism analysis were conducted by solving the three-dimensional unsteady Reynolds-averaged Navier–Stokes (RANS) equations, coupled with the shear stress transport (SST) k–ω turbulence model. The simulations were carried out under a Mach 2.8 inflow condition with a 50 kHz pulsed frequency for H2 jets. The results demonstrate that, compared to the steady jet case, the combined control scheme increases the combustion product mass flow rate by 27.1% and enhances combustion efficiency by 26.8%. The average temperature in the wake region increases by 65 K, while the total pressure recovery coefficient shows only a marginal change. The pressure disturbance center evolves along the outer edge of the counter-rotating vortex pair (CVP) and is eventually absorbed by the vortex core. This process generates favorable velocity and vorticity perturbations, which enhance O2 entrainment into the CVP and increase the average wake temperature. Meanwhile, the strengthened reflected shock induces favorable velocity perturbations in the upper shear layer of the wake and further elevates the local temperature. Full article
(This article belongs to the Section Aeronautics)
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22 pages, 13983 KB  
Article
Numerical Studies for the Application of the Methodology for Volume Loss of Cohesionless (Loose) Soils (VL,LSR) and the Additional Settlement (Smax) During Shield Tunneling
by Armen Z. Ter-Martirosyan, Ilnaz I. Mustakhimov and Ivan A. Tikhoniuk
Buildings 2025, 15(24), 4555; https://doi.org/10.3390/buildings15244555 - 17 Dec 2025
Viewed by 241
Abstract
This paper presents results of numerical modeling of tunneling using mechanized tunnel boring machines (TBMs) based on a methodology for determining the volume loss cohesionless (loose) soils, denoted as VL,LSR, for shallow tunnels in dispersive soils to estimate surface [...] Read more.
This paper presents results of numerical modeling of tunneling using mechanized tunnel boring machines (TBMs) based on a methodology for determining the volume loss cohesionless (loose) soils, denoted as VL,LSR, for shallow tunnels in dispersive soils to estimate surface and foundation on settlement natural ground. Existing methods for estimating ground surface and structural settlements have significant drawbacks, caused by several factors, including the complexity of determining volume loss using the proposed methodologies, a limited number of empirical parameters describing the technological features of TBM operations, the absence of methods in Russian regulatory documentation for determining volume loss in tunnels with diameters of 6 m or more, among other issues. The study aims to validate a previously developed method for estimating VL,LSR and an empirical equation for predicting surface settlements, Smax, to assess additional settlements induced by tunneling. The proposed volume loss methodology and the modified Smax expression from Peck R.B. (1969), derived from monitoring data, are used in empirical calculations and numerical modeling of surface and building settlements during TBM tunneling. Validation results include back-analysis of geotechnical “tunnel–ground–structure” interaction models, comparisons of additional settlements from design calculations and field monitoring data, as well as comparisons with existing empirical relationships and relevant regulatory documents, followed by recommendations for their integrated application. The validated methods demonstrate good agreement with observed monitoring data, while providing sufficient engineering safety margins, confirming the applicability of the VL,LSR and the modified Smax expression by Peck R.B. (1969) for predicting settlements of tunneling and identifying directions for further research. Full article
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17 pages, 2218 KB  
Article
Design of Freeform Illumination Systems Based on Integrated Mapping Method and Feedback Optimization
by Xiang Sun, Yuankang Chen, Lingbao Kong, Wen Lin, Xing Peng and Wenjie Xu
Photonics 2025, 12(12), 1200; https://doi.org/10.3390/photonics12121200 - 5 Dec 2025
Viewed by 355
Abstract
In the field of non-imaging optics, the use of freeform lenses for achieving uniform illumination is of significant research importance. However, existing studies have primarily focused on uniform illumination design for planar targets and have made remarkable progress, while relatively less attention has [...] Read more.
In the field of non-imaging optics, the use of freeform lenses for achieving uniform illumination is of significant research importance. However, existing studies have primarily focused on uniform illumination design for planar targets and have made remarkable progress, while relatively less attention has been paid to uniform illumination on curved surfaces. To address this, this paper proposes a design method for freeform lenses aimed at uniform illumination on curved surfaces. The key to this method lies in utilizing the first kind of surface integral Equation to transform the problem from the Cartesian coordinate system on the target surface into a planar coordinate system, thereby significantly reducing computational complexity. Simulation results confirm the feasibility of the proposed lens design method in enabling the realization of high-efficiency, high-uniformity illuminance distribution on a curved surface via secondary optics for LEDs. Full article
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18 pages, 35382 KB  
Article
Stabilized Radial Basis Function Finite Difference Schemes with Mass Conservation for the Cahn–Hilliard Equation on Surfaces
by Jinwei Qiao, Yuanyang Qiao and Yinnian He
Entropy 2025, 27(12), 1206; https://doi.org/10.3390/e27121206 - 28 Nov 2025
Viewed by 413
Abstract
It is well known that the Cahn–Hilliard equation satisfies the energy dissipation law and the mass conservation property. Recently, the radial basis function–finite difference (RBF–FD) approach and its numerous variants have garnered significant attention for the numerical solution of surface-related problems, owing to [...] Read more.
It is well known that the Cahn–Hilliard equation satisfies the energy dissipation law and the mass conservation property. Recently, the radial basis function–finite difference (RBF–FD) approach and its numerous variants have garnered significant attention for the numerical solution of surface-related problems, owing to their intrinsic advantage in handling complex geometries. However, existing RBF–FD schemes generally fail to preserve mass conservation when solving the Cahn–Hilliard equation on smooth closed surfaces. In this paper, based on an L2 projection method, two numerically efficient RBF–FD schemes are proposed to achieve mass-conservative numerical solutions, which are demonstrated to preserve the mass conservation law under relatively mild time-step constraints. Spatial discretization is performed using the RBF–FD method, while based on the convex splitting method and a linear stabilization technique, the first-order backward Euler formula (BDF1) and the second-order Crank–Nicolson (CN) scheme are employed for temporal integration. Extensive numerical experiments not only validate the performance of the proposed numerical schemes but also demonstrate their ability to utilize mild time steps for long-term phase-separation simulations. Full article
(This article belongs to the Section Thermodynamics)
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20 pages, 2580 KB  
Article
Hybrid Physics–Machine Learning Framework for Forecasting Urban Air Circulation and Pollution in Mountain–Valley Cities
by Lyazat Naizabayeva, Gulbakyt Sembina and Gulnara Tleuberdiyeva
Appl. Sci. 2025, 15(22), 12315; https://doi.org/10.3390/app152212315 - 20 Nov 2025
Viewed by 946
Abstract
Background: Almaty, located in a mountain–valley basin, frequently experiences stagnant conditions that trap pollutants and cause sharp diurnal contrasts in air quality. Current forecasting systems either offer detailed physical realism at high computational cost or yield statistically accurate but physically inconsistent results. [...] Read more.
Background: Almaty, located in a mountain–valley basin, frequently experiences stagnant conditions that trap pollutants and cause sharp diurnal contrasts in air quality. Current forecasting systems either offer detailed physical realism at high computational cost or yield statistically accurate but physically inconsistent results. Urban air quality in mountain–valley cities is strongly shaped by thermal inversions and weak nocturnal ventilation that trap pollutants close to the surface. We present a hybrid physics–machine-learning framework that combines a Navier–Stokes surface-layer model with data-driven post-processing to produce short-term forecasts of wind, temperature, and particulate matter while preserving physical consistency. The approach captures diurnal ventilation patterns and the well-known negative linkage between near-surface wind and particulate loadings during wintertime inversions. Compared with purely statistical baselines, the hybrid system improves short-range forecast skill and maintains interpretability through physically grounded diagnostics. Beyond Almaty, the workflow is transferable to other mountain–valley environments and is directly actionable for early warning, traffic and heating-related emission management, and health-risk communication. By uniting physically meaningful fields with lightweight Machine Learning correction, the method offers a practical bridge between computational fluid dynamics and operational decision support for cities facing recurrent stagnation episodes. Aim: Develop and verify a method for the diagnostics and short-term forecasting of surface circulation and particle concentrations in Almaty (2024), ensuring physical consistency of fields, increased forecast accuracy on 6–24 h horizons, and interpretability of risk factors. Compared to purely statistical baselines (R2 ≈ 0.55 for PM forecasts), our hybrid framework achieved a 16% gain in explained variance and reduced RMSE by 25%. This improvement was most evident during winter inversion episodes. Methods: This study introduces a hybrid modeling framework that integrates the Navier–Stokes equations with machine-learning algorithms to diagnose and forecast surface air circulation and particulate matter concentrations. The approach ensures both physical consistency and improved predictive accuracy for short-term horizons (6–24 h). The Navier–Stokes equations in the Boussinesq approximation, the energy equation, and K-closure particulate matter transport were used. The numerical solution is based on the projection method (convection—TVD/QUICK, pressure—Poisson equation). The ML module is gradient boosting and decision trees for meteorological parameters, lags, and diagnostic quantities. The 2024 data are cleaned, normalized, and visualized. Results: The hybrid model reproduces the diurnal cycle of ventilation and concentrations, especially during winter inversions. For 6 h: wind RMSE ≈ 1.2 m/s (R2 ≈ 0.71), temperature RMSE ≈ 1.8 °C (R2 ≈ 0.78), and particles RMSE ≈ 0.012 mg/m3 (R2 ≈ 0.64). Errors are higher for 24 h. A negative relationship between wind and concentration was established: +1 m/s reduces the median by 10–15% during winter nights. Conclusions: The approach can be generalized to other mountain–valley cities beyond Almaty. Combining the physical model and ML correction improves short-term predictive ability and maintains physical consistency. The method is applicable for air quality risk assessment and decision support; further clarification of emissions and consideration of urban canyon geometry are required. The results support early-warning systems, health risk communication, and urban planning. Full article
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23 pages, 2423 KB  
Article
Development, Implementation, and Experimental Validation of a Novel Thermal–Optical–Electrical Model for Photovoltaic Glazing
by Juan Luis Foncubierta Blázquez, Jesús Daniel Mena Baladés, Irene Sánchez Orihuela, María Jesús Jiménez Come and Gabriel González Siles
Appl. Sci. 2025, 15(22), 12041; https://doi.org/10.3390/app152212041 - 12 Nov 2025
Viewed by 348
Abstract
The use of semi-transparent photovoltaic (Solar PV) glass in buildings is an effective strategy for integrating renewable energy generation, solar control, and thermal comfort. However, conventional simulation models rely on global optical properties, neglecting spectral radiation and its propagation within the material. This [...] Read more.
The use of semi-transparent photovoltaic (Solar PV) glass in buildings is an effective strategy for integrating renewable energy generation, solar control, and thermal comfort. However, conventional simulation models rely on global optical properties, neglecting spectral radiation and its propagation within the material. This limits the accurate assessment of thermal comfort, light distribution, and performance in complex systems such as multi-layer glazing. This study presents the development, implementation, and experimental validation of a numerical model that reproduces the thermal, electrical, and optical behaviour of semi-transparent Solar PV glass, explicitly incorporating radiative transfer. The model simultaneously solves the conduction, convection, and electrical generation equations together with the radiative transfer equation, solved via the finite volume method across two spectral bands. The refractive index and extinction coefficient, derived from manufacturer-provided optical data, were used as inputs. Experimental validation employed 10% semi-transparent a-Si glass, comparing surface temperatures and electrical power generation. The model achieved average relative errors of 3.8% for temperature and 3.3% for electrical power. Comparisons with representative literature models yielded errors between 6% and 21%. Additionally, the proposed model estimated a solar factor of 0.32, closely matching the manufacturer’s 0.29. Full article
(This article belongs to the Section Applied Thermal Engineering)
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28 pages, 7142 KB  
Article
Deciphering Relative Sea-Level Change in Chesapeake Bay: Impact of Global Mean, Regional Variation, and Local Land Subsidence, Part 1: Methodology
by Yi Liu and Xin Zhou
Water 2025, 17(21), 3167; https://doi.org/10.3390/w17213167 - 5 Nov 2025
Cited by 1 | Viewed by 732
Abstract
The Chesapeake Bay (CB) region faces significant risks from relative sea-level change (RSLC), driven by global mean sea-level rise (GMSLR), regional sea-level rise (RSLR), and local land subsidence (LS). This study introduces a methodology to decipher RSLC trends in the CB area by [...] Read more.
The Chesapeake Bay (CB) region faces significant risks from relative sea-level change (RSLC), driven by global mean sea-level rise (GMSLR), regional sea-level rise (RSLR), and local land subsidence (LS). This study introduces a methodology to decipher RSLC trends in the CB area by integrating these components. We develop trend equations spanning 1900–2100, incorporating acceleration for GMSLR and RSLR since 1992, with linear LS estimation using tide gauge, satellite altimetry, and InSAR data. Our approach employs dynamic RSLC equations, Maclaurin series expansions, and inverse simulations to project RSLC trends through 2100. Stable RSLC rates require over 122 years of data for reliable linear trend estimation, with the Baltimore tide gauge providing the necessary long-term dataset. Similarity in monthly mean sea-level variations within a coastal region enables a new method to identify LS from short-term tide gauge data by correlating it with corresponding long-term data at Baltimore. LS is categorized into bedrock-surface subsidence (BSS) and compaction subsidence (CS), with methods proposed to map BSS contours and estimate CS. CS is further classified into primary consolidation, secondary consolidation, construction-induced, and negative subsidence to determine specific compaction types. The projection model highlights the dominant influence of GMSLR acceleration since 1992, with local LS and RSLR influenced by ocean circulation, density changes, and gravitational, rotational, and deformational (GRD) effects. This integrated approach enhances understanding and predictive reliability for RSLC trends, supporting resilience planning and infrastructure adaptation in coastal CB communities. Full article
(This article belongs to the Special Issue Climate Risk Management, Sea Level Rise and Coastal Impacts)
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15 pages, 21768 KB  
Article
Linear Heat Diffusion Inverse Problem Solution with Spatio-Temporal Constraints for 3D Finite Element Models
by Luis Fernando Alvarez-Velasquez and Eduardo Giraldo
Computation 2025, 13(11), 255; https://doi.org/10.3390/computation13110255 - 2 Nov 2025
Viewed by 351
Abstract
High-voltage ceramic insulators are routinely exposed to short-duration overvoltages such as lightning impulses, switching surges, and partial discharges. These events occur on microsecond to millisecond timescales and can produce highly localized thermal spikes that are difficult to measure directly but may compromise long-term [...] Read more.
High-voltage ceramic insulators are routinely exposed to short-duration overvoltages such as lightning impulses, switching surges, and partial discharges. These events occur on microsecond to millisecond timescales and can produce highly localized thermal spikes that are difficult to measure directly but may compromise long-term material integrity. This paper addresses the estimation of the internal temperature distribution immediately after a lightning impulse by solving a three-dimensional inverse heat conduction problem (IHCP). The forward problem is modeled by the transient heat diffusion equation with constant thermal diffusivity, discretized using the finite element method (FEM). Surface temperature measurements are assumed available from a 12 kV ceramic post insulator and are used to reconstruct the unknown initial condition. To address the ill-posedness of the IHCP, a spatio-temporal regularization framework is introduced and compared against spatial-only regularization. Numerical experiments investigate the effect of measurement time (T=60 s, 600 s, and 1800 s), mesh resolution (element sizes of 20 mm, 15 mm, and 10 mm), and measurement noise (σ=1 K and 5 K). The results show that spatio-temporal regularization significantly improves reconstruction accuracy and robustness to noise, particularly when early-time measurements are available. Moreover, it is observed that mesh refinement enhances accuracy but yields diminishing returns when measurements are delayed. These findings demonstrate the potential of spatio-temporal IHCP methods as a diagnostic tool for the condition monitoring of ceramic insulators subjected to transient electrical stresses. Full article
(This article belongs to the Section Computational Engineering)
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19 pages, 7798 KB  
Article
A Boundary-Implicit Constraint Reconstruction Method for Solving the Shallow Water Equations
by Dingbing Wei, Jie Yang, Ming Fang and Jianguang Xie
J. Mar. Sci. Eng. 2025, 13(11), 2036; https://doi.org/10.3390/jmse13112036 - 23 Oct 2025
Viewed by 524
Abstract
To improve the accuracy of second-order cell-centered finite volume method in near-boundary regions for solving the two-dimensional shallow water equations, a numerical scheme with globally second-order accuracy was proposed. Having the primary objective to overcome the challenge of accuracy degradation in near-boundary regions [...] Read more.
To improve the accuracy of second-order cell-centered finite volume method in near-boundary regions for solving the two-dimensional shallow water equations, a numerical scheme with globally second-order accuracy was proposed. Having the primary objective to overcome the challenge of accuracy degradation in near-boundary regions and to develop a robust numerical framework combining high-order accuracy with strict conservation, the key research objectives had been as follows: Firstly, a physical variable reconstruction method combining a vertex-based nonlinear weighted reconstruction scheme and a monotonic upwind total variation diminishing scheme for conservation laws was proposed. While the overall computational efficiency was maintained, linear-exact reconstruction in near-boundary regions was achieved. The variable reconstruction in interior regions was integrated to achieve global second-order accuracy. Subsequently, a flux boundary condition treatment method based on uniform flow was proposed. Conservative allocation of hydraulic parameters was achieved, and flow stability in inflow regions was enhanced. Finally, a series of numerical test cases were provided to validate the performance of the proposed method in solving the shallow water equations in terms of high-order accuracy, exact conservation properties, and shock-capturing capabilities. The superiority of the method was further demonstrated under high-speed flow conditions. The high-precision numerical model developed in this study holds significant value for enhancing the predictive capability of simulations for natural disasters such as flood propagation and tsunami warning. Its robust boundary treatment methods also provide a reliable tool for simulating free-surface flows in complex environments, offering broad prospects for engineering applications. Full article
(This article belongs to the Section Ocean Engineering)
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20 pages, 6071 KB  
Article
Study on Gas Pre-Extraction Law of Along-Layer Boreholes Based on Thermo-Hydro-Mechanical-Damage Coupled Model
by Biao Hu, Xuyang Lei, Lu Zhang, Hang Long, Pengfei Ji, Lianmeng Wang, Yonghao Ding and Cuixia Wang
Mathematics 2025, 13(21), 3375; https://doi.org/10.3390/math13213375 - 23 Oct 2025
Viewed by 400
Abstract
Modeling the pre-extraction of coalbed methane presents a significant mathematical challenge due to the complex interplay of multiple physical fields. This paper presents a robust mathematical model based on a thermo-hydro-mechanical damage (THMD) framework to describe this process. The model is formulated as [...] Read more.
Modeling the pre-extraction of coalbed methane presents a significant mathematical challenge due to the complex interplay of multiple physical fields. This paper presents a robust mathematical model based on a thermo-hydro-mechanical damage (THMD) framework to describe this process. The model is formulated as a system of coupled, non-linear partial differential equations (PDEs) that integrate governing equations for heat transfer, fluid seepage, and solid mechanics with a damage evolution law derived from continuum damage mechanics. A key contribution of this work is the integration of this multi-physics model, solved numerically using the Finite Element Method (FEM), with a statistical modeling approach using Response Surface Methodology (RSM) and Analysis of Variance (ANOVA). This integrated framework allows for a systematic analysis of the model’s parameter space and a rigorous quantification of sensitivities. The ANOVA results reveal that the model’s damage output is most sensitive to the borehole diameter (F = 2531.51), while the effective extraction radius is predominantly governed by the initial permeability (F = 4219.59). This work demonstrates the power of combining a PDE-based multi-physics model with statistical metamodeling to provide deep, quantitative insights for optimizing gas extraction strategies in deep, low-permeability coal seams. Full article
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14 pages, 1557 KB  
Article
Enhanced Thermal Performance of Variable-Density Maxwell Nanofluid Flow over a Stretching Sheet Under Viscous Dissipation: A Maritime Technology Perspective
by A. M. Amer, Nourhan I. Ghoneim, Shadi Alghaffari, Mohammad E. Gommosani and Ahmed M. Megahed
Modelling 2025, 6(4), 134; https://doi.org/10.3390/modelling6040134 - 22 Oct 2025
Viewed by 604
Abstract
This scientific research examines the intricate dynamics of Maxwell nanofluid flow across a stretching surface with Stefan blowing impacts, with a particular focus on maritime thermal management applications. The analysis integrates multiple physical phenomena including magnetohydrodynamic forces, the energy dissipation phenomenon, and thermal [...] Read more.
This scientific research examines the intricate dynamics of Maxwell nanofluid flow across a stretching surface with Stefan blowing impacts, with a particular focus on maritime thermal management applications. The analysis integrates multiple physical phenomena including magnetohydrodynamic forces, the energy dissipation phenomenon, and thermal density variations within Darcy porous media. Special attention is given to Stefan blowing’s role in modifying thermal and mass transfer boundary layers. We derive an enhanced mathematical formulation that couples Maxwell fluid properties with nanoparticle transport under combined magnetic and density-gradient conditions. Computational results demonstrate the crucial influence of viscous heating and blowing intensity on thermal performance, with direct implications for naval cooling applications. The reduced governing equations form a nonlinear system that requires robust numerical treatment. We implemented the shooting technique to solve this system, verifying its precision through systematic comparison with established benchmark solutions. The close correspondence between results confirms both the method’s reliability and our implementation’s accuracy. The primary results of this study indicate that raising the Stefan blowing and density parameters causes notable changes in the temperature and concentration fields. The Stefan blowing parameter enhances both temperature and concentration near the wall by affecting thermal diffusion and nanoparticle distribution. In contrast, the density parameter reduces these values because of increased fluid resistance. Full article
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