انجمن هیدرولیک ایران نشریه علمی هیدرولیک 2345-4237 21 3 2026 09 23 Analyzing incompressible fluid flow using an adaptive multi-resolution algorithm based on the meshless local Petrov-Galerkin method تحلیل جریان سیالات تراکم ناپذیر با الگوریتم چندمقیاسی پویا و تطبیقی مبتنی بر روش بدون‌شبکه پتروف–گالرکین محلی 248409 10.30482/jhyd.2026.570939.1758 FA سید مجتبی موسوی نژاد گروه عمران، دانشکده فنی و مهندسی فردوس، دانشگاه بیرجند، فردوس ، ایران 0000-0001-5722-2614 امیر کیوان شفیعی گروه مهندسی کامپیوتر، دانشکده فنی و مهندسی فردوس، دانشگاه بیرجند، بیرجند 0000-0003-2724-0349 Journal Article 2026 01 05 Introduction The Meshless Local Petrov-Galerkin (MLPG) method solves the weak form of equations locally without a background mesh, making it suitable for flows with moving boundaries or complex geometries. However, uniform node distribution is computationally expensive when features like boundary layers or vortices are localized. Recent adaptive advancements include error-estimator-guided h-adaptive MLPG and quadtree-based RBF-FD methods. This paper introduces a dynamic adaptive multiscale MLPG algorithm with four key contributions: Hierarchical basis functions preserving partition of unity and polynomial reproduction across resolution levels. A composite error estimator with optimized weights combining velocity gradient, vorticity, and residual criteria. Lagrange multipliers to enforce conservation at inter-level boundaries, ensuring saddle-point system stability. Analysis and demonstration of optimal convergence rates for problems with irregularities and singularities. Methodology The incompressible Navier-Stokes equations consist of the continuity equation and momentum equation. The weak form is expressed locally over subdomain Ω_i using weight function w. The computational domain is partitioned using quadtree structure in 2D or octree in 3D into different levels, with nodal spacing at level l given by h_l=h_0⋅2^(-l). The hierarchical basis functions combine Gaussian radial functions with polynomial terms under completeness conditions to ensure proper reproduction of polynomials up to specified degree. At inter-level boundaries, a C^1-continuous blending function is used with transition width coefficient w_T=3.0 to ensure smooth and continuous transition between levels. Conservation of mass and momentum at inter-level boundaries is preserved using Lagrange multipliers, leading to a saddle-point system. The stability of this system is guaranteed by satisfying the inf-sup condition with constant β>0 independent of refinement level h_l. A composite error estimator is employed to identify regions requiring refinement, combining three criteria with optimized weights: η_i=0.4ϵ ̃_(∇u,i)+0.35ϵ ̃_(ω,i)+0.25ϵ ̃_(r,i), (1) where the components represent normalized velocity gradient norm, vorticity norm, and equation residual respectively. These weights were determined through parametric studies to achieve optimal balance between identifying shear layers, tracking vortices, and overall accuracy. Key parameters were determined through sensitivity analysis: transition width w_T=3.0, refinement thresholds (θ,θ_c)=(0.3,0.1), and RBF shape parameter c=1.2h_avg. Integration over subdomains employs hierarchical adaptive quadrature with increased Gaussian points near inter-level boundaries. The saddle-point system is solved using restarted GMRES with block-diagonal preconditioning, showing convergence independent of refinement level with iteration counts remaining in the range 35-75 Results and Discussion The proposed method was tested on four standard benchmark problems. For the moving boundary flow problem with a circular obstacle at Reynolds number 200, AMR-MLPG achieved L2 error of 3.17×10(-4) using 24,362 nodes compared to uniform MLPG with error 4.28×10(-4) using 90,000 nodes, representing approximately 78% computational savings. The observed convergence rate was O(h^2.1) , exceeding the theoretical rate and consistent with super convergence theory in adaptive FEM. For the reentrant corner flow problem with an L-shaped domain at Reynolds number 500 featuring velocity singularity u∼r(2/3) at the corner, the measured grading ratio ρ=0.72±0.05 satisfies the theoretical condition, and mesh size scaling h(r)∼r0.41 agrees with theoretical value β=3/7≈0.43. The singularity exponent extracted from numerical results was 0.668, showing only 0.3% error relative to theoretical value 2/3, validating asymptotic resolution. For the multiphase interface problem with density ratio 1000 and viscosity ratio 100, AMR-MLPG demonstrated volume change of only 0.18% and interface error 2.36×10(-4) using 26,518 nodes, outperforming VOF-AMR with 0.75% volume change and 42,612 nodes. Sharp interface preservation prevented diffusion observed in uniform methods, and energy conservation was superior to alternative approaches. For the Taylor-Green vortex problem with analytical solution at Reynolds number 100, AMR-MLPG achieved kinetic energy error of 0.28% and vorticity error 3.42×10(-4) using 18,756 nodes, approaching the accuracy of spectral element methods. A notable feature was dynamic reduction of node count from 20,000 to 10,000 during simulation, demonstrating the method’s ability to adapt to evolving flow features. The super optimal convergence rate O(h2.1) observed in moving boundary and Taylor-Green problems exceeds the theoretical O(h2) for second-order bases. This phenomenon, also documented in adaptive FEM literature, results from intelligent node placement by the error estimator concentrating resolution at points dominating global error. Efficiency improvements ranging from 3.5 to 4.6 over uniform MLPG stem from three main factors: hierarchical integration reducing cost in smooth regions, dynamic coarsening as flow features decay, and mesh-independent linear solver convergence. Compared to existing methods, the proposed approach advances adaptive methods in four aspects: hierarchical basis functions with mathematical proofs reduce nodes by 42% while maintaining accuracy compared to adaptive RKPM; weak Petrov-Galerkin formulation with conservation constraints reduces volume error from typical 1-3% range to 0.18% compared to adaptive RBF-FD; Lagrange multiplier approach eliminates remeshing overhead for moving boundaries, reducing computational cost by 56% compared to adaptive SPH; and support domain flexibility improves corner error resolution by one order compared to adaptive h-FEM. Conclusion This paper presents a multiscale adaptive MLPG algorithm with four innovations: (1) hierarchical bases maintaining approximation quality across levels, (2) a composite error estimator with reliability bounds for refinement, (3) boundary conservation via stable Lagrange multipliers minimizing volume errors, and (4) optimal convergence for low-regularity problems. Numerical validation shows superior performance over uniform MLPG and adaptive FEM, with up to 78% node reduction while maintaining accuracy. The observed O(h²˙¹) convergence and dynamic adaptation make it suitable for complex flows with localized features, moving boundaries, and singularities. در این مقاله، یک الگوریتم پویا و تطبیقی مبتنی بر روش بدون‌شبکه MLPG برای حل عددی معادلات ناویر-استوکس تراکم‌ناپذیر ارائه می‌گردد. هسته اصلی این روش، ترکیب یک ساختار سلسله‌مراتبی چندمقیاسی (بر پایه چهارگانه‌درخت) با یک تخمین‌گر خطای ترکیبی هوشمند است که به‌طور پویا نواحی نیازمند به دقت بالاتر (مانند لایه‌های مرزی یا گردابه‌ها) را شناسایی و تمرکز گره‌های حل را در آن مناطق افزایش می‌دهد نوآوری‌های اصلی شامل ارائه ساختار توابع پایه سلسله‌مراتبی با حفظ خواص یکنواختی و بازسازی چندجمله‌ای، معرفی تخمین‌گر خطای ترکیبی مبتنی بر گرادیان سرعت، گرداب و باقی‌مانده معادلات است. همچنین از ضرایب لاگرانژ برای حفظ قوانین بقای جرم و تکانه در مرزهای بین سطوح استفاده می‌شود. در ادامه، تحلیل همگرایی برای مسائل دارای ناهمواری‌ها و تکینگی‌های هندسی انجام گردید.. بررسی‌های عددی روی چند مساله معیار نشان می‌دهد که این روش تطبیقی در مقایسه با روش MLPG یکنواخت، ضمن حفظ یا بهبود دقت، تا ۷۸ درصد در تعداد گره‌های محاسباتی صرفه‌جویی می‌کند. همچنین، نرخ همگرایی فوق‌بهینه‌ای در حدود O(h^2.1)مشاهده شده است. این الگوریتم به‌طور مؤثری قابلیت تطبیق پویا با ویژگی‌های در حال تکامل جریان را داشته و برای شبیه‌سازی جریان‌های پیچیده با مرزهای متحرک، چگالی‌های متغیر و تکینگی‌های هندسی مناسب است.

انجمن هیدرولیک ایران نشریه علمی هیدرولیک 2345-4237 21 3 2026 09 23 Numerical and experimental hydraulic modeling of flow under the influence of a central baffle structure in open channels using OpenFOAM software مدل‌سازی عددی - آزمایشگاهی هیدرولیک جریان تحت تاثیر سازه بافل مرکزی در مجاری روباز با استفاده از نرم‌افزار OpenFOAM 248361 10.30482/jhyd.2026.578810.1761 FA محمد خسروی گروه علوم و مهندسی آب، دانشکده کشاورزی دانشگاه شهرکرد الهام قنبری عدیوی گروه مهندسی آب دانشگاه شهرکرد 0000-0002-7781-0138 علی رئیسی گروه علوم و مهندسی آب، دانشکده کشاورزی دانشگاه شهرکرد غلامرضا شمس گروه مهندسی عمران دانشگاه شهرکرد نریمان مهرانفر گروه عمران، معدن و زمین شناسی، دانشکده پلی تکنیک، دانشگاه مونترال، کانادا Journal Article 2026 04 26 Introduction: This research delves into the intricate hydraulic dynamics of open channel flows, with a specific focus on the significant impact exerted by a central baffle structure when implemented within channels of varying geometric cross-sections—namely, simple and composite rectangular configurations. The overarching objective of this study is to meticulously evaluate and quantitatively compare how these distinct channel geometries, in conjunction with the central baffle, influence critical flow parameters. These include, but are not limited to, flow velocity, shear stress distribution, drag and lift forces acting on the structure, the rate of energy dissipation within the channel, and the detailed profiles of velocity and flow depth. A profound understanding of these interactions is not merely academic; it is fundamentally essential for the efficient design of hydraulic structures, the optimization of open channel conveyance systems, and the accurate prediction of various flow-related phenomena, such as erosion, sediment transport, and structural stability. Recognizing the complexity inherent in such flows, particularly the generation of vortices, turbulence, and free surface instabilities around obstructions, this investigation aims to provide a comprehensive elucidation of how the synergistic interplay between channel geometry and baffle design dictates overall flow behavior. The ultimate goal is to identify optimal configurations that enhance hydraulic performance and operational efficiency for a range of practical engineering applications. Methodology: The methodological framework of this research is strategically designed as a robust hybrid approach, integrating advanced numerical modeling techniques with rigorous experimental validation. For the numerical simulations, the widely recognized and powerful OpenFOAM software suite was employed. Specifically, the two-phase flow solver, commonly known as interFOAM, was selected for its proven efficacy in handling free surface flows and air-water interfaces. Complementing this, the k–ω SST turbulence model was adopted. This model offers a superior balance between accuracy and computational efficiency, particularly in predicting flow separation and adverse pressure gradients, which are characteristic of flows around bluff bodies like baffles. The geometric configurations under scrutiny comprised two distinct channel designs: a standard, simple rectangular channel and a more complex channel featuring a composite rectangular cross-section. In both channel types, a centrally positioned baffle structure was incorporated. Standard hydraulic boundary conditions were applied, including a specified inflow discharge rate at the channel inlet and an atmospheric pressure condition at the outlet to simulate open channel flow. After the computational fluid dynamics (CFD) simulations were executed and transient flow fields were established, the obtained numerical results—encompassing velocity profiles, flow depth variations, and shear stress distributions—were subjected to a stringent comparison against meticulously collected experimental data. The accuracy and reliability of the numerical model were quantitatively assessed using established statistical metrics such as absolute error, normalized mean squared error (NRMSE), and the correlation coefficient R2, thereby ensuring the fidelity of the simulation in representing the real-world hydraulic phenomena. Results and Discussion: The detailed analysis of the simulation outcomes yielded several key findings regarding the distinct hydraulic responses observed in the simple versus composite channel configurations. In the simple rectangular channel, the presence of the central baffle was found to induce significant flow perturbations. These included the generation of highly turbulent flow regimes, the formation of unstable vortex structures downstream of the baffle, and a notable increase in energy losses throughout the channel reach. Furthermore, the drag and lift forces exerted on the baffle exhibited considerable fluctuations, indicative of unsteady flow conditions. The shear stress distribution along the channel bed and walls was also found to be spatially variable and relatively elevated in this configuration. In stark contrast, the composite rectangular channel, when equipped with the same central baffle, presented a markedly different flow behavior. A primary observation was the substantial reduction in the drag force acting on the baffle, narrowing its range significantly (from a broad spectrum of 1.198 to 12.702 in the simple channel to a more constrained range of 4.99 to 6.53). Concurrently, the shear stress along the channel bed experienced a dramatic decrease, approaching near-zero values in certain regions. This indicates a substantial dampening of turbulent energy near the boundaries. However, this enhanced flow control came with a trade-off: the lift forces acting on the baffle became considerably more pronounced and exhibited greater oscillatory behavior, spanning a wider range from -9.035 to +10.316. A critical parameter, the energy dissipation rate, revealed a significant difference between the two setups. The composite channel exhibited a substantially higher energy dissipation rate, reaching approximately 75% of the total incoming flow energy, compared to roughly 33% in the simple channel. This heightened dissipation in the composite channel is primarily attributed to the synergistic interaction between the modified cross-section and the baffle, which effectively promotes the formation and shedding of large-scale vortices, thereby consuming kinetic energy more rapidly. Crucially, the rigorous validation of the numerical model against experimental data provided strong evidence for its predictive capabilities. The model achieved a high degree of accuracy, evidenced by a low mean error (3.81% for the simple channel and 2.35% for the composite channel), a low normalized mean squared error (NRMSE) of 0.076 and 0.083, respectively, and an exceptionally high correlation coefficient ® of 0.99. These metrics collectively affirm the model’s reliability in accurately simulating the complex flow phenomena observed in both channel configurations. Conclusion: This comprehensive study successfully elucidated the distinct hydraulic impacts of channel geometry (simple versus composite rectangular) when integrated with a central baffle structure in open channels. The composite channel configuration demonstrated a superior capacity for flow management, characterized by a significant reduction in drag forces and a more controlled dissipation of energy, albeit with increased oscillatory lift forces compared to the simple channel. The high fidelity of the OpenFOAM numerical model, validated against experimental data, underscores its utility for simulating such complex flows. These findings collectively highlight the significant potential of employing composite channel geometries in conjunction with appropriate flow-control structures like baffles to optimize the design and operational efficiency of hydraulic systems. در این پژوهش، اثر انسداد ناشی از بافل مرکزی بر رفتار هیدرولیکی جریان در دو نوع کانال روباز با مقطع مستطیلی ساده و مرکب به‌صورت آزمایشگاهی و عددی بررسی شد. نوآوری این مطالعه در تحلیل هم‌زمان اثر هندسه مرکب کانال و حضور بافل مرکزی بر الگوی توزیع تنش برشی، هیدرولیک جریان و استهلاک انرژی، با استفاده از مدل‌سازی سه‌بعدی در نرم‌افزار OpenFOAM با استفاده از حلگر interFOAM و مدل آشفتگی k–ω SST است. نتایج نشان داد که ترکیب هندسه مرکب و بافل مرکزی موجب کاهش نیروی درگ و افزایش نرخ استهلاک انرژی نسبت به کانال ساده می‌شود. نرخ استهلاک انرژی در کانال مرکب حدود 75 درصد و در کانال ساده حدود 33 درصد برآورد شد که ناشی از هم‌افزایی هندسه مرکب و بافل در تولید گردابه‌های بزرگ‌ و تغییرات ناگهانی سرعت و فشار است. تحلیل پروفیل عمق و سرعت نشان داد که عمق اولیه در کانال مرکب حدود 14/0 متر و در کانال ساده حدود 13/0متر است و سازه بافل موجب ایجاد اتلاف هدفمند انرژی در ناحیه پس از خود می‌شود. همچنین در کانال مرکب، بازتوزیع تنش برشی و شکل‌گیری نواحی جریان کم‌سرعت در پایین‌دست سازه مشاهده شد که بیانگر کارایی بیشتر این آرایش در کنترل انرژی جریان است. مقایسه نتایج عددی با داده‌های آزمایشگاهی نشان داد که مدل RANS به‌کاررفته توانایی بالایی در بازتولید مشخصات جریان دارد. یافته‌های این پژوهش می‌تواند در طراحی سازه‌های کنترل انرژی، حفاظت بستر و بهینه‌سازی مقاطع مرکب در کانال‌های روباز مورد استفاده قرار گیرد.

انجمن هیدرولیک ایران نشریه علمی هیدرولیک 2345-4237 21 3 2026 09 23 Trend Analysis of Precipitation, Annual Peak Discharge, and Flood Characteristics in the Kan River Basin, Tehran, Using Long-term Records تحلیل روند بارش، دبی اوج سالانه و ویژگی‌های سیلاب‌های رودخانه کن تهران بر پایه داده‌های بلندمدت بارش، هواشناسی و رخدادهای سیلاب 248362 10.30482/jhyd.2026.580010.1763 FA مرتضی شکری استادیار گروه عمران، دانشکده فنی مهندسی، دانشگاه بوعلی سینا، همدان، ایران 0000-0002-6642-1663 Journal Article 2026 04 30 Rapid urban expansion, land use change, and climate variability have significantly influenced the hydrological behavior of many watersheds surrounding large metropolitan areas. In Tehran, several mountainous and semi urban basins are increasingly exposed to short duration intense rainfall events that can trigger flash floods. Among these basins, the Kan River basin located in western Tehran plays an important role in regional hydrology, sediment transport, and flood generation processes. Understanding the temporal variability of precipitation and the behavior of peak river discharge in this basin is therefore essential for improving flood management and water resources planning. Despite the importance of this watershed, comprehensive analyses that simultaneously examine precipitation variability, annual peak discharge trends, and flood characteristics remain limited. Accordingly, this study aims to analyze precipitation trends, evaluate annual peak discharge behavior, and investigate the characteristics of recorded flood events in the Kan River basin in order to provide a clearer understanding of the basin’s hydrological response and its implications for flood management. In this research, long term observational data including daily and monthly precipitation records, meteorological data, annual peak discharge values, and flood event information from hydrometric and meteorological stations within the Kan River basin were used. First, temporal variations of precipitation were analyzed at both annual and seasonal scales to identify dominant rainfall patterns and interannual variability. Subsequently, the time series of annual peak discharge was evaluated to determine the behavior of extreme flow conditions. In the next step, flood events were examined through the analysis of flood hydrographs. Key hydrological indicators such as peak discharge magnitude, time to peak, flood duration, and hydrograph shape were extracted and analyzed to better understand the watershed response to rainfall events. This methodological framework enables a combined assessment of precipitation variability and hydrological response, which is particularly important for watersheds that are susceptible to flash flooding. The results indicate that precipitation in the Kan River basin exhibits considerable interannual and intra annual variability. A significant portion of the annual precipitation occurs during the cold and transitional seasons, mainly from October to May, while summer months contribute only a small fraction of the total annual rainfall. This temporal distribution corresponds to the semi arid Mediterranean type climate that characterizes the Tehran region. The analysis of annual peak discharge and flood events also reveals that the watershed is highly responsive to intense rainfall events. In several cases, flood hydrographs demonstrate rapid increases in discharge within short periods, indicating the potential for flash flood formation. Such behavior is typical of mountainous watersheds where steep slopes and limited infiltration capacity can accelerate runoff generation. The integrated analysis of precipitation patterns, peak discharge trends, and flood hydrograph characteristics provides a comprehensive picture of the hydrological behavior of the Kan River basin. Compared with studies that focus only on rainfall variability or discharge trends separately, this research offers a more holistic perspective on the mechanisms governing flood generation in the basin. Furthermore, the findings are consistent with previous studies conducted in the Tehran region that highlight the dominant role of cold season precipitation and extreme rainfall events in shaping regional flood regimes. By combining multiple datasets and hydrological indicators, the present study contributes to a better understanding of watershed dynamics and flood processes in semi arid mountainous environments. The outcomes of this research can support improved flood risk management, watershed planning, and infrastructure design in the Kan River basin. Knowledge of precipitation variability and peak discharge behavior can help authorities better anticipate flood hazards and develop more effective mitigation strategies. Moreover, the methodology applied in this study may be useful for similar watersheds in other semi arid regions where hydrological responses are strongly influenced by seasonal rainfall patterns and extreme events. رودخانه کن یکی از مهم‌ترین آبراهه‌های ارتفاعات شمال‌غرب تهران است که به‌دلیل شیب زیاد، بارش‌های رگباری و توسعه سریع شهری در پایین‌دست، پتانسیل بالایی برای رخداد سیلاب‌های ناگهانی دارد. در این پژوهش روند بلندمدت بارش، دبی اوج سالانه و ویژگی‌های سیلاب‌های موثر حوضه کن بر پایه داده‌های بارش، هواشناسی و دبی با دوره آماری حدود ۴۰ ساله مورد تحلیل قرار گرفته است. داده‌های بارش و دبی پس از کنترل کیفیت، تکمیل و یک‌دست‌سازی، به مقیاس‌های ماهانه و سالانه تبدیل شده و روند آن‌ها با استفاده از آزمون Mann–Kendall و برآورد شیب Sen’s slope بررسی شد. نتایج نشان داد بارش سالانه ایستگاه سنگان با میانگین حدود ۳۷۰ میلی‌متر و ضریب تغییرات ۲۸ درصد فاقد روند معنادار آماری بوده و تنها نوسانات بین‌سالی قابل‌توجهی را نشان می‌دهد. در مقابل، دبی اوج سالانه در ایستگاه سولقان با میانگین ۴۱ مترمکعب بر ثانیه و حداکثر رخداد ثبت‌شده حدود ۲۹۵ مترمکعب بر ثانیه دارای افزایش نوسانی و غیرمنظم است، اما روند آن نیز در سطح ۰٫۰۵ معنادار نیست. تحلیل رخدادهای سیلابی نشان داد که سیلاب‌های مؤثر عمدتاً ناشی از بارش‌های کوتاه‌مدت و پرفشار در نیمه سرد سال بوده و هیدروگراف آن‌ها دارای زمان اوج کوتاه، دامنه زیاد و حجم قابل‌توجه است. نتایج کلی پژوهش نشان می‌دهد اگرچه بارش سالانه روند مشخصی ندارد، اما افزایش شدت رگبارها و کاهش زمان تمرکز حوضه می‌تواند ریسک وقوع سیلاب‌های ناگهانی را در پایین‌دست افزایش دهد. این نتایج می‌تواند به‌عنوان مبنایی برای پایش سیلاب، مدیریت خطرپذیری مناطق شهری و برنامه‌ریزی سازه‌ای/غیرسازه‌ای در حوضه کن مورد استفاده قرار گیرد.

انجمن هیدرولیک ایران نشریه علمی هیدرولیک 2345-4237 21 3 2026 09 23 Integrated Analysis of Sefidrud Dam Operational Dynamics Over a 16 Year Water Year Period: Quantitative Evidence of Stationarity Failure in the Inflow–Storage–Outflow Cycle تحلیل یکپارچه دینامیک‌های عملیاتی سد سفیدرود در دوره ۱۶ سال آبی: شواهد کمّی از شکست ایستایی در چرخه ورودی–ذخیره–خروجی 248077 10.30482/jhyd.2026.581028.1765 FA هادی مدبری استادیار گروه پایش منابع آب پژوهشکده محیط زیست جهاد دانشگاهی، رشت. ایران 0009-0009-1975-0550 حسین حکیمی خوانسر 2- دانشجوی دکترا، گروه مهندسی آب، دانشگاه تبریز و کارشناس کنترل و پایداری، وزارت نیرو- شرکت سهامی آب منطقه‌ای گیلان، ایران عباس حیدری کارشناس برق – الکترونیک، رییس سد و نیروگاه سد سفیدرود، وزارت نیرو شرکت سهامی آب منطقه‌ای گیلان، ایران مرتضی کریمی پژوهشگر گروه پایش منابع آب، پژوهشکده محیط زیست جهاد دانشگاهی، رشت، ایران Journal Article 2026 05 18 Introduction Dams are designed based on the assumption of stationarity and recoverability to an equilibrium state. However, growing evidence shows that climatic and managerial pressures violate this assumption, leading to non‑stationary behavior. In recent literature, "stationarity failure" refers to the collapse of structural relationships among inflow, storage, and outflow – a condition where the system loses its ability to return to a previous equilibrium. The Sefidrud Dam (nominal capacity ~310 MCM) is a strategic infrastructure in the Sefidrud basin, playing a vital role in agricultural water supply, flood control, and hydropower generation. It has faced concurrent pressures from droughts, altered runoff patterns, and increasing downstream demands. Previous studies have been mostly univariate (e.g., trend analysis of inflow or water level alone), neglecting the closed "inflow–storage–outflow" cycle as a coherent dynamic system. This study focuses on four operational variables to seek quantitative evidence of stationarity failure at the Sefidrud Dam using a 16‑year daily dataset and an integrated multi‑method approach. Methodology Daily data of four variables – inflow (IFR), reservoir storage volume (RSV), reservoir water level (RWL), and total outflow (OFR) – were collected from the Sefidrud Dam monitoring network over 16 water years (from October 2009 to September 2025). After outlier screening and removal of days with missing values, the final dataset comprised 5,792 valid days. To detect structural and behavioral changes, a comprehensive analytical framework was applied: (1) Pettitt non‑parametric test for abrupt change‑point detection in the mean of time series; (2) Mann–Kendall test coupled with Sen's slope estimator to assess monotonic long‑term trends; (3) STL (Seasonal‑Trend decomposition using Loess) to separate trend, seasonal, and residual components; (4) rolling window correlation (365‑day window) to examine the temporal evolution of pairwise relationships (IFR–RSV, RSV–OFR, IFR–OFR); (5) continuous wavelet transform (CWT) using the Morlet wavelet (cmor1.5‑1.0) on the RSV time series to identify shifts in dominant oscillation scales. Additionally, a sensitivity test was performed by removing irrigation months (May to September) and re‑running trend analyses on the remaining data to assess whether seasonal agricultural releases were the primary driver of observed changes. All computations and visualizations were carried out in Python using libraries pymannkendall, statsmodels, and pywt Results and Discussion Descriptive statistics showed that IFR and OFR had very high coefficients of variation (149% and 162%, respectively), indicating strong daily fluctuations and right‑skewed distributions, while the CV of water level was only about 4%, reflecting the reservoir's regulatory role. Reservoir storage volume (RSV) exhibited an intermediate behavior, with its CV increasing from ~18% in early years to ~30% in later years – an early sign of weakening storage stability. The Pettitt test identified a significant structural break (p < 0.001) for all four variables around water year 2015–2016. Mean RSV decreased from 278.1 MCM before the break to 174.6 MCM after the break, a drop of 37.2%. The Mann–Kendall test indicated significant downward trends for all variables (p < 0.05), but Sen's slope values for IFR and OFR were negligible, whereas the slope for RSV was -0.0483 MCM/day. Annual inflow volumes remained roughly constant (~50 MCM/year) across the two periods, confirming that storage decline was not caused by systematic inflow reduction. STL decomposition revealed that the trend component of RSV dropped sharply after 2015–2016, while the seasonal component remained stable throughout – indicating that the changes were non‑seasonal and structural in nature. Rolling correlation analysis showed that the correlation between IFR and RSV fell from about 0.68 in the early period to 0.22 after the break (collapse of the inflow–storage linkage), whereas the correlation between RSV and OFR increased from 0.41 to 0.79. This concurrent shift demonstrates a transition from an inflow‑driven operational regime to a storage‑driven regime, where release decisions increasingly depend on available storage rather than on incoming flows. Daily storage changes (ΔS) after the break exhibited larger interquartile range and negative skewness, indicating more frequent and rapid reservoir drawdowns. Continuous wavelet transform (CWT) revealed a striking shift: before 2015–2016, most wavelet power was concentrated at the annual scale (~365 days), reflecting long‑term planning and seasonal cycles. After the break, power shifted markedly toward shorter scales of 60–120 days, indicating dominance of reactive, short‑term decision‑making. The sensitivity test – removing irrigation months – showed that the downward trend of RSV remained statistically significant (p < 0.001) with only a slight reduction in Sen's slope, proving that seasonal agricultural releases were not the primary cause of the structural failure. Taken together, these multiple lines of quantitative evidence confirm that after water year 2015–2016 the Sefidrud Dam is no longer in a recoverable steady state and has experienced "stationarity failure." Conclusion This study provides convergent quantitative evidence – a ~37% storage decline, collapse of inflow–storage correlation, increased short‑term fluctuations, and a wavelet spectral shift from annual to 60–120‑day scales – demonstrating stationarity failure at the Sefidrud Dam. Annual inflow reduction played no decisive role; instead, endogenous system pressures (operational patterns, rising demand, managerial constraints) are the main drivers. The integrated analytical framework (change‑point test, trend analysis, STL, rolling correlation, and wavelet analysis) can serve as a general tool for dynamic health monitoring and early regime‑shift detection in other reservoir systems. Based on the findings, it is recommended to: (1) dynamically update reservoir performance curves to match the post‑failure regime; (2) integrate continuous wavelet analysis into early warning systems as a leading indicator of instability; (3) employ data‑driven and machine learning models (e.g., LSTM with SHAP) to restore or strengthen the functional inflow–storage linkage. Ultimately, this study highlights that dam performance assessment should not be limited to water deficit indicators or inflow trends; rather, "system dynamic health" and the stability of internal control linkages must be placed at the center of management and decision‑making. پایداری عملکرد مخازن بزرگ به توانایی آن‌ها در حفظ یک تعادل بلندمدت میان جریان ورودی، حجم ذخیره و جریان خروجی وابسته است. با این حال، شواهد فزاینده‌ای نشان می‌دهد که بسیاری از سامانه‌های مخزنی تحت فشارهای اقلیمی و مدیریتی، رفتار غیرایستا و تغییر رژیم را تجربه می‌کنند. در این مطالعه، دینامیک‌های عملیاتی سد سفیدرود با استفاده از داده‌های روزانه چهار متغیر کلیدی جریان ورودی (IFR)، حجم ذخیره مخزن (RSV)، تراز سطح آب (RWL) و جریان خروجی کل (OFR) در دوره ۱۶ سال آبی (۱۳۸۸–۱۴۰۴) مورد تحلیل قرار گرفت. برای شناسایی تغییرات ساختاری و رفتاری سامانه، مجموعه‌ای از روش‌های آماری و چندمقیاسی شامل آزمون نقطه تغییر Pettitt، آزمون روند Mann–Kendall همراه با شیبSen ، تجزیه STL، همبستگی پویای پنجره‌ای و تحلیل موجک پیوسته (CWT) به‌کار گرفته شد. نتایج نشان‌دهنده وقوع یک شکست ساختاری معنادار در حوالی سال آبی ۱۳۹۴–۱۳۹۵ است که با کاهش حدود ۳۷٪ حجم ذخیره مخزن، افت تراز سطح آب، فروپاشی همبستگی بین IFR و RSV و افزایش نوسانات کوتاه‌مدت همراه بوده است. تحلیل فصلی و آزمون حساسیت با حذف دوره آبیاری کشاورزی نشان داد که رهاسازی‌های فصلی، هرچند موجب تشدید نوسانات کوتاه‌مدت می‌شوند، عامل اولیه این تغییر رژیم نیستند. جابه‌جایی توان موجک RSV از مقیاس‌های سالانه به مقیاس‌های ۶۰–۱۲۰ روزه نیز بیانگر گذار سامانه از بهره‌برداری مبتنی بر برنامه‌ریزی بلندمدت به تصمیم‌گیری‌های واکنشی و کوتاه‌مدت است. این شواهد نشان می‌دهد که سد سفیدرود پس از سال ۱۳۹۴–۱۳۹۵ دیگر در یک حالت steady-state قابل بازگشت قرار ندارد و دچار «شکست ایستایی» شده است.

انجمن هیدرولیک ایران نشریه علمی هیدرولیک 2345-4237 21 3 2026 09 23 Predicting tunnel water inflow with FEM and nonlinear regression: effects of permeability anisotropy پیش‌بینی جریان آب ورودی به تونل با استفاده از روش اجزای محدود و برازش غیرخطی: اثرات ناهمسانگردی نفوذپذیری 248078 10.30482/jhyd.2026.582050.1767 FA امیر حسین شفیعی استادیار گروه مهندسی عمران، دانشکده مهندسی عمران و معماری، دانشگاه شهید چمران اهواز، ایران 0000-0003-3204-3737 سارینا احمدی دانشکده مهندسی عمران و معماری، دانشگاه شهید چمران اهواز محمد عزیزی پور دانشیار دانشکدۀ مهندسی عمران و معماری، دانشگاه شهید چمران اهواز 0000-0003-3895-0354 هادی فرهادیان دانشیار گروه مهندسی معدن، پردیس مهندسی، دانشگاه بیرجند، بیرجند Journal Article 2026 05 18 Introduction: The safe and cost-effective design and construction of tunnels need comprehensive geological, hydrological, environmental, geotechnical, and seismological information. Among the most critical challenges in tunneling is groundwater inflow into the underground excavation, particularly when the tunnel alignment lies below the water table. Several studies have focused on predicting the water inflow into tunnels using analytical methods (Freeze and Cherry 1979; Heuer 1995; El Tani 2003; Moon and Fernandez 2010), numerical simulations (Jing 2003; Aryafar et al. 2009; Butscher 2012; Aalianvari et al. 2013; Farhadian and Bahmani Shahraki 2024), and empirical approaches (McFeat-Smith et al. 1998; Katibeh and Aalianvari 2009; Farhadian and Katibeh 2017). Although extensive research has been conducted on tunnel inflow under the simplifying assumption of isotropic soil, only a limited number of studies have quantified tunnel inflow in the presence of anisotropic permeability. Accordingly, this study aims to determine the groundwater inflow rate into a circular tunnel embedded in an anisotropic medium across a wide range of influencing parameters using the finite element method. In addition, an equation is developed, using the nonlinear least square method, to estimate the inflow rate to a circular tunnel, without the need for numerical modeling of the domain. Methodology: This study aims at modeling flow into a circular tunnel and estimating the overall flowrate to the tunnel, using finite element method. The initial position of the groundwater table was defined by imposing fixed-head flow boundary conditions along the vertical boundaries. In contrast, a no-flow condition was applied at the bottom boundary. Regarding mechanical constraints, the vertical boundaries were restricted to vertical displacement only, thereby preventing any horizontal movement. The base boundary was fully fixed, restricting displacements in both the horizontal and vertical directions. Model dimensions are another critical factor that can significantly influence the computed flow rate. As the model extent increases, the water inflow rate initially decreases and then gradually converges toward a constant value (Moon and Fernandez 2010; Butscher 2012; Nikvar Hassani et al. 2016). Su et al. (2017), indicated that boundary effects can be neglected when the model extent, defined as the perpendicular distance from the tunnel center to the vertical and bottom boundaries, exceeds 50 times the tunnel diameter. In the present study, the maximum tunnel diameter considered was 12 m; therefore, a model extent of 600 m was adopted consistently for all cases. In the present study, the initial and final number of elements were set to 5000 and 50000, respectively, over five adaptive iterations. This means the analysis began with a coarse mesh of 5000 elements, which was automatically refined in successive iterations, ultimately reaching a mesh density of 50000 elements in the final step. Results and Discussion: The results indicated that increasing the horizontal to vertical permeability ratio (Kh/Kv) markedly enhances water flow rate (q); for instance, when Kv = 1 × 10⁻⁶ m/s, the inflow rate at Kh/Kv = 20 is nearly six times greater than Kh/Kv = 1. Thus, ignoring the permeability anisotropy could lead to a significant underestimation of the flow rate to the tunnel. It was seen that for a constant Kv, an increase in the anisotropy ratio results in a smoother and more gradual phreatic surface around the tunnel. In contrast, lower values of Kh/Kv lead to a steeper drawdown, indicating a more pronounced reduction in pore water pressure close to the tunnel boundary. I was also observed that for the highest anisotropy ratio, the phreatic line may even extend above the tunnel crown. Using a dataset produced by this verified model, a predictive model was developed to estimate the inflow rate (q) as a function of the anisotropy ratio using nonlinear least-squares regression. Statistical evaluation of the proposed model yielded the coefficient of determination R2 = 0.986, the root mean square error RMSE = 0.014, and the mean absolute percentage error MAPE = 5.56%, demonstrating the high predictive accuracy of the model. However, to quantitatively assess the goodness-of-fit of the proposed model, a hypothesis test was performed on the normalized residuals. In the present study, the z-test was employed, assuming the null hypothesis that the normalized residuals follow a normal distribution with a mean of zero and a standard deviation of one. The resulting p-value was 0.93, which is considerably higher than the significance level of α = 0.05, indicating that there is insufficient evidence to reject the null hypothesis. Conclusion: A total number of 500 finite element analyses were conducted to evaluate the effect of permeability anisotropy, considering anisotropy ratios (Kh/Kv) ranging from 1 to 20. The results indicated that as Kh/Kv increases, the inflow rate also increases. The anisotropy ratio was also found to affect the configuration of the phreatic line. Higher anisotropy ratios promote more pronounced horizontal flow, resulting in a gentler groundwater drawdown near the tunnel. Subsequently, a nonlinear least-squares regression was employed to develop a model for the water inflow rate in anisotropic media. The obtained results demonstrated a high level of accuracy of the model. احداث تونل یکی از اجزای اساسی زیرساخت‌های عمرانی در راستای توسعه پایدار کشورها به شمار می‌رود. رشد سریع جمعیت و افزایش تقاضا برای شبکه‌های نوین حمل‌ونقل، انتقال آب و انرژی و توسعه صنایع موجب افزایش مستمر نیاز به احداث تونل‌ها شده است. تونل‌ها اغلب در زیر سطح آب زیرزمینی ساخته می‌شوند؛ در چنین شرایطی، ارزیابی دقیق میزان جریان آب ورودی برای طراحی سیستم زهکشی ضروری است. در این پژوهش، نرخ جریان آب ورودی به تونل‌های دایره‌ای با استفاده از روش اجزای محدود و با در نظر گرفتن ناهمسانگردی نفوذپذیری محیط پیرامون، در دامنه وسیعی از پارامترهای ورودی، مورد ارزیابی قرار گرفت. سپس، یک مدل پیش‌بینی برای نرخ جریان ورودی با استفاده از روش حداقل مربعات غیرخطی توسعه داده شد. نتایج نشان داد که یک تابع توانی قادر است جریان ورودی را با دقت بالایی پیش‌بینی کند، به‌طوری‌که مقدار ضریب تعیین R2برابر با 986/0 بوده و مقادیر RMSE و MAE نیز پایین به دست آمدند. همچنین، با افزایش نسبت نفوذپذیری قائم به افقی، سطح ایستابی در مجاورت تونل شیب بیشتری پیدا می‌کند.

انجمن هیدرولیک ایران نشریه علمی هیدرولیک 2345-4237 21 3 2026 09 23 Numerical modeling of the performance of a rotating semicircular gate in a trapezoidal canal in free flow conditions مدل‌سازی عددی عملکرد دریچه نیم‌دایره‌ای دوار در کانال ذوزنقه‌ای با شرایط جریان آزاد 248079 10.30482/jhyd.2026.583794.1771 FA سمیرا یوسفی گروه مهندسی آب دانشگاه لرستان 0009-0009-5329-3146 حجت الله یونسی گروه مهندسی آب، دانشگاه لرستان 0000-0002-5145-6185 بابک شاهی نژاد گروه مهندسی آب دانشگاه لرستان 0000-0002-8756-7610 امیر حمزه حقی آبی گروه مهندسی آب دانشگاه لرستان 0000-0001-9512-0360 رسول دانشفراز گروه مهندسی عمران دانشگاه مراغه 0000-0003-1012-8342 Journal Article 2026 05 29 Introduction With population growth and the decline of water resources, optimal management of water resources, enhancement of hydraulic performance, and improvement of water distribution efficiency have become essential. Semi-circular radial gates require less force for operation due to their rotational movement around a vertical axis. On the other hand, Trapezoidal canals are the most common canal type used in irrigation and drainage networks due to their hydraulic and structural stability. Since Experimental studies are costly and time-consuming; therefore, numerical simulation is widely used to obtain reliable results for evaluating hydraulic behavior. Thus, the present study aims to numerically investigate the performance of a semi-circular rotating gate in a trapezoidal canal under free flow conditions using the Flow-3D software. The main objectives include evaluating turbulence models, analyzing stage-discharge relationships, identifying the inflection angle, and assessing energy losses for different wall slopes, transition lengths, and gate opening angles. The results of numerical model are validated by comparing simulation results with experimental data. If successfully validated, researchers can confidently use this numerical approach without costly experiments. Methodology sing galvanized steel sheets inside a rectangular flume, trapezoidal canals with bottom widths of 0.2, 0.3, and 0.4 m and corresponding side slopes of 0.44, 0.31, and 0.20 were constructed. To connect the canal to the semi-circular rotating gate, three gradual transition lengths of 0.6, 0.9, and 1.2 m were used.in the laboratory, Flow depth was measured by using a point gauge with an accuracy of 0.1 mm, discharge was measured with an electromagnetic flowmeter accurate to 0.01 lit/sec., and velocity measurements were conducted using a Velocity Profiler. Numerical modeling was performed using Flow-3D software. Gate opening angles ranged from 50° to 80° with 5° increments, and discharge rates ranged from 0.024 to 0.036 m³/s with 0.002 increments Mesh size was determined through a mesh convergence analysis. Using three turbulence models—standard k-ε, RNG, and LES—the water surface profile along the canal and the vertical velocity profile at the 2 m section were computed, and the best model for simulation was selected. Finally, using the numerical model results, the effects of variable parameters on water surface profiles, transverse profile variations, stage-discharge relationships, and energy loss were investigated and compared with experimental data. Results and Discussion Comparison of numerical and experimental results showed that all three turbulence models (standard k-ε, RNG k-ε, and LES) systematically underpredicted water depth and overpredicted velocity. This error arises from the isotropic Reynolds stress assumption in RANS models, which contradicts the highly anisotropic flow in the jet impingement zone. As wall slope decreases, flow moves more freely across the canal, increasing anisotropy. In the steep slope (0.44), flow converges at the canal centerline, reducing jet anisotropy. In the mild slope (0.20), jets move freely, creating a stronger impingement zone with higher anisotropy. LES, by directly resolving the three-dimensional flow structure, simulates this anisotropy better and performs superiorly for velocity profiles. However, RNG performs better for water surface profiles and energy loss due to its correction term in the dissipation rate equation. Downstream of the gate, impingement of flows from both sides creates turbulence and a hydraulic jump (hump), whose location depends on the gate opening angle. As opening angle increases, the upstream-downstream depth difference decreases, and turbulence reduces. Wall slope significantly affects the flow field; as slope decreases from 0.44 to 0.20, cross-sectional area increases, flow becomes less concentrated, and impingement intensifies, increasing turbulence. Canal slope dominates the effect of transition length. In longer transitions, flow becomes more uniform and fully developed, reducing downstream turbulence. In the steep slope (0.44), increasing transition length has little effect. Maximum energy loss occurs at L=0.6 m. As bottom width increases (slope decreases), flow capacity decreases, and the stage-discharge curve slope increases, meaning small discharge changes cause significant depth changes. At small opening angles, the gate acts like an orifice with very low flow efficiency. As opening angle increases, outlet area and flow capacity increase. The results indicate a change in the hydraulic behavior of the flow within the 60-65degree range. Conclusion Comparison of numerical and experimental results showed that no single turbulence model is superior in all aspects. The appropriate model should be selected based on the output required. Flow behavior strongly depends on side slope. In the mild slope (0.20), jets impinge with maximum energy, creating a highly turbulent zone with non-uniform Reynolds stress distribution. As gate opening angle increases, the stage-discharge curve slope decreases. At small angles, the gate acts as an orifice. Numerical model predictions showed good agreement with experimental data. با توجه به کاربرد گسترده کانال‌های ذوزنقه‌ای در شبکه‌های انتقال و توزیع آب، هدف این پژوهش بررسی عملکرد هیدرولیکی دریچه نیم‌دایره‌ای دوار نصب‌شده در یک کانال ذوزنقه‌ای با استفاده از نرم‌افزار FLOW-3D است. مدل‌سازی عددی بر اساس داده‌های آزمایشگاهی برای کانالی با سه شیب دیواره جانبی و سه طول تبدیل تدریجی در محل اتصال کانال به دریچه انجام شد. در این مطالعه، اثر زاویه بازشدگی دریچه، طول تبدیل تدریجی، شیب دیواره جانبی و دبی جریان بر پروفیل سطح آب، منحنی دبی–اشل و افت کل انرژی بررسی شد. مقایسه مدل‌های آشفتگی نشان داد که مدل RNG در مقایسه با مدل‌های LES و K-ε، با خطایی کمتر از ۱۰ درصد، دقت بیشتری در پیش‌بینی پروفیل سطح آب دارد. نتایج همچنین نشان داد که شیب دیواره جانبی مهم‌ترین پارامتر مؤثر بر رفتار هیدرولیکی جریان است و میزان تأثیر طول تبدیل تدریجی به شیب دیواره جانبی وابسته است؛ به‌گونه‌ای که در کانال‌هایی با شیب جانبی بیشتر، افزایش طول تبدیل تأثیر قابل‌توجهی بر پارامترهای هیدرولیکی ندارد. منحنی دبی–اشل نیز بیانگر تغییر رفتار هیدرولیکی جریان در محدوده زاویه بازشدگی ۶۰ تا ۶۵ درجه است. علاوه بر این، نتایج تحلیل آماری نشان داد که مدل عددی توانسته است منحنی دبی–اشل و افت کل انرژی را با دقتی بیش از ۹۰ درصد شبیه‌سازی کند.