Search Results (327)

Various nature-based solutions (NbS)—such as constructed wetlands, drainage ditches, and vegetated buffer strips—have recently demonstrated strong potential for mitigating pollutant transport in open channels and river systems. Numerical modeling is a widely adopted and effective approach for assessing the performance of these interventions. This study presents the first development of a two-dimensional (2D) meshless advection–diffusion model based on an Eulerian smoothed particle hydrodynamics (SPH) framework, specifically designed to simulate passive pollutant transport in open channel flows. The proposed model marks a pioneering application of the ESPH technique to environmental pollutant transport problems. It couples the 2D depth-averaged shallow water equations with an advection–diffusion equation to represent both fluid motion and pollutant concentration dynamics. A uniform particle arrangement ensures that each fluid particle interacts symmetrically with eight neighboring particles for flux computation. To represent the pollutant transport process, the dispersion coefficient is defined as the sum of molecular and turbulent diffusion components. The turbulent diffusion coefficient is calculated using a prescribed turbulent Schmidt number and the eddy viscosity obtained from a Smagorinsky-type mixing-length turbulence model. Three analytical case studies, including one-dimensional transcritical open channel flow, 2D isotropic and anisotropic diffusion in still water, and advection–diffusion in a 2D uniform flow, are employed to verify the model’s accuracy and convergence. The model demonstrates first-order convergence, with relative root mean square errors (RRMSEs) of approximately 0.2% for water depth and velocity, and 0.1–0.5% for concentration. Additionally, the model is applied to a laboratory experiment involving 2D pollutant dispersion in a 90° junction channel. The simulated results show good agreement with measured velocity and concentration distributions. These findings indicate that the developed model is a reliable and effective tool for evaluating the performance of NbS in mitigating pollutant transport in open channels and river systems. Full article

Fluid dispersion directly influences the transport, mixing, and efficiency of hydrogen storage in depleted gas reservoirs. Pore structure parameters, such as pore size, throat geometry, and connectivity, influence the complexity of flow pathways and the interplay between advective and diffusive transport mechanisms. Hence, these factors are critical for predicting and controlling flow behavior in the reservoirs. Despite its importance, the relationship between pore structure and dispersion remains poorly quantified, particularly under elevated flow conditions. To address this gap, this study employs pore network modeling (PNM) to investigate the influence of sandstone and carbonate structures on fluid flow properties at the micro-scale. Eleven rock samples, comprising seven sandstone and four carbonate, were analyzed. Pore network extraction from CT images was used to obtain detailed pore structure parameters and their statistical measures. Pore-scale simulations were conducted across 60 scenarios with varying average interstitial velocities and water as the injected fluid. Effluent hydrogen concentrations were measured to generate elution curves as a function of injected pore volumes (PV). This approach enables the assessment of the relationship between the dispersion coefficient and pore structure parameters across all rock samples at consistent average interstitial velocities. Additionally, dispersivity and n-exponent values were calculated and correlated with pore structure parameters. Full article

This study presents the implementation of a scalar transport algorithm in the recently developed General Ocean Model (GOM), a three-dimensional, unstructured grid, finite volume/finite difference model. Solving the advection–diffusion transport equation is an essential part of any ocean circulation model since the baroclinic density gradient distinguishes saline water from freshwater. To achieve both high accuracy and computational efficiency, we adopted a second-order semi-implicit Total Variation Diminishing (TVD) scheme. The TVD approach, known for its ability to suppress non-physical oscillations near steep gradients, provides a higher-fidelity representation of salinity fronts without introducing significant numerical artifacts. The TVD algorithm is constructed with the first-order Upwind scheme, which is known for suffering from excessive numerical diffusion, and the higher-order anti-diffusive flux term. The implemented transport algorithm is evaluated using two standard test cases, an ideal lock exchange problem and a U-shaped channel problem, and it is further applied to simulate salinity dynamics in Mobile Bay, Alabama. The model results from both the first-order Upwind and second-order TVD schemes are compared. The results indicate that the TVD scheme marginally improves the resolution of salinity fronts while maintaining computational stability and efficiency. The implementation enables a flexible and straightforward transition between the first-order scheme, which is faster than the second-order scheme, and the second-order scheme, which is less diffusive than the first-order scheme, enhancing the GOM’s capability for realistic and efficient salinity simulations in a tidally driven estuarine system. Full article

Dredging of fine sediments and dumping of fines at disposal sites produce passive plumes behind the dredging equipment. Each type of dredging method has its own plume characteristics. All types of dredging operations create some form of turbidity (spillage of dredged materials) in the water column, depending on (i) the applied method (mechanical grab/backhoe, hydraulic suction dredging with/without overflow), (ii) the nature of the sediment bed, and (iii) the hydrodynamic conditions. A simple parameter to represent the spillage of dredged materials is the spill percentage (R_spill) of the initial load. In the case of cutter dredging and hopper dredging without overflow, sediment spillage is mostly low, with values in the range of 1% to 3%, The spill percentage is higher, in the range of 3% to 30%, for hopper dredging of mud with intensive overflow. Spilling of dredged materials also occurs at disposal sites. The spill percentage is generally low, with values in the range of 1% to 3%, if the load is dumped through bottom doors in deep water, creating a dynamic plume which descends rapidly to the bottom with cloud velocities of 1 m/s. The most accurate approach to study passive plume behavior is the application of a 3D model, which, however, is a major, time-consuming effort. A practical 1D plume dispersion model can help to identify the best parameter settings involved and to conduct fast scan studies. The proposed 1D model represents equations for dynamic plume behavior, as well as passive plume behavior including advection, diffusion and settling processes. Full article

This study enhances the classical deterministic SIR model by incorporating soliton-like dynamics and gradient-induced diffusion, effectively capturing the complex spatiotemporal patterns of disease transmission within nomadic populations. The proposed model incorporates an advection–diffusion mechanism that modulates the spatial gradients in infection dynamics, transitioning from highly localized infection peaks to distributed infection fronts. We discussed the role of diffusion coefficients in shaping the spatial distribution of susceptible, infected, and recovered populations, as well as the impact of gradient-induced advection in mitigating epidemic intensity. Numerical simulations demonstrate the effects of varying key parameters such as transmission rates, recovery rates, and advection–diffusion coefficients on the epidemic’s progression. The soliton-like dynamics ensure the stability of infection waves over time, specifying targeted intervention strategies such as localized quarantines and vaccination campaigns. This model underscores the critical importance of spatial heterogeneity and mobility patterns in managing infectious diseases. The applicability of the model has been tested using the AIDS data from the last 25 years. Full article

Various numerical techniques have been developed to address multiple problems in computational fluid dynamics (CFD). The finite volume method (FVM) is a numerical technique used for solving partial differential equations that represent conservation laws by dividing the domain into control volumes and ensuring flux balance at their boundaries. Its conservative characteristics and capability to work with both structured and unstructured grids make it suitable for addressing issues related to fluid flow, heat transfer, and diffusion. This article introduces an FVM for the linear advection and nonlinear Burgers’ equations through a fifth-order targeted essentially non-oscillatory (TENO5) scheme. Numerical experiments showcase the precision and effectiveness of TENO5, emphasizing its benefits for computational fluid dynamics (CFD) simulations. Full article

This study utilized the FVCOM model to establish a hydrodynamic model for the waters from Haikou to Danzhou. Based on this framework, a numerical model for oil spill drift and diffusion was developed using the Lagrangian particle method, incorporating processes such as advection, diffusion, spreading, emulsification, dissolution, volatilization, and shoreline adsorption. Sea experiments involving drifters and dye were conducted to validate the oil spill model. The model was subsequently applied to analyze the impacts of tidal phases and wind fields on oil spill trajectories, predict affected areas, and assess risks to environmentally sensitive zones. The results demonstrate that the hydrodynamic model accurately reproduces the tidal current characteristics of the study area. Validation using drifter and dye experiments confirmed that the model’s predictive error remains within 20%, meeting operational forecasting standards. Potential sources of error include uncertainties in wind–wave–current interactions and discrepancies in windage coefficients between oil spills and drifters. Tidal currents and wind fields were identified as the dominant drivers of oil spill drift and diffusion. Under southerly wind conditions, the oil spill exhibited the largest spatial extent, covering 995.25 km² with a trajectory length of 226.92 km. A sensitivity analysis highlighted the Lingao Silverlip Pearl Oyster Marine Protected Area and Shatu Bay Beach as high-risk regions. The developed model provides critical technical support for oil spill emergency response under diverse environmental conditions, enabling proactive pathway forecasting and preventive measures to mitigate ecological damage. Full article

The emergence of exascale computing systems presents both opportunities and challenges in scientific computing, particularly for complex mathematical models requiring high-performance implementations. This paper addresses these challenges in the context of biomedical applications, specifically focusing on tumor angiogenesis modeling. We present a parallel implementation for solving a system of partial differential equations that describe the dynamics of tumor-induced blood vessel formation. Our approach leverages the Julia programming language and its CUDA capabilities, combining a high-level paradigm with efficient GPU acceleration. The implementation incorporates advanced optimization strategies for memory management and kernel organization, demonstrating significant performance improvements for large-scale simulations while maintaining numerical accuracy. Experimental results confirm the performance gains and reliability of the proposed parallel implementation. Full article

Empirical equations were developed by many investigators to determine the reaeration coefficients (Ka) required for predicting dissolved oxygen concentrations (DO) in surface waters, especially rivers, lakes, and reservoirs. However, these equations yield a wide range of Ka values. In this paper, an integrated numerical-modeling-based technique was developed to check the validity of the equations before using them in water quality modeling for rivers, lakes, and reservoirs. Depending on direct field measurements at the Hilla River headwater (Saddat Al-Hindiyah Reservoir, Iraq), the temporal oxygen mass transport at the water surface was estimated numerically by solving the one-dimensional advection diffusion equation and then using each Ka empirical equation separately in the numerical model obtained the best specific-waterbody equation. The DO modeling results showed that using a reservoir reaeration coefficient of 0.1 day⁻¹ at 20 °C predicts the best DO simulation with low MAEs of 0.4987 and 0.7880 mg/L during the study years 2021 and 2022, respectively, compared to the field data. However, using the Ka empirical equations simulates the DO with wide-ranging statistical errors even though the temporal Ka values have a similar trend during the year. It was noticed that the empirical equations produced maximum Ka values of (0.0080–0.0967 day⁻¹) and minimum Ka values of (0.00052–0.0267 day⁻¹) in 2021 and maximum Ka values of (0.0079 to 0.0951 day⁻¹) and minimum Ka values of (0.00012 and 0.0231 day⁻¹) in 2022. The present equation selection technique revealed that Broecker et al.’s equation followed by Smith’s equation, developed in 1978, are the best selection for water quality modeling at the Hilla River headwater (MAEs: 0.1347 and 0.1686 mg/L in 2021, respectively; and MAEs: 0.1400 and 0.1744 mg/L in 2022, respectively). Hence, it is necessary to find good agreement for the equation-based prediction of DO, DO source–sink, and Ka values compared to the validated model before making selection. Full article

Oil spills represent a critical environmental hazard with far-reaching ecological and economic consequences, necessitating the development of sophisticated modelling approaches to predict, monitor, and mitigate their impacts. This study presents a computationally efficient and physically grounded modelling framework for simulating oil spill drift in marine environments, developed using Python coding. The proposed model integrates core physical processes—advection, diffusion, and degradation—within a simplified partial differential equation system, employing an integrator for numerical simulation. Building on recent advances in marine pollution modelling, the study incorporates real-time oceanographic data, satellite-based remote sensing, and subsurface dispersion dynamics into an enriched version of the simulation. The research is structured in two phases: (1) the development of a minimalist Python model to validate fundamental oil transport behaviours, and (2) the implementation of a comprehensive, multi-layered simulation that includes NOAA ocean currents, 3D vertical mixing, and support for inland and chemical spill modelling. The results confirm the model’s ability to reproduce realistic oil spill trajectories, diffusion patterns, and biodegradation effects under variable environmental conditions. The proposed framework demonstrates strong potential for real-time decision support in oil spill response, coastal protection, and environmental policy-making. This paperwork contributes to the field by bridging theoretical modelling with practical response needs, offering a scalable and adaptable tool for marine pollution forecasting. Future extensions may incorporate deep learning algorithms and high-resolution sensor data to further enhance predictive accuracy and operational readiness. Full article

This study introduces a novel one-dimensional Fractional Time–Space Stochastic Advection–Diffusion Equation that revolutionizes the modeling of moisture transport within atmospheric boundary layers adjacent to oceanic surfaces. By synthesizing fractional calculus, advective transport mechanisms, and pink noise stochasticity, the proposed model captures the intricate interplay between temporal memory effects, non-local turbulent diffusion, and the correlated-fluctuations characteristic of complex ocean–atmosphere interactions. The framework employs the Caputo fractional derivative to represent temporal persistence and the fractional Laplacian to model non-local turbulent diffusion, and incorporates a stochastic term with a $1/f$ power spectral density to simulate environmental variability. An efficient numerical solution methodology is derived utilizing complementary Fourier and Laplace transforms, which elegantly converts spatial fractional operators into algebraic expressions and yields closed-form solutions via Mittag–Leffler functions. This method’s application to a benchmark coastal domain demonstrates that stronger advection significantly increases the spatial extent of conditions exceeding fog formation thresholds, revealing advection’s critical role in moisture transport dynamics. Numerical simulations demonstrate the model’s capacity to reproduce both anomalous diffusion phenomena and realistic stochastic variability, while convergence analysis confirms the numerical scheme’s robustness against varying noise intensities. This integrated fractional stochastic framework substantially advances atmospheric moisture modeling capabilities, with direct applications to meteorological forecasting, coastal climate assessment, and environmental engineering. Full article

Robust epidemiological models are essential for managing COVID-19, especially in diverse urban settings. In this study, we present a fractional advection–diffusion–reaction model to analyze COVID-19 spread in three major Turkish cities: Ankara, Istanbul, and Izmir. The model employs a Caputo-type time-fractional derivative, with its order dynamically determined by the Hurst exponent, capturing the memory effects of disease transmission. A nonlinear reaction term models self-reinforcing viral spread, while a Gaussian forcing term simulates public health interventions with adjustable spatial and temporal parameters. We solve the resulting fractional PDE using an implicit finite difference scheme that ensures numerical stability. Calibration with weekly case data from February 2021 to March 2022 reveals that Ankara has a Hurst exponent of 0.4222, Istanbul 0.1932, and Izmir 0.6085, indicating varied persistence characteristics. Distribution fitting shows that a Weibull model best represents the data for Ankara and Istanbul, whereas a two-component normal mixture suits Izmir. Sensitivity analysis confirms that key parameters, including the fractional order and forcing duration, critically influence outcomes. These findings provide valuable insights for public health policy and urban planning, offering a tailored forecasting tool for epidemic management. Full article

This article presents a new approach to solving fuzzy advection–diffusion equations using double fuzzy transforms, called the double fuzzy Yang–General transform. This unique double fuzzy transformation is a combination of single fuzzy Yang and General transforms. Some of the basic properties of this new transform include existence and linearity and how they relate to partial derivatives. A solution framework for the linear fuzzy advection–diffusion equation is developed to show the application of the double fuzzy Yang–General transform. To illustrate the proposed method for solving these equations, we have included a solution to a numerical problem. Full article

Longitudinal dispersion coefficient is a key parameter governing solute transport in porous media, with significant implications for various industrial processes. However, the impact of microfractures on the longitudinal dispersion coefficient remains insufficiently understood. In this study, pore-scale direct numerical simulations are performed to analyze solute transport in microfractured porous media during unstable miscible displacement. Spatiotemporal concentration profiles were fitted to the analytical solution of the convection–dispersion equation to quantify the longitudinal dispersion coefficient across different microfracture configurations. The results indicate that the longitudinal dispersion coefficient is highly sensitive to microfracture characteristics. Specifically, an increased projection length of microfractures in the flow direction and a reduced lateral projection length enhance longitudinal dispersion at the outlet. When Peclet number ≥1, the longitudinal dispersion coefficient follows a three-stage variation pattern along the flow direction, with microfracture connectivity and orientation dominating its scale sensitivity. Furthermore, both diffusion-dominated and mixed advective-diffusion regimes are observed. In diffusion-dominated regimes, significant channeling alters the applicability of traditional scaling laws, with the relationship between longitudinal dispersion coefficient and porosity holding only when the Peclet number is below 0.07. These results provide a comprehensive scale-up framework for CO₂ miscible flooding in unconventional reservoirs and CO₂ storage in saline aquifers, offering valuable insights for the numerical modeling of heterogeneous reservoir development. Full article

Urumqi is located at the northern foot of the Tianshan Mountains. Its topographical features have a significant impact on the transport and dispersion of air pollutants. Moreover, its winter is extremely long, lasting up to six months. A combination of an irrational energy consumption structure, unique meteorological conditions, and complex geographical terrains has led to a substantial increase in NO₂ emissions, severely damaging the local ecological environment. In this study, we integrate Geographic Information System (GIS) and Computational Fluid Dynamics (CFD). By leveraging GIS’s powerful spatial analysis capabilities and CFD’s high-precision fluid simulation technology, we significantly enhance the simulation accuracy of complex phenomena like airflow and pollutant diffusion. Additionally, the inverse distance weighted interpolation method is comprehensively employed to analyze the Air Quality Indices (AQIs) of typical pollutants in different districts of Urumqi during winter. The results reveal that high altitude causes instability of the dominant near-surface winds within the atmospheric boundary layer. The increasing frequency of surface calm winds reduces the advective transport of atmospheric pollutants. Topography and winter meteorological conditions are identified as the primary factors contributing to pollutant accumulation. This research not only unveils the fundamental mechanisms of pollutant dispersion in mountainous terrains but also validates the practicality of coupling GIS and CFD, providing a theoretical basis for pollution dispersion studies in this region. This study reveals the general laws of pollutant dispersion in mountainous terrain, resolves the issue of establishing complex geographical models, and demonstrates the feasibility of coupling the GIS and CFD. Meanwhile, it provides a theoretical basis for pollution dispersion in this region. Full article