Search Results (343)

The prediction of deep-sea mining sediment plumes is essential for assessing and mitigating the environmental impacts on vulnerable deep-sea ecosystems. In this paper, the numerical simulation method is adopted to predict the sediment plume transportation. Fluid dynamics are governed by the incompressible Navier–Stokes equations, coupled with the Standard k–ε turbulence model to capture turbulent diffusion. The air–water free surface is tracked by a high-resolution Volume of Fluid (VOF) method. The pressure–velocity coupling utilizes the PISO algorithm. Sediment transport is governed by the advection–diffusion equation. The mathematical model is validated through experiments. There is a good consistency between the experiment results and the numerical results, which proves that the numerical method can be applied. The study calculates the diffusion range and characteristics of plumes under different free stream velocities, injection velocities and discharge densities. The results indicate that an increase in free stream velocity enhances the development of turbulence, but conversely restricts the expansion of the mixing zone between the plume and the ambient water. A greater injection velocity leads to a wider distribution range of the plume, while inhibiting the development of local turbulence. A higher plume discharge density results in a larger horizontal distribution range, while hindering the effective mixing between the plume and the ambient water body. Full article

Advection–diffusion–reaction-type interface models have wide-ranging applications in environmental science, chemical engineering, and biological systems, particularly in modeling pollutant transport in groundwater, reactive flows, and drug diffusion across biological membranes. This paper presents a novel numerical method for the solution of these models. The proposed method integrates the meshless collocation technique with the finite difference method. The temporal derivative is approximated using a finite difference scheme, while spatial derivatives are approximated using radial basis functions. The interface across the fixed boundary is treated with discontinuous diffusion, advection, and reaction coefficients. The proposed numerical scheme is applied to both linear and non-linear models. The Gauss elimination method is used for the linear models, while the quasi-Newton linearization method is employed to address the non-linearity in non-linear cases. The $L_{\infty }$ error is computed for varying numbers of collocation points to assess the method’s accuracy. Furthermore, the performance of the method is compared with the Haar wavelet collocation method and the immersed interface method. Numerical results demonstrate that the proposed approach is more efficient, accurate, and easier to implement than existing methods. The technique is implemented in MATLAB R2024b software. Full article

Microplastic pollution in riverine ecosystems poses critical environmental challenges, yet current modeling approaches inadequately capture the spatial heterogeneity and topological complexity of fluvial systems. This study develops an innovative spatiotemporal graph convolutional network (ST-GCN) framework that integrates hydrological connectivity, flow parameters, and microplastic characteristics for simultaneous migration pathway identification and pollution source tracing. This model constructs multi-scale graph representations encoding system structure and transport dynamics, implements spatial-temporal convolution layers with adaptive attention mechanisms, and employs a backpropagation-based algorithm for inverse source identification. Validation using 18 months of field observations from 45 monitoring nodes across a 127 km river reach demonstrates 87.3% pathway prediction accuracy and 94.3% source localization accuracy (R² = 0.841, p < 0.001), representing substantial improvements over conventional advection–diffusion models. The framework successfully identified three pollution sources during a real contamination incident within 6 h of detection, enabling rapid regulatory intervention. This research advances environmental modeling by demonstrating that graph neural networks effectively capture transport processes in networked hydrological systems, providing practical tools for watershed management and evidence-based pollution control decision-making. Full article

Accurate simulation of boundary layer wind field structures is essential for evaluating tropical cyclone (TC) wind hazards and supporting engineering design in coastal regions. However, existing models often assume radially symmetric and homogeneous surface conditions, leading to limited accuracy near landfall where surface roughness varies significantly. This study conducts a comprehensive evaluation of four representative TC boundary layer models of M95, K01, Y21a, and Y21b, under both idealized and real TC case conditions. The idealized experiments are used to clarify the role of vertical advection and turbulent diffusion in shaping the TC boundary layer, while the landfalling case of Typhoon Mangkhut (2018) is simulated to examine the impacts of surface roughness parameterization. Results show that Y21a, which incorporates nonlinear vertical advection, produces stronger and more realistic super-gradient phenomenon than linear models of M95 and K01. Furthermore, the model of Y21b, which accounts for spatially varying drag coefficients and using a terrain-following coordinate system, successfully reproduces the asymmetric wind patterns observed in the WRF simulations during landfall, achieving the highest correlation (R = 0.93). When the spatially varying drag coefficients incorporated into the linear models, their correlation with WRF improved markedly by about 37%. These findings highlight the necessity of incorporating nonlinear advection, dynamic turbulence, and surface heterogeneity for physically consistent TC boundary layer simulations. The results provide valuable guidance for improving parametric wind field models and enhancing TC wind hazard assessments over complex coastal terrains. Full article

In this work, we propose a new physics-informed neural network framework based on the method of separation of variables (SVPINN) to solve the distributed-order time-fractional advection–diffusion equation. We develop a new method for calculating the distributed-order derivative, which enables the fractional integral to be modeled by a network and directly solved by combining automatic differentiation technology. In this way, the approximation of the distributed-order derivative is integrated into the parameter training system of the network, and the data-driven adaptive learning mechanism is used to replace the numerical discretization scheme. In the SVPINN framework, we decompose the kernel function of the Caputo integral into three independent functions using the method of separation of variables, and apply a neural network as a surrogate model for the modified integral and the function related to the time variable. The new physical constraint generated by the modified integral serves as an extra supervised learning task for the network. We systematically evaluated the feasibility of the SVPINN on several numerical experiments and demonstrated its performance. Full article

The role of sedimentary heterogeneity in reactive transport processes is becoming increasingly important as closed open-pit lignite mines are converted into post-mining lakes or pumped hydropower storage reservoirs. Flooding of the open pits introduces constant oxygen-rich inflows that reactivate pyrite oxidation within internal mine dumps. A reactive transport model coupling groundwater flow, advection–diffusion–dispersion, and geochemical reactions was applied to a 2D cross-section of a water-saturated mine dump to determine the processes governing pyrite oxidation. Spatially correlated fields representing permeability and pyrite distributions were generated via exponential covariance models reflecting the end-dumping depositional architecture, supported by a suite of scenarios with systematically varied correlation lengths and variances. Simulation results covering a time span of 100 years quantify the impact of heterogeneous permeability fields that result in preferential flow paths, which advance tracer breakthrough by ~15 % and increase the cumulative solute outflux up to 139 % relative to the homogeneous baseline. Low initial pyrite concentrations (0.05 wt %) allow for deeper oxygen penetration, extending oxidation fronts over the complete length of the modeling domain. Here, high initial pyrite concentrations (0.5 wt %) confine reactions close to the inlet. Kinetic oxidation allows for more precise simulation of redox dynamics, while equilibrium assumptions substantially reduce the computational time (>10×), but may oversimplify the redox system. We conclude that reliable risk assessments for post-mining redevelopment should not simplify numerical models by assuming average homogeneous porosity and mineral distributions, but have to incorporate site-specific spatial heterogeneity, as it critically controls acid generation, sulfate mobilization, and the timing of contaminant release. Full article

The rational placement of pollutant monitoring sensors has long been a prominent research focus in ocean environment science. Our method integrates an incremental Proper Orthogonal Decomposition with a mobility-constrained sensor selection strategy, enabling efficient monitoring and dynamic adaptation to spatio-temporal field changes. At each time step, the position of the sensors is updated based on the incoming measurements to minimize the reconstruction error while adhering to movement constraints. This online approach considers the need for mobility distance, making it suitable for long-term deployments in resource-limited scenarios. The proposed framework is validated in three scenarios: a linear advection–diffusion system with multiple moving pollution sources, the distribution of particulate matter with an aerodynamic diameter smaller than 2.5 μm (PM2.5) across the United States, and scalar transport in flows past side-by-side cylinder arrays in the ocean. The results demonstrate that the method achieves high reconstruction accuracy with significantly fewer sensors. This study conducts a comparative analysis of three typical mobility constraints and their respective effects on reconstruction accuracy. In addition, the proposed localized sensor mobility strategy effectively tracks evolving plume structures and maintains a low approximation error, providing a generalizable solution for sparse monitoring of the marine environment. Full article

Urban shallow lakes are sentinel ecosystems whose stability is increasingly threatened by acute, sediment-laden storm floods. While chronic nutrient loading has been extensively studied, rapid risk assessment tools for short-pulse disturbances are still missing. Our aim was to develop a resilience-based, process-linked framework that couples depth-averaged hydrodynamics, advection-diffusion sediment transport and light-driven macrophyte habitat suitability to quantify hour-scale ecological risk and week-scale recovery. The ecological risk model integrates a depth-averaged hydrodynamic module, an advection–diffusion sediment transport routine, and species-specific light-suitability functions. We tested the model against field observations from Xinglong Lake (Chengdu, China) under 5-year and 50-year design storms. Ecological risk exhibited a clear west-to-east gradient. Under the 5-year storm, high-risk cells (complete inhibition) formed a narrow band at the eastern inlet and overlapped 82% with the SSC > 0.1 kg m⁻³ plume at 6 h; several western macrophyte beds returned to “suitable” status by 72 h. In contrast, the 50-year event pushed R > 0.9 over all macrophyte beds, with slow recovery after 192 h. Lake-scale risk peaked above 80% within 24 h for both return periods, but residual risk remained elevated in the 50-year scenario owing to the larger spatial footprint. The study provides a transferable early-warning tool for lake managers to decide when to trigger low-cost interventions and species-specific resilience rankings to guide targeted vegetation protection in shallow urban lakes worldwide. Full article

Mineral dust plays a vital role in the Earth’s climate system, influencing radiation, cloud formation, biogeochemical cycles, and air quality. Accurately simulating dust transport in atmospheric models remains challenging, particularly for coarse and super-coarse particles, which are often underrepresented due to limitations in model physics and numerical treatment. Observations have shown that particles larger than 20 μm can remain airborne longer than expected, suggesting that standard gravitational settling formulations may be insufficient. One potential contributor to this discrepancy is the numerical diffusion introduced by advection schemes used to model sedimentation processes. In this study, we compare the commonly used first-order upwind advection scheme, which is highly diffusive, to a third-order scheme (UNO3) that reduces numerical diffusion while maintaining computational efficiency. Using 2-D sensitivity tests, we show that UNO3 retains up to 50% more dust mass for the coarsest particles compared to the default scheme, although overall dust lifetime shows little change. In 3-D simulations of the ASKOS 2022 dust campaign, both schemes reproduced similar large-scale dust patterns, with UNO3 yielding slightly lower dust. Overall, domain-averaged dust load differences remain small (less than 2%), with minor decreases in fine dust ~3% and slight increases in coarse dust ~2%, indicating that reducing numerical diffusion modestly enhances the presence of larger particles. Near the surface, UNO3 produces a ~4% increase in dust concentration, with local differences up to 50 μg/m³. These results highlight that while numerical diffusion does affect dust transport—especially for super-coarse fractions—its impact is relatively small compared to the larger underestimation of super-coarse dust commonly observed in models compared to measurements. Addressing the fundamental physics of super-coarse dust emission and lofting may therefore be a higher priority for improving dust model fidelity than further refining advection numerics. Future studies may also consider implementing more computationally intensive schemes, such as the Prather scheme, to further minimize numerical diffusion where highly accurate size-resolved transport is critical. Full article

Reconstructing the deep water salinity during the Last Glacial Maximum (LGM, 26.5~19 ka BP), corresponding to Marine Isotope Stage 2, the most recent and coldest period, is crucial for understanding glacial deep ocean circulation variation and its effect on the climate. The South China Sea (SCS) is one of the largest marginal seas in the western Pacific Ocean, where LGM deep water salinity reconstruction remains unexplored. This study employs pore water [Cl⁻] profiles acquired from boreholes of Site U1499 of IODP Expedition 367 and Sites U1431 and U1433 of IODP Expedition 349 to reconstruct the LGM salinity in the deep SCS. Utilizing a one-dimensional diffusion-advection numerical model, the LGM salinity of the deep northern SCS is determined to be 35.68 ± 0.04 g/kg, and that of the deep central SCS is 35.61 ± 0.03 g/kg, revealing an intra-basin salinity gradient of ~0.07 g/kg. LGM salinity gradients within the SCS were reduced relative to modern ones, indicating attenuated deep circulation within the SCS during the LGM. Furthermore, a diminished salinity gradient (Δ = 0.02 g/kg) across the Luzon Strait between the SCS and Pacific and an enhanced vertical stratification between Upper Circumpolar Deep Water (UCDW) and Lower Circumpolar Deep Water (LCDW) collectively support a sluggish deep Pacific circulation during the LGM. Full article

Accurate precipitation nowcasting is essential for short-term forecasting, but it remains challenging due to the dynamic nature of rainfall mechanisms. This study implements and evaluates two schemes for improving precipitation nowcasting: (1) an advection–diffusion scheme and (2) an advection–diffusion scheme integrated with the linear theory of orographic precipitation. These schemes are implemented into the Local Analysis and Prediction System (LAPS) to produce short-term precipitation forecasts and applied to a case study involving a rainfall event over the Athens metropolitan area in Greece. These schemes are compared against the default LAPS nowcasting module based on a first-order advection scheme (control). The first-order advection scheme, while computationally efficient, lacks the ability to simulate rainfall field evolution due to its exclusion of diffusion processes and orographic effects, leading to inaccurate nowcasts. To address these limitations, the advection–diffusion scheme is introduced to capture the precipitation evolution, and the third scheme integrates the linear theory of orographic precipitation to account for the influence of topography. Preliminary results show improvements in the spatiotemporal distribution of the nowcasted precipitation. These findings suggest that incorporating diffusion and orographic effects can enhance the accuracy of short-term precipitation forecasts, though further evaluation across diverse meteorological events is needed to confirm general applicability. Full article

This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially symmetric periodic boundary conditions, achieving exponential convergence and reduced computational cost compared to traditional methods. The FGIG method uniquely combines Fourier series for spatial periodicity and Gegenbauer polynomials for temporal integration within a Galerkin framework, resulting in highly accurate numerical and semi-analytical solutions. Unlike traditional approaches, this method eliminates the need for time-stepping procedures by reformulating the problem as a system of integral equations, reducing error accumulation over long-time simulations and improving computational efficiency. Key contributions include exponential convergence rates for smooth solutions, robustness under oscillatory conditions, and an inherently parallelizable structure, enabling scalable computation for large-scale problems. Additionally, the method introduces a barycentric formulation of the shifted Gegenbauer–Gauss (SGG) quadrature to ensure high accuracy and stability for relatively low Péclet numbers. This approach simplifies calculations of integrals, making the method faster and more reliable for diverse problems. Numerical experiments presented validate the method’s superior performance over traditional techniques, such as finite difference, finite element, and spline-based methods, achieving near-machine precision with significantly fewer mesh points. These results demonstrate its potential for extending to higher-dimensional problems and diverse applications in computational mathematics and engineering. The method’s fusion of spectral precision and integral reformulation marks a significant advancement in numerical PDE solvers, offering a scalable, high-fidelity alternative to conventional time-stepping techniques. Full article

One of the key tasks in the geological disposal of radioactive waste is to investigate the blocking ability of different host rocks on nuclide migration in the disposal site. This study conducted experimental and numerical methods to the adsorption, diffusion, and advection–dispersion behavior of ⁹⁹Tc in three types of rocks: granite, clay rock, and mudstone shale, with a focus on the influence of anion exclusion during migration. The research results found that the three types of rocks have no significant adsorption effect on ⁹⁹Tc, and the anion exclusion during diffusion and advection–dispersion processes can block small “channels”, causing some nuclide migration to lag, and accelerate the nuclide migration rate in larger “channels”. In addition, parameters characterizing the size of anion exclusion in different migration behaviors, such as effective diffusion coefficient (De) and immobile liquid region porosity (${\theta }_{im}$), were fitted and obtained. Full article

The impact of cosmic rays is crucial to understand the energetic plasma outflows coming out from the Galactic centers against the strong gravitational potential well. Cosmic rays can interact with thermal plasma via streaming instabilities and produce hydromagnetic waves/fluctuations. During the propagation of cosmic rays it can effectively diffuse and advect through the thermal plasma which results the excitation of Alfvén waves. We are treating thermal plasma, cosmic rays and self-excited Alfvén waves as fluids and our model is referred as multi-fluid model. We investigate steady-state transonic solutions for four-fluid systems (with forward as well as backward propagating self-excited Alfvén waves) with certain boundary conditions at the base of the potential well. As a reference model, a four-fluid model with cosmic-ray diffusion, wave damping and cooling can be studied together and solution topology can be analyzed with different set of boundary conditions available at the base of the gravitational potential well. We compare cases with enhancing the backward propagating self-excited Alfvén waves pressure and examining the shifting of the transonic point near or far away from the base. In conclusion we argue that the variation of the back-ward propagating self-excited Alfvén waves significantly alters the transonic solutions at the base. Full article

This paper investigates a slow–fast stochastic reaction–diffusion–advection equation with Hölder-continuous coefficients, where the irregularity of the coefficients presents significant analytical challenges. Our approach fundamentally relies on techniques from Poisson equations in Hilbert spaces, through which we establish optimal strong convergence rates for the approximation of the averaged solution by the slow component. The key advantage that this paper presents is that the coefficients are merely Hölder continuous yet the optimal rate can still be obtained, which is crucial for subsequent central limit theorems and numerical approximations. Full article