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Providing a clear description of the theory of polydisperse multiphase flows, with emphasis on the mesoscale modelling approach and its relationship with microscale and macroscale models, this all-inclusive introduction is ideal whether you are working in industry or academia. Theory is linked to practice through discussions of key real-world cases (particle/droplet/bubble coalescence, break-up, nucleation, advection and diffusion and physical- and phase-space), providing valuable experience in simulating systems that can be applied to your own applications. Practical cases of QMOM, DQMOM, CQMOM, EQMOM and ECQMOM are also discussed and compared, as are realizable finite-volume methods. This provides the tools you need to use quadrature-based moment methods, choose from the many available options, and design high-order numerical methods that guarantee realizable moment sets. In addition to the numerous practical examples, MATLAB scripts for several algorithms are also provided, so you can apply the methods described to practical problems straight away.

Atmospheric dispersion models are applied to describe and predict the dispersion of emitted plumes. Here, we describe the Lagrangian Atmospheric Radionuclide Transport Model (ARTM) 2.8.0 which was developed to simulate the atmospheric dispersion of the emissions of nuclear facilities under routine operation for regulatory purposes over annual time scales. ARTM includes a diagnostic wind field model and a particle dispersion model. It simulates size-dependent wet and dry deposition, plume rise and γ-cloud shine of radioactive exhaust plumes in the simulation domain. This work presents an extensive overview of the different components of the model and of the physical and mathematical concepts of ARTM. We investigate the dependence of the plume dispersion in terms of plume volume, position of maximum concentration and dry deposition rates on key input parameters such as atmospheric stability, surface roughness, zero plane displacement height, source height and the particle size in the case of particulate matter tracers. The results indicate a strong dependence of plume volume and position of the maximum concentration on the stability as well as a minor influence on surface roughness. The source height above ground level has a low impact on the plume volume as the zero plane displacement only slightly affects the position of maximum concentration. Strong turbulence under unstable conditions tends to reduce the impact of sedimentation and decreases deposition in general. This computational model serves to advance the understanding of the dispersion of radioactive plumes in the boundary layer.

In a complex environment such as an urban area, accurate prediction of the atmospheric dispersion of airborne harmful materials such as radioactive substances is necessary for establishing response actions and assessing risk or damage. Given the variety of urban atmospheric dispersion models available, evaluation and inter-comparison exercises are vital for assessing quantitatively and qualitatively their capabilities and differences. To that end, the European Commission/Directorate General Joint Research Centre with support from the European Commission/Directorate General-Migration and Home Affairs, and with the contribution of the U.S. Defense Threat Reduction Agency, launched the Urban Dispersion INternational Evaluation Exercise (UDINEE) project. Within UDINEE, nine atmospheric dispersion models are evaluated and intercompared. Sulphur hexafluoride concentrations from puffs released near the ground during the Joint Urban 2003 (JU2003) field experiment are used in UDINEE to evaluate atmospheric dispersion models. The JU2003 experiment is chosen because UDINEE aims at the better understanding of modelling capabilities for radiological dispersal devices in urban areas, and the neutrally-buoyant puff releases performed in the JU2003 experiment are the closest scenario to this purpose. The present study evaluates the capability of models at simulating the presence and concentration levels of the tracer at sampling locations. The fraction of predicted concentrations and time-integrated concentrations within a factor-of-two of observations are less than 0.36 and 0.4 respectively. The analysis reveals an improvement in the performance of models by using time-varying inflow conditions. Since the simulation of the dispersion of puff release is particularly challenging, the results of UDINEE could constitute a benchmark for future model developments.

Numerical models are widely used to simulate volcanic gas dispersion and estimate local emission sources. However, significant uncertainties arise from the approximations inherent in their physical formulations. Recent advances in high-performance computing (HPC) have enabled high-resolution simulations with minimal numerical diffusion, revealing previously unnoticed limitations in the Monin–Obukhov Similarity Theory used within atmospheric gas dispersion models. One key issue is the determination of the minimum vertical turbulence diffusion coefficient (Kz min ) in the atmospheric surface layer (ASL), which plays a crucial role in reducing biases in advection–diffusion models caused by inadequate turbulence representation. In this study, we refine the Eulerian passive gas transport model DISGAS (v. 2.5.1) using measured data on fumarolic and diffuse CO₂ fluxes and air concentrations, along with local wind measurements collected during an ad hoc field campaign from 4 to 10 May 2023. To account for uncertainties in gas flow rates and turbulent velocity fluctuations, we conducted a statistically robust set of simulations by varying CO₂ fluxes and Kz min values. Model outputs were compared with in situ CO₂ concentration measurements at fixed monitoring stations. Results indicate that during stable atmospheric conditions, setting Kz min within the range of 1.5–2 m 2  s −1 significantly improves agreement with observations and reduces systematic biases in source estimation. These findings refine model parameterization to better represent turbulence under stable atmospheric conditions at La Solfatara crater during the May 2023 survey. Moreover, the proposed methodology can be adopted for automated data assimilation workflows aimed at constraining unknown fumarolic gas source fluxes in other volcanic settings. Graphical Abstract

The role of modelling the atmospheric dispersion of pollutants at microscale, the scale that allows to resolve explicitly the presence of obstacles, is becoming increasingly important for performing air quality assessments in cities, as well as for regulatory purposes and for the design of pollution control strategies. However, the use of microscale models can be computationally demanding, both in terms of time and CPUs required, especially if the computational domain considers wide spatial extension and the simulation considers long time periods. This article proposes the application of a kernel method as the concentration calculation methodology inside microscale Lagrangian particle dispersion models (LPDMs) in order to reduce the required computational time. In these models, the concentration is normally estimated with the box-counting method, while the use of this alternative method, based on the use of the statistical technique of kernel density estimation, allows for a reduction of numerical particles emitted during the simulation, while guaranteeing a similar accuracy to that of the box-counting method. It therefore enables an optimization of computational efficiency. In an earlier manuscript, the kernel method was applied inside the LPDM of the PMSS (Parallel-Micro-SWIFT-SPRAY) system to perform high-resolution simulations of line sources, enabling an 80% simulation time reduction. In this article, additional features of this method are developed within the Micro-SPRAY model and tested through two test cases. The kernel method has been applied to estimate the pollutant concentrations of point sources as well as to compute the corresponding deposition at building-resolving scale. The results with tiled and nested configurations of domains are also verified.

The capabilities of nine atmospheric dispersion models in predicting near-field dispersion from puff releases in an urban environment are addressed under the Urban Dispersion INternational Evaluation Exercise (UDINEE) project. The model results are evaluated using tracer observations from the Joint Urban 2003 (JU2003) experiment where neutrally-buoyant puffs were released in the downtown area of Oklahoma City, USA. Sulphur hexafluoride concentration time series measured at ten sampling locations during four daytime and four night-time puff releases are used to evaluate how the models simulate the puff passage at the measurement locations. The neutrally-buoyant puff releases in the JU2003 experiment are the closest scenario to radiological dispersal device (RDD) releases in urban areas, and therefore, UDINEE is a first step towards improving the emergency response to an RDD explosion in the urban environment. We investigate for each puff and sampler the model capability of simulating the peak concentration; the peak and puff arrival times; and time duration, defined as the period over which concentrations exceed 10% of the peak concentration. This analysis points out differences on the performance of models: the fraction within a factor-of-two values ranges from 0.10 to 0.6 for peak concentration, from 0 to 1 for the peak and arrival times, and from 0 to 0.8 for the time duration. The results reveal that the characteristics of the release site largely influence the model simulation as it affects initial puff size and the initial downwind spread of the puff.

The present work develops a model for the turbulent velocity spectra that considers the anomalous behaviour of the turbulent flow. The β-model assumes that the standard Kolmogorov phenomenology is valid only in active turbulence regions, and it proposes an expression for the turbulent velocity spectra in the inertial subrange that is a function of the Hausdorff fractal dimension. From this idea, expressions are obtained for the components of the turbulent velocity spectra that describe the turbulence that exists in geophysical turbulence above the ocean and in very stable situations in the planetary boundary layer where intermittent turbulence occurs. With these spectra, the main parameters used in dispersion models are obtained, that is, the eddy diffusivity and the Lagrangian time scale. The eddy diffusivity is used in an Eulerian dispersion model to estimate the concentration of contaminants in the stable boundary layer. The results obtained are compared with experimental data and other models in the literature.

A comparison between a puff atmospheric dispersion model (hereafter: PuM) and a Lagrangian particle model (hereafter: LPM) was conducted for a real case of emissions from an industrial plant, in the context of a complex and coastal site. The PuM’s approach is well-known and widely adopted worldwide, thanks to the authoritative suggestions by the US-EPA for regulatory use as, according to the definitions included in its guidelines, an “alternative” to “preferred” models; LPMs are more advanced models and have gained reliability over the last two decades. Therefore, it is of interest to provide insights into the decision to adopt or recommend, in the field of atmospheric impact assessment, a more advanced, but more knowledge- and resource-intensive, modeling tool, rather than an established albeit less accurate one. An inter-comparison of the two approaches is proposed based on the use of various statistical and comparative parameters with the goal of studying their differences in reproducing maps of ground-level ambient concentration statistics for assessment purposes (annual means, hourly peaks). The models were tested under a year-long simulation. The dispersion from both a point and a volume source, belonging to an existing industrial plant, was analyzed separately. The inter-comparison was performed through the analysis of 2D ground concentration maps, scatterplots, and three classical indices from the 2D maps of annual concentration statistics. To correlate the differences among models with site characteristics, the statistics were analyzed not only globally, but also according to distance from the source, the elevation, and the land-use classification. The analysis shows that around-its-axis plume dispersion in LPM is lower than in PuM over all the land-use types except water surfaces, in agreement with the theoretical basis provided by the models. Because of its more advanced theoretical formulation, e.g., in the interaction of the plume with the complex terrain and the three-dimensional wind field, an LPM used as a comparison term allowed us to highlight the weaknesses of a more traditional approach, such as PuM, in reproducing effects such as plume up-sloping, deflection, channeling, confinement, and wind shear diffusion.

Ambient air pollution remains the major environmental cause of disease. Accurate assessment of population exposure and small-scale spatial exposure variations over long time periods is essential for epidemiological studies. We estimated annual exposure to fine and coarse particulate matter (PM2.5, PM10), and nitrogen oxides (NOx, NO2) with high spatial resolution to examine time trends 2000‒2018, compliance with the WHO Air Quality Guidelines, and assess the health impact. The modelling area covered six metropolitan areas in Sweden with a combined population of 5.5 million. Long-range transported air pollutants were modelled using a chemical transport model with bias correction, and locally emitted air pollutants using source-specific Gaussian-type dispersion models at resolutions up to 50 × 50 m. The modelled concentrations were validated using quality-controlled monitoring data. Lastly, we estimated the reduction in mortality associated with the decrease in population exposure. The validity of modelled air pollutant concentrations was good (R2 for PM2.5 0.84, PM10 0.61, and NOx 0.87). Air pollution exposure decreased substantially, from a population weighted mean exposure to PM2.5 of 12.2 µg m−3 in 2000 to 5.4 µg m−3 in 2018. We estimated that the decreased exposure was associated with a reduction of 2719 (95% CI 2046–3055) premature deaths annually. However, in 2018, 65%, 8%, and 42% of residents in the modelled areas were still exposed to PM2.5, PM10, or NO2 levels, respectively, that exceeded the current WHO Air Quality Guidelines for annual average exposure. This emphasises the potential public health benefits of reductions in air pollution emissions.

The prediction of river planimetric evolution and related interactions with anthropic activities and public safety is one of the most critical aspects in the planning of a sustainable land‐use. Since the beginning of the past century, a large number of theoretical and experimental studies have focused on the investigation of river meandering dynamics, coming to sometimes contrasting conclusions in the forecast of the associated bend sequence pattern. Drawing inspiration from the phenomenological equivalence between fluid‐dynamic and morpho‐dynamic dispersion within the river floodplain, the present contribution proposes an explicit analytical solution in terms of scale‐dependent and equilibrium sinuosity. Such analytical solution, which reveals the strong dependence of river equilibrium planform on valley bank‐full velocity distribution, is successfully validated on the basis of a field data set provided via a restoration pilot project by Basilicata Region Environment and Energy Department (Italy), and further discussed by related lagrangian simulations. Moreover, the governing equation from which the equilibrium solution originates is shown to be compatible with the interpretation of near‐equilibrium dynamics highlighted by stochastic numerical experiments documented in the literature.