Parallel Implementation of a Lagrangian Stochastic Model for Pollution Dispersion

A radiative transfer solver that implements the LTSn method was optimized and parallelized using the MPI message passing communication library. Timing and profiling information was obtained for the sequential code in order to identify performance bottlenecks. Performance tests were executed in a distributed memory parallel machine, a multicomputer based on IA-32 architecture. The radiative transfer equation was solved for a cloud test case to evaluate the parallel performance of the LTSn method. The LTSn code includes spatial discretization of the domain and Fourier decomposition of the radiances leading to independent azimuthal modes. This yields an independent radiative transfer equation for each mode that can be executed by a different processor in a parallel implementation. Speed-up results show that the parallel implementation is suitable for the used architecture.

Density-dependent social behaviors such as swarming and schooling determine spatial distribution and patterns of resource use in many species. Lagrangian (individual-based) models have been used to investigate social groups arising from hypothetical algorithms for behavioral interactions, but the Lagrangian approach is limited by computational and analytical constraints to relatively small numbers of individuals and relatively short times. The dynamics of "group properties", such as population density, are often more ecologically useful descriptions of aggregated spatial distributions than individual movements and positions. Eulerian (partial differential equation) models directly predict these group properties; however, such models have been inadequately tied to specific individual behaviors. In this paper, I present an Eulerian model of density-dependent swarming which is derived directly from a Lagrangian model in which individuals with limited sensing distances seek a target density of neighbors. The essential step in the derivation is the interpretation of the density distribution as governing the occurrence of animals as Poisson points; thus the number of individuals observed in any spatial interval is a Poisson-distributed random variable. This interpretation appears to be appropriate whenever a high degree of randomness in individual positions is present. The Eulerian model takes the form of a nonlinear partial integro-differential equation (PIDE); this equation accurately predicts statistically stationary swarm characteristics, such as expected expected density distribution. Stability analysis of the PIDE correctly predicts transients in the stochastic form of the aggregation model. The model is presented in one-dimensional form; however, it illustrates an approach that can be equally well applied in higher dimensions, and for more sophisticated behavioral algorithms.

An improved treatment of advection is essential for atmospheric transport and chemistry models. Eulerian treatments are generally plagued with instabilities, unrealistic negative constituent values, diffusion, and dispersion errors. A higher-order Eulerian model improves one error at significant cost but magnifies another error. The cost of semi-Lagrangian models is too high for many applications. Furthermore, traditional trajectory “Lagrangian” models do not solve both the dynamical and tracer equations simultaneously in the Lagrangian frame. A fully Lagrangian numerical model is, therefore, presented for calculating atmospheric flows. The model employs a Lagrangian mesh of particles to approximate the nonlinear advection processes for all dependent variables simultaneously. Verification results for simulating sea-breeze circulations in a dry atmosphere are presented. Comparison with Defant’s analytical solution for the sea-breeze system enabled quantitative assessment of the model’s convergence and stability. An average of 20 particles in each cell of an 11 × 20 staggered grid system are required to predict the two-dimensional sea-breeze circulation, which accounts for a total of about 4400 particles in the Lagrangian mesh. Comparison with Eulerian and semi-Lagrangian models shows that the proposed fully Lagrangian model is more accurate for the sea-breeze circulation problem. Furthermore, the Lagrangian model is about 20 times as fast as the semi-Lagrangian model and about 2 times as fast as the Eulerian model. These results point toward the value of constructing an atmospheric model based on the fully Lagrangian approach.

Analytical dispersion model for the chain of primary and secondary air pollutants released from point source

A 3D Lagrangian particle model has been presented for the atmospheric dispersion of the toxic pollutants released from industrial stacks. As the mean wind speed and direction is changed with height in a real atmosphere, the height of the exhaust stack may have a strong impact on the pollutant dispersion and ground concentrations. An elevated continuous release of non-buoyant gas in a neutrally stratified atmosphere has been simulated, for various stack heights. The turbulent atmospheric parameters like vertical profiles of fluctuat ing wind velocity components and eddy lifetime were calculated using a semi-empirical mathematical model. The numerically calculated horizontal and vertical dispersion coefficients (σy and σz) are compared with the Pasquill's empirical σ's. The ground concentration as a function of downwind distance has been compared with the Green glow data. The ground concentrations for various release heights were compared with the Gaussian plume model. The comparison indicated a need for using either a modified Gaussian model or a 3D numerical mathematical model for pollutant dispersion and ground concentration calculations. Copyright © 2002 John Wiley & Sons, Ltd.

In recent years, artificial intelligence has been widely used in the field of meteorology. However, it is perhaps less known that AI-based tools have been used for over 30 years in the modeling of pollutant dispersion in the atmosphere.In the early 1990s, Slovenia and other parts of Europe faced significant air pollution problems caused by SO₂ emissions from coal-fired power plants without desulfurization systems. Due to the highly complex terrain, simple physical Gaussian dispersion models were not suitable for reconstructing the dispersion of SO₂ in the atmosphere, while complex numerical Lagrangian particle dispersion models were still in development.Therefore, as early as 1992, we modeled air pollution using a Multilayer Perceptron Artificial Neural Network (MLPANN). We developed the world's first comprehensive method for selecting training samples, features, and the topology of the neural network, enabling the model to learn from measured meteorological variables and pollutant concentrations around the power plant to predict SO₂ concentrations at a selected location in advance.This type of artificial neural network remains the foundation for various derived structures used for machine learning from data even today.In the following decades, we expanded the use of MLPANN to ozone prediction. Researchers from other Slovenian research groups also worked on this topic. Meanwhile, the use of these and similar tools in pollutant dispersion modelling began to grow on a global scale.Together with Brazilian researchers, we successfully applied MLPANN for predicting diffuse solar radiation. In this field, we also managed to develop a spatially transferable model, which is not a common capability for artificial neural network-based models.For the classification of wind fields based on measurements from ground-based meteorological stations, we used a Kohonen neural network.Later, we added another tool called "Gaussian processes" (which, like MLPANN, is a universal approximator) and the tool "decision trees." We expanded the use to point-based forecasting of basic meteorological variables. In recent years, with high computational capabilities available even without supercomputers, we have been using these tools for surrogate models that can represent or predict pollutant concentration fields in the atmosphere, not only for individual points but for entire areas around pollution sources.Other Slovenian groups from Slovenian Meteorological Agency, the Department of Meteorology, and the Faculty of Computer Science have, in recent years, used machine learning for global medium-range forecasts of daily averages of meteorological variables and for post-processing weather forecasts from physical models.In the presentation, we will explain the basic principles of building models based on artificial neural networks in a way that is understandable to laypeople. For experts in the field, we will showcase numerous examples of their application. For the latter group, we hope these examples will inspire others to expand the use of these modern tools even further.

A hybrid model for ozone forecasting

Mathematical and numerical methods are used to simulate physical and chemical processes when building models of pollutants dispersion in the air and on the soil surface. Based on meteorological data and information on the source of emissions, these models characterize both the primary pollutants entering the atmosphere directly and the secondary ones formed as the result of complex chemical reactions. These models are important for the air quality management system, as they allow monitoring emissions into the atmosphere, predicting their distribution, as well as developing effective strategies intended for reducing harmful substances in the atmosphere. The article presents an overview of computational methods used to simulate the pollutants dispersion in atmospheric air and on the soil surface, such as the Gaussian torch model, the Lagrangian dispersion stochastic model, and the Eulerian model of atmospheric diffusion. The practical application of the considered models showed sufficient reliability and validity of the air and soil pollution levels forecast. The simulation uses computer programs that include algorithms for solving the mathematical equations that control pollutant dispersion. The dispersion models are used to estimate the concentration of air pollutants or toxins. They can also be used to predict future concentrations under certain scenarios. They are useful for studying the pollutants that disperse over long distances and can initiate reactions in the atmosphere. Such software products are as follows: AEROPOL, AERMOD, GRAL, TAPM CSIRO, CALPUFF, HYSPLIT, etc. A method of processing information about the pollution sources and the environmental parameters, based on the HYSPLIT program, is proposed to form maps of the volume and surface activity of radionuclides. This method was applied to analyze the process of the plutonium isotopes dispersion as a result of the movement of air masses in the places of fires in April 2020 in the exclusion zone of the Chornobyl NPP, as well as the associated hazard for the population health and the environment.

As part of an ongoing effort to develop verification and validation (V&V) standards for using computational fluid dynamics (CFD) in the evaluation of medical devices, we have developed idealized flow-based verification benchmarks to assess the implementation of commonly cited power-law based hemolysis models in CFD. Verification process ensures that all governing equations are solved correctly and the model is free of user and numerical errors. To perform verification for power-law based hemolysis modeling, analytical solutions for the Eulerian power-law blood damage model (which estimates hemolysis index (HI) as a function of shear stress and exposure time) were obtained for Couette and inclined Couette flow models, and for Newtonian and non-Newtonian pipe flow models. Subsequently, CFD simulations of fluid flow and HI were performed using Eulerian and three different Lagrangian-based hemolysis models and compared with the analytical solutions. For all the geometries, the blood damage results from the Eulerian-based CFD simulations matched the Eulerian analytical solutions within ∼1%, which indicates successful implementation of the Eulerian hemolysis model. Agreement between the Lagrangian and Eulerian models depended upon the choice of the hemolysis power-law constants. For the commonly used values of power-law constants (α = 1.9-2.42 and β = 0.65-0.80), in the absence of flow acceleration, most of the Lagrangian models matched the Eulerian results within 5%. In the presence of flow acceleration (inclined Couette flow), moderate differences (∼10%) were observed between the Lagrangian and Eulerian models. This difference increased to greater than 100% as the beta exponent decreased. These simplified flow problems can be used as standard benchmarks for verifying the implementation of blood damage predictive models in commercial and open-source CFD codes. The current study only used power-law model as an illustrative example to emphasize the need for model verification. Similar verification problems could be developed for other types of hemolysis models (such as strain-based and energy dissipation-based methods). However, since the current study did not include experimental validation, the results from the verified models do not guarantee accurate hemolysis predictions. This verification step must be followed by experimental validation before the hemolysis models can be used for actual device safety evaluations.

Emergent vegetation has a significant impact on floating particle transport and diffusion in open channel flow. The random walk model of a Lagrangian approach has proven more than suitable to describe the rather unpredictable moving trajectory of particles within emergent vegetation. However, compared to the large computational costs of the Lagrangian model, which also requires more input data, a simplified model based on the Eulerian approach can be by far preferable and cost‐effective for rapid first‐order prediction of particle transport and diffusion within vegetated areas. In this study, we developed a one‐dimensional advection‐diffusion model to simulate particle transport processes within vegetated areas, and to explore the impacts of vegetation on particles transport, diffusion and removal. The model parameters, including the probability of a particle colliding with a stem, and the probability of it being temporarily trapped or permanently captured by a stem, as well as the mean retention time that govern the random walk model, are introduced to estimate the mean velocity, diffusion coefficient, removal rate of particles of Eulerian model, distinguishing from the standard advection and diffusion parameters. The validity of the parameters is verified through the stochastic model with a large number of realizations. The comparison between the dispersal kernel as well as the spatio‐temporal distribution of floating particles predicted by Eulerian model and stochastic model is quite satisfactory and suggests that the Eulerian model we proposed is properly described.

For gas turbine combustors using liquid fuel injectors, introducing the spray into crossflowing air to achieve superior fuel-air mixing characteristics can improve performance and reduce emissions. Robust numerical design tools are needed to accelerate the development of low-emissions technologies. CFD models are used to assess the design, performance, and emissions of novel combustion systems. Atomization modelling is often facilitated by using the Lagrangian approach with breakup models rather than the more complex and computationally expensive higher-fidelity Volume-of-Fluid (VOF) approach. However, breakup models used in state-of-the-art CFD rely on empirical constants that have not yet been fully calibrated for jets in crossflow or for representative gas turbine conditions. Coupling the Lagrangian and VOF approaches could deliver a better compromise between accuracy and computational cost. Among the few studies conducted on the VOF-Lagrangian approach for jets in crossflow, validation was often limited to the near-field spray trajectory under low Weber numbers using either non-turbulent jets or water at ambient pressure. The predictive capabilities in the far-field region were only validated using deterministic breakup models and for non-turbulent jets under low pressure conditions. This study proposes and validates a novel numerical methodology for coupling the Lagrangian and VOF approaches using a Stochastic Secondary Droplet (SSD) breakup model with Adaptive Mesh Refinements (AMR) for turbulent liquid fuel jets in high-speed crossflow at more representative conditions. The predictions within both near and far-field breakup regions were validated using experimental datasets at high pressures (1–8 bar), Weber numbers (720–1172) and momentum flux ratios (6–33). The predictive capabilities and computational cost were also compared to the Lagrangian approach used with LES and used with an unsteady RANS numerical methodology previously developed and validated by the authors. The effects of different VOF-Lagrangian transition criteria on the computational cost were also assessed and recommendations have been provided for further improvements. The overall predictive capabilities of LES were significantly improved by the novel hybrid methodology proposed by the authors. Although it tends to underpredict the spray trajectory and Sauter Mean Diameter (SMD), it better captures the SMD in the wake region of the jet and the overall droplet velocities compared to the URANS methodology.

Eulerian multi-fluid modeling for the numerical simulation of coalescence in polydisperse dense liquid sprays

Pollution is a major problem in all countries, even developed ones. It is the major environmental negative impact of anthropogenic activities affecting ecology. There are two major ways for assessment of negative impact of motor transport flow intensity and pollution level: monitoring the air or modeling pollutant dispersion. It is very important to estimate different unknown air modeling programs. In this work modeling is to be executed by the US EPA (United States Environmental Protection Agency) the so‐called “the best possible existing software for strategic environmental assessment”. That is also recommended by the Ministry of Environment of the Republic of Lithuania. In this work pollution modeling was executed for the northern part of Vilnius (the network of streets Geležinis Vilkas ‐ Ozas ‐ Kalvarijos). For motor vehicle pollution mathematical modeling, it is necessary to evaluate meteorological parameters like temperature, humidity, the wind direction and speed. Modeling software can also estimate relief conditions. Pollution emission measurements were used, and pollution dispersion modeling was performed. The main target was to evaluate pollutant dispersion from motor transport in the analysed area of Vilnius. During investigation maximum hourly, daily and annual concentrations of carbon monoxide, nitrogen oxide, sulphur dioxide, volatile organic compounds and particulate matter were observed.

The unpredictable water pollution incident of the Yellow River Basin is an important part of the emergency work. Based on the Saint-venant equation set, a 1-D pollutant dispersion model is built for the middle and lower reaches of the Yellow River. It calibrates key parameters with the valley characteristics, rapidly and effectively achieves the forecasting of pollutant dispersion using implicit finite difference scheme in this paper. The model can maximize the information obtained from the available data and adapt to the fast evolution of the river bed as well as other external changes. The experimental results show that the model provides a strong support for relevant decision makers with high usability and reliability.

Purpose: To analyze and compare two motion models constructed from 4D‐CT using deformable registration using two different computation approaches: Eulerian and Lagrangian. Method and Material: Accurate motion modeling within the lung is an important consideration in different clinical applications. We consider 4D‐CT scans for three patients treated in radiotherapy for lung cancer. 4D‐CTs were acquired using a 4‐slice fan‐beam CT scanner (GE Lightspeed QX/i; GE Heathcare Technologies, Waukesha, WI), and a respiratory surrogate (Real‐time Position Management; Varian Medical Systems, Palo Alto, CA). Two motion models were constructed from vector fields computed with demons algorithm with Gaussian regularization. We used also a image pre‐treatment method, a priori lung density modification, to handle this limitation of the demons algorithm. The first model, obtained with the Eulerian approach, uses small deformation estimations between successive phases of the 4D‐CT. The second model, obtained with the Lagrangian approach, was generated by estimation of larger deformations between the end‐exhale phase and all other states. The models were validated and compared using consistency (symmetry and transitivity) and accuracy (based on landmark points) metrics. Results: Mean values of accuracy were on the order of the image resolution and comparable to inter‐observer variability (1.9 mm), with slightly better results for the Lagrangian approach: 2.3 mm vs. 2.6 mm. The differences were not statistically significant for consistency.Conclusions: The results of this study suggest that the Lagrangian approach is more appropriate to use for generating a 4D‐CT motion model with deformable registration. In ongoing works, lung and GTV contours are used in order to conclude on the superiority of one motion model over the other for an automatic contour propagation tool, and for lung physiological information computation and analysis.