The paper discusses the numerical modeling of transport and diffusion of air pollutants in the atmospheric boundary layer. There was developed a mathematical model of industrial emissions spread in the atmosphere taking into account the deposition velocity of fine particles. The model is described by multidimensional partial differential equations with appropriate initial and boundary conditions. The basic laws of hydrothermodynamics were used in deriving the model. In order to obtain the numerical solution of the problem, we used one of the splitting methods according to physical processes involved (transport, diffusion and absorption), as well as a second-order implicit finite-difference scheme in time. Analysis of numerical results showed that the developed computational algorithm provides sufficient accuracy of the problem solution compared with field measurement data and it has a certain advantage over other numerical methods. In the course of computational experiments, there was determined the degree of influence of such parameters as wind speed and direction, absorption coefficient and physicomechanical properties of particles on the process of atmospheric air pollutants dispersion.

This article presents an algorithm for the numerical solution of a mathematical model that calculates the value of the density of harmful substances at different times and at different places of the region.

Accurate and computationally efficient prediction of radioactive plume dispersion is essential for rapid risk assessment and emergency response in the event of accidental atmospheric releases. This study presents a three-dimensional, mass-conservative numerical framework for simulating mesoscale transport and transformation of radionuclides under varying meteorological conditions. The proposed model is based on the advection–diffusion equation and incorporates key physical processes, including turbulent diffusion, gravitational settling, precipitation washout, radioactive decay, surface absorption, and re-emission. A hybrid numerical scheme is developed that combines a semi-implicit Crank–Nicolson discretization for diffusion terms with a second-order Total Variation Diminishing (TVD) scheme employing a Van Leer limiter for advection. To ensure computational efficiency and stability, the governing equations are solved using an alternating direction implicit (ADI) strategy, leading to tridiagonal systems efficiently handled via the Thomas algorithm. In addition, a modified parameterization of turbulent diffusion coefficients is introduced, extending classical Pasquill–Gifford formulations to better represent mesoscale atmospheric behavior with bounded dispersion characteristics. Computational experiments simulating iodine-131 release under different atmospheric stability classes and meteorological conditions demonstrate that the proposed framework reproduces physically consistent plume structures and maintains strict mass conservation with negligible numerical errors. The results highlight the dominant role of advective transport and precipitation scavenging under moderate wind conditions, as well as strong localization effects under stable atmospheric stratification. The proposed model provides a practical compromise between the simplicity of Gaussian plume approaches and the high computational cost of full-physics atmospheric models, making it suitable for rapid engineering calculations and integration into decision-support systems for radiological emergency management.

Accurate and computationally efficient prediction of radioactive plume dispersion is essential for rapid risk assessment and emergency response in the event of accidental atmospheric releases. This study presents a three-dimensional, mass-conservative numerical framework for simulating mesoscale transport and transformation of radionuclides under varying meteorological conditions. The proposed model is based on the advection–diffusion equation and incorporates key physical processes, including turbulent diffusion, gravitational settling, precipitation washout, radioactive decay, surface absorption, and re-emission. A hybrid numerical scheme is developed that combines a semi-implicit Crank–Nicolson discretization for diffusion terms with a second-order Total Variation Diminishing (TVD) scheme employing a Van Leer limiter for advection. The framework is intended as a computationally tractable engineering model; operational applicability requires further assessment using measured runtime performance and independent physical validation. In addition, a modified parameterization of turbulent-diffusion coefficients is introduced, extending classical Pasquill–Gifford formulations to better represent mesoscale atmospheric behavior with bounded dispersion characteristics. The numerical implementation is verified against an analytical constant-coefficient advection–diffusion solution using concentration-error norms, plume-moment errors, mass-balance analysis, and grid-refinement tests. Additional idealized iodine-131 simulations illustrate the behavior of the framework under moderate-wind and stable atmospheric conditions. The results highlight the dominant role of advective transport and precipitation scavenging under moderate wind conditions, as well as strong localization effects under stable atmospheric stratification. The proposed model provides a practical compromise between the simplicity of Gaussian plume approaches and the high computational cost of full-physics atmospheric models, indicating its potential for rapid engineering calculations, subject to further validation against atmospheric observations and established operational dispersion models.

We report the verification and validation of the numerical core of an atmospheric flow and pollutant-dispersion module, in which the Reynolds-averaged Navier–Stokes equations with a k–ε closure and an advection–diffusion equation for pollutants are discretised by a conservative finite-volume method. Convective schemes, linear solvers and the pressure-correction algorithm were tested against manufactured solutions, a Poisson problem, a positivity problem and the lid-driven cavity. The street-canyon prototype itself was verified with a manufactured solution on its own grid, a turbulent-channel test of the wall functions and an empty-domain test of the inflow profiles; these tests revealed two implementation errors, which were corrected. The corrected model, with standard constants, was validated against the Karlsruhe street-canyon wind-tunnel data, and the computed wall concentrations agree with the measurements within a factor of two. A sensitivity study was carried out to assess the effect of the grid, the turbulent Schmidt number, the inflow turbulence, the convective scheme and the domain size on the results.