For the stable development of society, one of the factors is air quality control, since today reducing the negative impact of pollutants on human health and the ecosystem is especially relevant and in demand. Based on the above, the article examines an important factor: the movement of gravitational deposition of dust and fine aerosol particles on the Earth’s surface, which depends on the physical properties of the dispersion phase, temperature, dynamic and kinematic viscosity of the atmospheric air mass, and the horizontal and vertical components of wind speed. Atmospheric stratification affects the deposition of harmful substances in the atmosphere. A mathematical model is presented that takes into account the rate of particle sedimentation, where formulas are provided for calculating it depending on the physical and mechanical properties and characteristics of the medium. For the settling rate of spherical aerosol particles, the Stokes equation is used, which considers all the forces influencing the settling rate. To calculate the dynamic and kinematic viscosity of air, which significantly influences the deposition rate of dust and fine aerosol particles, a regression model is provided that takes into account the temperature and pressure of the atmospheric air mass, and the results of numerical calculations are presented in the form of graphs and histograms.

Моделирование распространения загрязняющих примесей в атмосфере является одной из важнейших задач в экологических исследованиях и охране окружающей среды. Для исследования данного процесса широко используется уравнение адвекции-диффузии. Точность численного решения задач, сформулированных на основе уравнения адвекции-диффузии, во многом определяется способом аппроксимации членов, описывающих учитываемые эффекты, включая перенос, турбулентную диффузию, поглощение примеси, свойства частиц примеси, рельеф местности и т.д. В данной работе внимание сосредоточено на ряде вопросов, касающихся построения математической модели исследуемого процесса, разработки численного алгоритма решения задачи на основе разностной схемы Кранк-Николсона, повышения эффективности алгоритма за счет параллелизации вычислительных процедур, а также анализа точности и сходимости используемого численного метода, применительно к решению задачи распространения примеси в атмосфере.

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.