A Mass-Conservative Crank–Nicolson–TVD–ADI Framework for Mesoscale Simulation of Radioactive Plume Dispersion

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.