Adaptive Stabilized Finite Element Modeling of Advection-Dominated Air Pollution Plumes

Abstract

Accurate simulation of convection-dominated pollutant transport remains a significant challenge due to the presence of steep concentration gradients and the numerical instabilities associated with standard finite element discretizations. This study presents an adaptive Streamline Upwind/Petrov–Galerkin (SUPG) finite element framework for solving two-dimensional advection–diffusion equations governing atmospheric pollutant dispersion. The proposed methodology combines SUPG stabilization with a residual-based a posteriori error estimator to automatically guide local mesh refinement, thereby improving solution accuracy while reducing unnecessary computational effort. The adaptive algorithm iteratively identifies regions with large discretization errors and selectively refines the mesh to accurately resolve localized pollutant plumes and sharp concentration fronts. The numerical performance of the proposed framework is evaluated through representative single-source and two-source pollutant transport problems. Convergence studies, computational efficiency analysis, and comparisons with uniform mesh refinement demonstrate that the adaptive approach achieves lower numerical errors and reduced computational cost for an equivalent number of degrees of freedom. The results further show that the adaptive strategy effectively captures the interaction of multiple pollutant plumes while maintaining numerical stability under convection-dominated conditions. These findings confirm that the proposed adaptive SUPG framework provides an accurate, robust, and computationally efficient numerical tool for atmospheric pollutant transport simulations and establishes a reliable foundation for extending the methodology to more complex environmental transport problems involving nonlinear processes, heterogeneous media, and time-dependent emission scenarios.