Development of Numerical Models for 1D and 2D Pollutant Transport Problems Using the Leapfrog Method with Additional Numerical Filters - Hafiyyan, Qalbi; Nirmala, Azwa; Murad, Murad; Bachtiar, Vivi; Sumiyattinah, Sumiyattinah (Indonesian Journal of Multidisciplinary Science, 2026)
Pollutant transport in aquatic environments has become a critical environmental issue due to increasing contamination from industrial, domestic, and agricultural activities, which threaten ecosystems and human health. Understanding pollutant behavior through numerical modeling is essential for effective monitoring and mitigation strategies. This study aims to develop and evaluate a numerical model for simulating one- and two-dimensional pollutant transport using the advection–diffusion equation as the governing framework. The method employed is a finite difference approach based on the Leapfrog scheme combined with the Hansen numerical filter to improve model stability and simplicity. The model is tested through several benchmark cases, including pure advection, advection–diffusion, and Gaussian pulse scenarios in both one- and two-dimensional domains, with results compared to analytical solutions. The findings indicate that the proposed Leapfrog–Hansen model demonstrates good agreement with analytical solutions and achieves relatively small error values, particularly in one-dimensional cases. The results also show that spatial and temporal discretization significantly influence model stability and accuracy, where smaller step sizes generally improve performance but may reduce accuracy due to excessive filtering. In conclusion, the Leapfrog–Hansen model provides a simple yet effective alternative for pollutant transport simulation, especially for one-dimensional problems, with potential applications in environmental analysis and decision-making