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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Zelisha Pitriatuz Zahra Fauzi
IPB University
Mathematics

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Numerical Solution of 2D Advection-Diffusion for River Pollutant Transport using the Finite Element Method Muhamad Adzka Rizkia; Rahma Alya Zahrani; Zelisha Pitriatuz Zahra Fauzi; Foky Michelin; Najwaa Alifya Azka; Faiza Mayla Sabita; Mualim Arya Ilyas Wiradinata; Ferdy Aliansyah Hasyim; Mochamad Tito Julianto; Sri Nurdiati; Mohamad Khoirun Najib; Syukri Arif Rafhida
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.42814

Abstract

Pollutant dispersion in rivers is governed by advection, diffusion, and the physical characteristics of the channel. This paper models two-dimensional pollutant transport using the advection-diffusion equation and solves it numerically with the Finite Element Method (FEM) under five scenarios: constant flow with a single pollutant source, flow that follows a meandering channel, constant flow with two sources, the presence of a rock obstacle, and an irregular river domain. Simulations are implemented in Mathematica through domain construction, mesh generation, and a Finite Element-based numerical solution. The results show that flow velocity is the primary driver of plume movement, while diffusion smooths concentration gradients. Comparative analysis across the five scenarios demonstrates that obstacle-containing and irregular domains produce the widest plume spreading and the strongest concentration deformation compared to the straight-channel case. Peak concentrations also decrease more rapidly in multi-source and irregular-flow scenarios due to enhanced mixing and plume interaction. Physical obstacles and channel irregularities generate loacal recirculation zones and plume deviation, producing more realistic pollutant transport behavior than simplified channer models. These findings highlight the importance of geometry-aware flow representations for understanding river pollutant transport in numerical modelling studies.
Co-Authors Faiza Mayla Sabita Ferdy Aliansyah Hasyim Foky Michelin Mochamad Tito Julianto Mualim Arya Ilyas Wiradinata Muhamad Adzka Rizkia Najib, Mohamad Khoirun Najwaa Alifya Azka Rahma Alya Zahrani Sri Nurdiati Syukri Arif Rafhida