A Finite-Difference Diffusion Model for the Surface Spreading of Plastic Pollution in Beira Lake, Colombo, Sri Lanka

Abstract

Plastic pollution of urban inland waters is a growing environmental problem in Sri Lanka, yet the spatial spread of plastic debris across Beira Lake, the most prominent urban lake in Colombo, has never been described mathematically.

This paper develops and numerically solves a computational- mathematics framework for the spreading of plastic across

the surface of Beira Lake using the diffusion equation as the governing model. Plastic released at a source (the St. Bastian Canal inflow) spreads outward and smooths over the lake surface through turbulent mixing and dispersion, with a first-order loss term representing removal by sinking, beaching and biofouling.

The two-dimensional diffusion equation is solved by the finite- difference method using the explicit forward-time centred-space

(FTCS), implicit backward-Euler and Crank–Nicolson schemes; the stability of each is established by the von Neumann method, yielding the classical diffusion-number restriction r ≤ 1 4 for the explicit scheme and unconditional stability for the implicit

schemes. The solver is verified against the exact Gaussian heat- kernel solution, and a grid-refinement study confirms second- order spatial accuracy, the L

∞ error falling from 4.33×10−5 to

6.75×10−7 as the grid is refined (observed order p ≈ 2.00). The verified scheme is then applied to an idealised representation of Beira Lake with a continuous plastic source; the computed simulations reproduce the outward diffusive spreading of plastic, a smooth concentration gradient decaying with distance from the

source, and the accumulation of plastic along the enclosed no- flux shoreline. The study provides a transparent, reproducible

and low-cost, numerically validated tool for predicting plastic- concentration patterns, ready to be calibrated once field measure- ments of plastic concentration in Beira Lake become available.