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.
