An Analytical Solution for Advection-Diffusion Equation with Advection–Dominated Term using Multiple-Scale Expansion Methods

Sulaiman, Albert
Mubarak, Mubarak

Journal of The Physical Society of Indonesia
Vol. 1 No. 2 (2025): October 2025

In this study, we solved the advection-diffusion sediment transport equation by taking into account the settling velocity and employing a multiple-scale expansion to approximate the dominant advection. We obtained an analytical solution in terms of the Green’s function.  The model results showed that, during one tidal cycle, TSS was concentrated at the surface and eventually transported to the sea. The pattern of TSS distribution was consistent with both constant and linear time-dependent river discharge. The simulation revealed that the concentration of TSS offshore was higher than near the estuaries, in agreement with our observations.