Analytical solution for the stationary model of pollutant propagation in an aquatic medium

Solução analítica do modelo estacionário de propagação de poluentes em meio aquático

Abstract

This work presents a new analytical approach for solving pollutant dispersion problems along irregular-shaped water bodies. In this approach, the advection-diffusion equation is expressed in terms of orthogonal curvilinear coordinates, defined by the velocity potential and the corresponding stream function for inviscid flows. The boundary condition rewritten in terms of these new coordinates is reduced to a classical third kind one, i.e., the derivative of the concentration distribution with respect to the stream function is proportional to the numerical value of the local pollutant concentration. The solution obtained from the proposed formulation was employed to simulate pollutant dispersion (thermotolerant coliforms) along the Pampa Creek, a tributary of the Sinos River at the outskirts of Novo Hamburgo city, South Region of Brazil. The results obtained reproduce the qualitative behavior of the expected concentration distribution.

Keywords:
advection-diffusion equation; analytical solutions; mass transport; orthogonal curvilinear coordinates system; pollutant dispersion.