ANALYSIS OF POLLUTANT CONCENTRATION IN SURFACE WATERS USING ONE - DIMENSIONAL ADVECTION DIFFUSION EQUATION WITH TEMPORALLY VARYING COEFFICIENTS

Abstract

The aim of this study is to provide an analysis on pollutant concentration in surface waters using one – dimensional advection diffusion equation with temporally varying coefficients. Numerical and analytical solutions are obtained for one - dimensional Advection Diffusion Equations with variable coefficients in a finite medium. Finite Difference and Laplace Transforms Methods are applied to solve the Advection Diffusion Equation with temporally varying coefficients. Absolute error obtained from comparing analytical and numerical solutions at different points reveals that the numerical scheme is accurate. Simulations based on the validated numerical scheme are obtained. Simulations on the effect of dispersion and velocity coefficients (based on Peclet number) on pollutant concentration show that concentration increases around the source point and gradually decreases with increasing distance from the source point. It further shows that concentration is higher for Peclet number much greater than one as compared to Peclet numbers much less than or equal to one. Effect of temporally varying velocity and dispersion coefficients on pollutant concentration is also presented. The findings show that concentration is higher for exponentially decreasing dispersion in an exponentially accelerating flow and lower for exponentially increasing dispersion in an exponentially accelerating flow.