NUMERICAL SIMULATION OF EFFECTS OF VELOCITY AND DIFFUSION COEFFICIENT ON CONCENTRATION OF CONTAMINANTS IN FLUID FLOW

Abstract

The study developed and implemented Implicit and explicit schemes for solving one dimensional convection –diffusion equation modeling concentration of contaminant in a fluid flow .The study uses method of lines and exact method to further verify the numerical solution obtained. Stability of the scheme was analyzed and accuracy of the solution to the contaminant transport equation was validated by exact solution. Graphical illustration of the solution for varying velocity and diffusion coefficient is given, Errors in the methods tabulated. The explicit method (EM) involved one unknown on left hand side (LHS) of the scheme while implicit method (IM) involved several unknowns on LHS of the scheme and method of lines (MOL) involved semi-discretization method. In the study, we examined effect of velocity and diffusion coefficient on concentration of contaminant in a fluid flowing .Comparison of solution from the methods stated was done. The developed, numerical schemes were developed and MATLAB used generate and in analyze the results. The results showed that concentration of contaminants increased inversely with fluid velocity and directly with diffusion coefficient. Therefore, for proper treatment of water for example, it is necessary to increase the flow velocities to reduce the concentration of contaminants. The implicit Method significantly agreed to exact method to three decimals than the explicit method which was much more inaccurate because of unconditional stability. As Velocity increases the concentration of contaminant decreases and as diffusion coefficient increases the concentration of contaminant increases.