Consistency And Stability Analysis of a Mathematical Model of Chlorine Concentration in Contact Tanks Using Numerical Solution of A 1- Dimensional Convection- Diffusion Equation

Abstract

In this paper we consider the consistency and stability analysis of the modified convection diffusion equation: ut ut +mux − nLuxx = 0, which describes the mass transfer of chlorine in contact tank water disinfectant. We employ the concept of Dufort-Frankel based on Richardson’s scheme to discretize the modified equation. This resulted to a numerical scheme algorithm. The consistency was analyzed by Taylor’s expansion of the discretized scheme, which was found to be consistent with the original modified equation. In addition, stability was analyzed by using matrix method. The numerical computation results showed that the scheme was conditionally stable. This has been concluded by numerical computations to illustrate the consistence and stability of the scheme.