NUMERICAL MODELLING OF SOLUTE TRANSPORT IN OPEN CHANNELS

Abstract

The potential environment hazards posed by the release of treated and untreated industrial and municipal wastes have been recognized in recent years. The introduction of potentially harmful contaminants in streams has to be regulated so that their concentrations remain below the permissible limits. For this purpose, it is necessary to determine how these contaminants disperse and diffuse as they move downstream. In general, the transport of contaminants depends on the physical and chemical properties of the contaminant and characteristics of the stream and the rate of discharge. The contaminant is transported by molecular and turbulent diffusion and by advection. The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has to be modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes are investigated to solve the advective equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all six schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, Hi explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produces large numerical oscillations. The polynomial interpolation scheme yields the best result for a trapezoidal distribution among all seven schemes investigated. The polynomial scheme is also extended to solve advective-diffusion equation and is found to predict the concentration front accurately. The second—order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third — and fourth-order) accurate -sche—mes.