One-dimensional numerical model for unsteady solute transport in open channels under multi-point loading

Abstract

A numerical method for solving the unsteady-one-dimensional advection-dispersion equation for solute transport in streams and channels imposed with multiple point-loading is presented. The numerical technique proposes to solve the equation, which also includes a first-order decay term and a loading term, using techniques similar to those employed by the finite volume method (FVM). The channel length is segmented into cells and the solution aims at evaluating the concentrations at the cell interfaces or the internal nodes, at prescribed time steps for the steady condition of the flow. The results are computed commencing from a specified time level with known spatial concentration within the domain. It is assumed that the boundary nodes at the two ends of the channel, one each at the upstream and the downstream, are specified with solute concentration values or its spatial gradient at all times. Unlike the standard within-the-cell spatial approximations of a variable assumed in the finite volume or finite element schemes, the proposed method models the spatial variation of the solute concentration within a cell by an analytical expression in terms of the concentrations at the two boundary nodes of the cell and the influx rate of point-loading, if any, located within the cell. Using such a closed-form function based upon the true nature of the problem not only helps in capturing the spatial variation of concentration within a cell more precisely but also allows a better approximation of its spatial gradients at the cell interfaces, thus helping to achieve a more accurate computation of the inter-cell dispersive fluxes. The performance of the proposed algorithm is evaluated against analytical benchmarks, a standard finite difference scheme, and one public-domain computational package. Data sets reported from field tests are used for demonstrating the potential of the technique in simulating real situations.