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Finite difference scheme for longitudinal dispersion in open channels

Author(s): Z. AHMAD; U.C. Kothyari; K.G. Ranga Raju

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Abstract: The available analytical and numerical solutions of the equation for longitudinal dispersion in open channels are limited to uniform flows. Presented in this paper is a solution technique based on combined operator approach where advection and diffusion processes of longitudinal dispersion equation are treated concurrently in non-uniform flows. A variable size spatial grid based finite difference solution of the advection process has been obtained by developing a variable spatial grid so that the root of the trajectory of the concentration characteristic passes through the computational nodes. For solution of the diffusion process, Crank-Nicholson scheme has been used. To eliminate the possibility of numerical oscillations, weighting coefficient has been introduced to the pollutant concentration in the time stepping. Proof-of-the-concept tests have been made using the existing numerical and analytical solutions as the basis. The model has been extended by incorporating in it the one-dimensional grid search method for determination of DL values using observed temporal variation of concentration (C-t curves) at two or more stations. Finally, a procedure of computing the C-t curves at downstream locations is presented in the paper.

DOI: https://doi.org/10.1080/00221686.1999.9628255

Year: 1999

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