Optimised Muskingum-Cunge solution method for solute transport with equilibrium Freundlich reactions

Because of its simplicity and efficiency, the Muskingum-Cunge (M-C) method is a widely used modelling tool applied to flood routing problems. However, in the M-C method, there is an infinite number of combinations of spatial and temporal step sizes for which the solution is feasible and not all of these lead to accurate results. This has been a major criticism of the method. The same approach has been adopted here to solve the problem of nonlinear reactive solute transport. An optimised M-C scheme is proposed and tested which is very simple and efficient as compared with existing standard numerical solutions such as the Crank-Nicolson scheme. The optimisation principles are: (1) that the column holdup (area above the breakthrough curve normalised by the column length) is maintained; and (2) that the truncation error produced by the numerical scheme is minimised. The conditions derived are shown to be satisfactory for the mildly nonlinear reactions of the Freundlich-type typical of reactive chemical transport in soil.