To solve numerically the contaminant transport equations many schemes have been proposed in the past. However, until now none of the proposed explicit schemes can achieve both satisfactory accuracy and good stability. Among the commonly used schemes, the central difference scheme has a serious problem with stability; the QUICK scheme is stable only for the Courant number equal to 0.7807; and the Holly-Preissmann scheme produces poor accuracy for Courant numbers larger than 0.8 and becomes unstable when the Courant number equals one....[ Read more ]

To solve numerically the contaminant transport equations many schemes have been proposed in the past. However, until now none of the proposed explicit schemes can achieve both satisfactory accuracy and good stability. Among the commonly used schemes, the central difference scheme has a serious problem with stability; the QUICK scheme is stable only for the Courant number equal to 0.7807; and the Holly-Preissmann scheme produces poor accuracy for Courant numbers larger than 0.8 and becomes unstable when the Courant number equals one.

Based on the method of characteristics (MOC) and the Her-mite interpolation polynomial technique, a new three-point sixth-order MOC scheme has been presented and explored for contaminant transport in an open channel. The higher accuracy of the proposed scheme has been proved by comparing the results with the analytical solutions and results obtained using other schemes. The von Neumann stability analysis and the example computations indicate that the proposed scheme is stable for the whole range of Courant numbers from zero to two. This is a significant advantage for an explicit scheme. The practical significance of this stability domain enlargement is the fact that we can use a much larger time step for a given accuracy. For example, for real length of δx = 2,OOOm and a flow velocity of 2.Om/s, the proposed scheme gives the same accuracy as QUICK and the Holly-Preissmann scheme with δt ≅ 20min which is twice the time step required by the other two schemes. It must be emphasized that 20min is still a reasonable time in practice as the field data is usually hourly collected. In addition, for a given δt, the proposed scheme allows much shorter δx. This is crucial as peak flow values are discretizing dependent.

The new scheme has been applied to model contaminant transport in the kinematic and non-inertial flow fields (the simplification forms of Saint-Venant unsteady flow equations). In modeling the contaminant transport in unsteady flow, the proposed scheme has been applied not only for computing the contaminant transport but also for computing the unsteady flow (i.e., the kinematic and the non-inertial waves), which also means that the scheme can certainly be applied alone to model the kinematic waves or the non-inertial waves in an open channel.