A new model describing convective-dispersive phenomena derived by using the mixing-cell concept (Q5961831)

The main purpose is to present a novel model based on the mixing cell concept, and an optimal interval of time \(\Delta t\to 0\) for describing convective-dissipative phenomena. This model is governed by a system of \(n\)th-order ordinary differential equations, the solutions to which describe the concentration of the substance considered as a function of time and distance (which is reflected by the parameter \(n\)). Various forms of this model are derived for one-dimensional transport under different initial and boundary conditions. Mathematically, the mixing-cell concept is equivalent to the backward finite-difference approximation of spatial derivatives.NEWLINENEWLINENEWLINEThe authors show advantages of their model, for example: (i) the model can be considered functionally equal to the one-dimensional convective dispersion equation under steady state flow; (ii) the algebraic formulas of the new models for concentrations are explicit and are very simple to use and to program; (iii) the model can be used to solve solute contaminant transport in a natural river; and (iv) the model can be used to solve non-point pollution problems for agricultural watersheds. The results obtained by this model are compared with the exact solutions, and are found to be in very good agreement.