Numerical solution of the differential equation for moving front dispersion

It is shown that the differential equations presented by Struck (1992, Water Resour. Res., 28(11): 2973-2980) for moving front dispersion are hyperbolic, and general expressions for the velocity of the front and the concentration at the front are presented. The method of solution known as the method of characteristics (not to be confused with the method known in groundwater transport modeling as the method of characteristics) is presented for solving the system of equations for moving front dispersion. Jumps are shown to be allowable across the characteristics, and the jump conditions are presented. The numerical method is outlined for the case of a pulse of concentration at a point of an infinitely long streamline. The numerical solution is validated by comparison with an exact solution.