Advection-dispersion simulation by minimization characteristics and alternate direction-explicit methods

An accurate, stable and explicit split-operator scheme is developed for the solution of the unsteady advection-dispersion equation in two dimensions. The advection step is treated by the minimization characteristics method, which generates a class of finite difference schemes through Lp-error-norm minimization of the numerical approximation to the exact solution obtained by the method of characteristics. The scheme obtained from the minimax approximation (p = ∞) is found to be superior to that obtained from the least squares approximation (p = 2) and that from the minimum absolute, difference approximation (p = 1). The scheme is also more accurate than the other commonly used backward characteristics schemes based on the same computational effort for comparison. The dispersion step is solved by using the alternate direction-explicit difference to the axial dispersions and the forward-centered difference to the cross-dispersion. In the absence of the cross-dispersion the above scheme is unconditionally stable. The resulting split operator scheme is accurate, computationally efficient, and easy to program and requires small core storage.