INVESTIGATION OF USE OF REACH-BACK CHARACTERISTICS METHOD FOR 2D DISPERSION-EQUATION

Abstract

The use of the Holly-Preissmann two-point scheme has been very popular for the calculation of the dispersion equation. The key to this scheme is to use the characteristics method incorporating the Hermite cubic interpolation technique to approximate the trajectory foot of the characteristics. This method can avoid the excessive numerical damping and oscillation associated with most finite difference schemes for advection computation. On the basis of the fundamental idea of the Holly-Preissmann two-point scheme, a new technique is introduced herein for the computation of the two-dimensional dispersion equation. This new scheme allows the characteristics projecting back several time steps to fall on the spatial or temporal axis, while the characteristics foot is still solved by the Holly-Preissmann two-point method. The diffusion portion of the dispersion equation is solved by the commonly used Crank-Nicholson method. The calculation for these two processes consisting of advection and diffusion is carried out separately but consecutively in one time step, a method known as the split operator algorithm. A hypothetical model was constructed to demonstrate the applicability of this new technique for the calculation of the pure advection and dispersion equation in two dimensions.