An interpolation-corrected modified method of characteristics to solve advection-dispersion equations

Numerical dispersion, numerical oscillation, and peak clipping are common numerical difficulties in solving advection-dispersion equations. The development of numerical approaches that can handle these numerical difficulties with reasonable computational efforts is an ongoing challenge. In this paper, an interpolation-corrected modified method of characteristics (ICMMOC) is proposed for solving advection-dispersion equations. The ICMMOC is an improved version of the modified method of characteristics (MMOC). It uses a high-order (second-order or higher) interpolation scheme to reduce numerical dispersion and an interpolation-correction procedure to eliminate numerical oscillation. A simple peak capturing scheme to overcome the peak clipping problem is also developed in this study. Simulation results show that the ICMMOC is able to overcome the aforementioned numerical difficulties for a large range of grid Peclet numbers.