MACCORMACK SCHEME BASED NUMERICAL SOLUTION OF ADVECTION-DISPERSION EQUATION

ABSTRACT Accurate solution of the Advection-Dispersion equation by numerical methods is difficult due to the presence of artificial diffusion induced while approximating the advective term. Many numerical schemes have been developed to solve Advection- Dispersion equation. In the present study, the performance of MacCormack scheme coupled with an implicit finite difference scheme has been investigated while solving Advection-Dispersion equation for wide range of Courant and Peclet numbers. MacCormack scheme is chosen due to its simplicity. The advective part is solved by MacCormack scheme and the advective concentration so obtained is used in the dispersive part as source/sink term to obtain the final concentration. The results indicate that the scheme works very well for low and medium Peclet numbers. However, it produces overshoot and oscillations at high Peclet numbers. The effect of Courant number is insignificant at low and medium Peclet numbers. But at high Peclet numbers, the magnitude of overshoot and oscillations decrease with an increase in Courant number.

Перевод пока недоступен