Numerical solution of the Burgers equation associated with the phenomena of longitudinal dispersion depending on time.

In this study, the Burgers equation governing the time-dependent dispersion phenomena is solved numerically using the finite difference scheme and the Runge-Kutta 4 algorithm with appropriate initial and boundary conditions. Two time-dependent dispersion functions have been implemented to analyze the spatio-temporal variation in the domain. For the values of K and K < 1.2 years, a significant retention of the mass of solute is observed when the dispersion function is asymptotic. The results obtained show that the concentration profiles are similar when the values of K and K ≥ 1.2 years. These results demonstrate the importance of the nature of the dispersion function on the retention capacity of solutes in the porous medium.