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(L) and K(A) < 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(L) and K(A) ≥ 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.