An analytical Solution to Bi-dimensional Unsteady Contaminant Transport Equation with Arbitrary Initial and Boundary Conditions

In this research, the analytical solution to bi-dimensional Advection-Dispersion-Equation was obtained in the finite domain at the open channels using Generalized Integral Transform Technique (GITT). The upstream boundary condition was considered Dirichlet type with arbitrary and irregular time pattern of the entrance concentration. The downstream, right and left bank boundary condition was considered zero gradient. The initial condition function was assumed in the general form. The Evaluation of the derived solution was performed using two hypothetical examples and by comparing the results with the analytical solution resulting from the Green’s Function Method (GFM). In this way, in the first example, the entrance concentration from the upstream boundary was assumed zero and the initial condition function was considered impulsive at the specific point at the domain. At the second example, the irregular time pattern function of the entrance concentration from the upstream boundary and impulsive initial condition function was considered simultaneously. The results of both examples were compared with the results of GFM and the concentration contours at different times were presented. The results show good agreement between the proposed solution and the GFM solution and report the performance of the proposed solutions is satisfactory and accurate. The proposed analytical solution has high flexibility in adopting the various functions as the initial and boundary conditions. So it is very applicable and useful for verification of the two-dimensional complex numerical models.