A semianalytical method for solving equations describing the transport of contaminants in two-dimensional homogeneous porous media

The two-dimensional convection-dispersion equation with most complex boundary and initial conditions does not have an exact analytical solution and is therefore solved numerically. However, the solutions obtained with several traditional finite difference or finite element techniques typically exhibit spurious oscillation or numerical dispersion when convection is dominant. The semianalytical model proposed in this paper avoids such oscillations and numerical dispersion when convection dominates. The semianalytical model is the solution of (n + m − 1)-order ordinary differential equations that are derived from the two-dimensional convection dispersion equation. The semianalytical model describes the contaminant concentration as a function of time and space, the space is reflected in parameters n and m. The results calculated with the semianalytical model are in good agreement with those obtained from the exact solution of a corresponding two-dimensional convection-dispersion equation, but the semianalytical model greatly simplifies the computation, making solutions for complex boundary and initial conditions possible.