Dispersion in Three Dimensions: Approximate Analytic Solutions

Solutions to three-dimensional convection dispersion equation under different boundary conditions are obtained by integrating the appropriate Green's functions. Two approximations are used during the integration. First, error function differences are approximated by exponential functions through Taylor expansion. Second, the time integral is approximated by Laplace method. The error introduced due to these approximations is analysed and discussed. The pollution source is assumed to be an arbitrary function of time and of finite size in space. The boundary conditions considered are of a stream in a horizontal flow field and a water table in a vertical flow field. Such solutions have potential use in quick preliminary analysis of groundwater pollution problems.