Analytical solutions for transport in porous media with Gaussian source terms

Analytical solutions for the advective-dispersion equation for solute trans port in porous media commonly assume a uniform distribution of mass within the source term. This paper derives an analytical solution for transport in porous media for a source term whose mass; is distributed as a bivariate G aussian spatial function. The solution is an extension of existing analytic al solutions using a Green's function approach to separate out one-dimensio nal terms in a manner similar to previous authors. This approach illustrate s the relationship of the bivariate Gaussian source term solation to of her Green's function solutions and thus leads to a set of solutions for advect ive-dispersive transport with various source term and domain geometries. Co mparison of point, bivariate Gaussian, and uniform source term solutions fi nds the greatest differences' near the source, with discrepancies decreasin g with travel distance.