1D CONVECTION-DIFFUSION IN POROUS MEDIA: A UNIFIED SOLUTION FROM BOUNDED DOMAIN TO HALF-SPACE

Source abstract

We present a unified analytical solution of the 1D convection-diffusion equation for constant-velocity solute transport in porous media, valid on both a bounded interval $[0,L]$ and the half-space $[0,+\infty[$. Via the Laplace transform, the Green's function is inverted through two equivalent routes -- residue calculus and Poisson summation -- and we justify the limit $L\to+\infty$, recovering the classical Ogata-Banks solution. Results are validated against a finite-volume scheme and compared with Genuchten's analytical solution, with observed discrepancies traced to differing outlet boundary conditions.