paper

1D Convection-Diffusion in Porous Media: A Unified Solution from Bounded Domain to Half-Space

arXiv:2609.13618 · doi:10.37418/amsj.15.3.4

Abstract

We present an analytical solution for 1D atmospheric pollutant dispersion in a bounded domain. Using coordinate transformation and spectral decomposition, we obtain a Fourier series solution for time-dependent wind velocity. For constant wind, Laplace inversion yields dual representations via residue calculus and Poisson summation. The solution extends to semi-infinite domains, recovering classical error-function profiles.

24 pages, 4 figures,