PreprintarXiv licencearXiv
1D Convection-Diffusion in Porous Media: A Unified Solution from Bounded Domain to Half-Space
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.
Versions
Related
- Subdivision-based collocation methods for time fractional convection diffusion reaction equation with environmental and biomedical applications
- On the optimal decay rate of global solutions to the convection-diffusion equation with zero-mass initial data
- A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation
- Leak localisation with a measure source convection-diffusion model
- Large self-similar solutions of a convection--diffusion equation
BibTeX
@misc{ayena2026convectiondiffusion,
title = {{1D Convection-Diffusion in Porous Media: A Unified Solution from Bounded Domain to Half-Space}},
author = {Koffi Ognandon Ayena and Amah Séna D'almeida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13618},
eprint = {2609.13618},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13618},
}
RIS
TY - UNPB
TI - 1D Convection-Diffusion in Porous Media: A Unified Solution from Bounded Domain to Half-Space
AU - Koffi Ognandon Ayena
AU - Amah Séna D'almeida
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.13618
UR - https://arxiv.org/abs/2609.13618
AB - 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.
ER -