Classical Integral Transform Technique solver to the multilayer Adevction-Diffusion Equation

ADE_CITT provides the closed form analytical solution to the transient (heat) Advection-Diffusion Equation (ADE) in a one-dimensional multi-layer composite medium of a finite length via the Classical Integral Transform Technique (CITT). The solver considers Dirichlet piece-wise linear boundary conditions on the start/top of the domain and either Dirichlet, Neumann or Robin constant boundary conditions at the bottom end of the domain. This solution was derived for predicting shallow subsurface thermal field evolution under climate change and was subsequently applied for predicting groundwater temperatures in Berlin, Germany (sample data provided).

The full study is available at https://doi.org/10.5281/zenodo.20730014

Environment setup

python pip install requirements.txt

Example code

• Script for validationg the CITT solution is available in validation.ipynb
• Example script for predicting shallow subsurface thermal field evolution under climate change is availalbe in example.ipynb

Data Disclaimer

This project uses publicly available data from the following official sources:

Senatsverwaltung für Mobilität, Verkehr, Klimaschutz und Umwelt Berlin Data obtained from the Wasserportal Berlin

Deutscher Wetterdients (DWD) Data accessed via the climate data

The original data remain the property of their respective providers. The versions included here have been cleaned, processed, and reformatted for the purposes of this project. This repository does not claim ownership of the original data. Users seeking authoritative or updated versions of the datasets should consult the respective official data portals.