timflow, a multi-layer analytic element model

timflow is a Python package for the modeling of multi-layer groundwater flow with analytic elements. The package is split into two main submodules: timflow.steady for steady-state flow and timflow.transient for modeling transient flow. Both modules may be applied to an arbitrary number of aquifers and leaky layers. The head, flow, and leakage between aquifers may be computed semi-analytically at any point in space and time.

The design of timflow is object-oriented and has been kept simple and flexible. New analytic elements may be added to the code without making any changes in the existing part of the code. timflow is coded in Python and uses numba to speed up evaluation of the line elements and inverse Laplace transforms. The transient submodule is based on the Laplace-transform analytic element method. The solution is computed analytically in the Laplace domain and converted back to the time domain numerically using the algorithm of De Hoog, Stokes, and Knight.

Installation

timflow requires Python >= 3.11 and can be installed from PyPI:

pip install timflow

To install all optional dependencies (for running tests and building docs):

pip install timflow[dev]

Documentation

The documentation is hosted on readthedocs.

History

timflow combines the old packages TimML and TTim. Git history is maintained within this new package, but the old repositories are still available for searching through old issues, pull requests, and other information.

Citation

Some of the papers that you may want to cite when using timflow are:

• Steady-state flow:
  • Bakker, M., and O.D.L. Strack. 2003. Analytic Elements for Multiaquifer Flow. Journal of Hydrology, 271(1-4), 119-129. https://doi.org/10.1016/S0022-1694(02)00319-0 or here.
• Transient flow:
  • M. Bakker. 2013. Semi-analytic modeling of transient multi-layer flow with TTim. Hydrogeology Journal, 21: 935-943. https://doi.org/10.1007/s10040-013-0975-2 or here.
  • M .Bakker. 2013. Analytic modeling of transient multi-layer flow. In: Advances in Hydrogeology, edited by P Mishra and K Kuhlman, Springer, Heidelberg, 95-114. Available here.