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.
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