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and Hydrology","monthly_downloads":1756,"total_dependent_repos":0,"total_dependent_packages":0,"readme":"\u003cimg src=\"./docs/_static/timflow_logo.jpeg\" width=\"300\"\u003e\n\n[![PyPI - Version](https://img.shields.io/pypi/v/timflow)](https://pypi.org/project/timflow/)\n[![General](https://github.com/timflow-org/timflow/actions/workflows/ci-general.yml/badge.svg)](https://github.com/timflow-org/timflow/actions/workflows/ci-general.yml)\n[![Steady](https://github.com/timflow-org/timflow/actions/workflows/ci-steady.yml/badge.svg)](https://github.com/timflow-org/timflow/actions/workflows/ci-steady.yml)\n[![Transient](https://github.com/timflow-org/timflow/actions/workflows/ci-transient.yml/badge.svg)](https://github.com/timflow-org/timflow/actions/workflows/ci-transient.yml)\n[![Documentation Status](https://readthedocs.org/projects/timflow/badge/?version=latest)](https://timflow.readthedocs.io/en/latest/?badge=latest)\n[![Ruff](https://img.shields.io/endpoint?url=https://raw.githubusercontent.com/astral-sh/ruff/main/assets/badge/v2.json)](https://github.com/astral-sh/ruff)\n\n# timflow, a multi-layer analytic element model\n\n`timflow` is a Python package for the modeling of multi-layer groundwater flow with analytic\nelements. The package is split into two main submodules: `timflow.steady` for steady-state flow\nand `timflow.transient` for modeling transient flow. Both modules may be applied to an\narbitrary number of aquifers and leaky layers. The head, flow, and leakage between\naquifers may be computed semi-analytically at any point in space and time.\n\nThe design\nof `timflow` is object-oriented and has been kept simple and flexible.\nNew analytic elements may be added to the code without making any changes in the\nexisting part of the code. `timflow` is coded in Python and uses `numba` to speed up\nevaluation of the line elements and inverse Laplace transforms.\nThe `transient` submodule is based on the Laplace-transform analytic element\nmethod. The solution is computed analytically in the Laplace domain and converted back\nto the time domain numerically usig the algorithm of De Hoog, Stokes, and Knight.\n\n## Installation\n\n`timflow` requires Python \u003e= 3.11 and can be installed from PyPI:\n\n`pip install timflow`\n\nTo install all optional dependencies (for running tests and building docs):\n\n`pip install timflow[dev]`\n\n## Documentation\n\nThe documentation is hosted on [readthedocs](https://timflow.readthedocs.io).\n\n## History\n\n`timflow` combines the old packages [`TimML`](https://github.com/mbakker7/timml)\nand [`TTim`](https://github.com/mbakker7/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.\n\n## Citation\n\nSome of the papers that you may want to cite when using `timflow` are:\n\n* Steady-state flow:\n  * Bakker, M., and O.D.L. Strack. 2003. Analytic Elements for Multiaquifer Flow.\n  Journal of Hydrology, 271(1-4), 119-129. [https://doi.org/10.1016/S0022-1694(02)00319-0](https://doi.org/10.1016/S0022-1694(02)00319-0)\n* Transient flow:\n  * M. Bakker. 2013. Semi-analytic modeling of transient multi-layer flow with TTim.\n  Hydrogeology Journal, 21: 935-943. [https://doi.org/10.1007/s10040-013-0975-2](https://doi.org/10.1007/s10040-013-0975-2)\n  * M .Bakker. 2013. Analytic modeling of transient multi-layer flow. In: Advances in\n  Hydrogeology, edited by P Mishra and K Kuhlman, Springer, Heidelberg, 95-114. 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