gwassess

Analytical Solutions for the Richards Equation in 2D and 3D Domains

gwassess is a python package that implements analytical and reference solutions to the Richards equation in 2D and 3D domains. The package provides benchmark solutions for testing numerical solvers of unsaturated flow in porous media.

Installation

gwassess is a standard python package that can be installed from source:

cd gwassess
pip install .

Or install directly from the repository:

pip install git+https://github.com/g-adopt/gwassess.git

Usage

Basic usage example for the Tracy 2D analytical solution:

import gwassess
import numpy as np

# Initialize Tracy solution with soil and domain parameters
solution = gwassess.TracyRichardsSolution2D(
    alpha=0.328,      # Exponential soil parameter [1/m]
    hr=-15.24,        # Reference pressure head [m]
    L=15.24,          # Domain size [m]
    theta_r=0.15,     # Residual water content [-]
    theta_s=0.45,     # Saturated water content [-]
    Ks=1.0e-05        # Saturated hydraulic conductivity [m/s]
)

# Evaluate pressure head at a point
x, y, t = 7.62, 7.62, 1000.0
h = solution.pressure_head_specified_head(x, y, t)
print(f"Pressure head at ({x}, {y}) at time {t}: {h:.6f} m")

# Or use Cartesian coordinates
X = [7.62, 7.62]
h = solution.pressure_head_cartesian(X, t, bc_type='specified_head')

Available Solutions

TracyRichardsSolution2D

Analytical solution for 2D Richards equation with exponential soil properties. Provides both steady-state and transient solutions with two boundary condition types:

• Specified head on all boundaries
• No-flux on lateral boundaries

Reference: Tracy, F. T. (2006). Clean two- and three-dimensional analytical solutions of Richards' equation for testing numerical solvers. Water Resources Research, 42(8). https://doi.org/10.1029/2005WR004638

VauclinRichardsSolution2D

Reference solution for 2D infiltration benchmark with Haverkamp soil model. This is a numerical benchmark without closed-form analytical solution, but provides standard problem setup for comparison.

Reference: Vauclin, M., Khanji, D., & Vachaud, G. (1979). Experimental and numerical study of a transient, two-dimensional unsaturated-saturated water table recharge problem. Water Resources Research, 15(5), 1089-1101.

CockettRichardsSolution3D

Reference solution for 3D heterogeneous benchmark with Van Genuchten soil model. Provides spatially varying material properties and standard problem setup.

Reference: Cockett, R., Heagy, L. J., & Haber, E. (2018). Efficient 3D inversions using the Richards equation. Computers & Geosciences, 116, 91-102.

Documentation

For complete API reference and examples, see the docstrings in each module:

• gwassess.tracy - Tracy 2D analytical solutions
• gwassess.vauclin - Vauclin 2D reference solution
• gwassess.cockett - Cockett 3D reference solution

License

gwassess is licensed under the GNU Lesser General Public License v3 (LGPLv3). See LICENSE.txt for details.

Contributing

Contributions are welcome! Please submit issues and pull requests on GitHub: https://github.com/g-adopt/gwassess