mashadab / VarSatFlow

VarSatFlow: A Variably Saturated groundwater Flow model to simulate large scale multidimensional problems proposed in Shadab and Hesse (2024), Advances in Water Resources, Elsevier. The repository has 1D/2D codes of VarSatFlow model to replicate to the corresponding figures.

VarSatFlow: A Variably Saturated groundwater Flow model (Paper PDF)

In this repository, we present an efficient, conservative and large scale numerical simulator for variably saturated flow in the limit of negligible capillary forces. The model modifies Richards equation to capture complete saturation. Here we implement a tensor product grid-based conservative finite difference solver. The codes are written in Open Source Discrete Operator Toolbox (PyDOT) developed by Shadab based on Hesse's toolbox in MATLAB (MDOT). The codes include one and two-dimensional tests which have been validated with Hydrus simulations, experiments and hydraulic theory. The repository contains codes of variably saturated groundwater model to replicate all the main manuscript figures in Shadab and Hesse (2024), Advances in Water Resources, Elsevier.

Figure : Gravity-dominated drainage of multiple saturated drops across an unsaturated porous medium. Here $s_w$ is the water saturation, i.e., fraction of pore space occupied by water phase.

Associated Papers / Citations to use

[1] Shadab, M.A. and Hesse, M.A., 2024. A hyperbolic-elliptic PDE model and conservative numerical method for gravity-dominated variably-saturated groundwater flow, Advances in Water Resources, Elsevier.

[2] Shadab, M. A. and Hesse, M. A., 2024. mashadab/VarSatFlow: v1.0 (v1.0). Zenodo. https://doi.org/10.5281/zenodo.11398273

Authors

• Mohammad Afzal Shadab ([e-mail])
• Marc Andre Hesse ([e-mail])

Affiliation

Oden Institute for Computational Engineering and Sciences / Jackson School of Geosciences / University of Texas Institute for Geophysics The University of Texas at Austin

Example: Infiltration in soil with an impermeable soil layer leading to formation of a perched water table

Woods_Hesse_upwinding_hyperbolic_Richards_final_fs4by8_0.975_140by80_tf14.0_S_w_mesh.mov

Video : Flux partitioning in a steady gravity current passing symmetrically over a barrier. $s_w$ is the water saturation which is the fraction of pore space occupied by water. Left: Actual video, Right: Saturated region being tracked with solid red line being saturated-unsaturated region boundary.

Figure : Flux partitioning in a steady gravity current passing over a barrier. (a-d): Experiments conducted by Hesse and Woods (2010). (e-f): Simulations performed using the VarSatFlow model.

(i) Dependence of the flux partitioning, $Q_b/(Q_a+Q_b)$, on the source location, $L_a/(L_a+L_b)$, with subscript a is left side and b is right side variable.

The panel labels give the dimensionless source locations, $L_a/(L_a+L_b)$.

Dependences

VarSatFlow requires the following packages to function:

• Python version 3.5+
• Numpy >= 1.16
• scipy >=1.5
• matplotlib >=3.3.4

Quick Usage

After cloning the repository and installing the required libraries, run the python files corresponding to the figure numbers as given in the paper. Codes can be run either directly or on an IDE such as Anaconda Spyder. Use %matplotlib qt to change the plotting from inline to separate window in Spyder. The Solver folder contains the auxillary code. The source folder src contains two subfolders. The main codes corresponding to Figures are in the subfolder MainCodes whereas the resulting plots are collected in the subfolder Figures. The name of the Python code bears the same figure number as given in the paper.

Non-dimensionalization

The depth coordinate $z$ is scaled with characteristic length $z_0$, time is scaled with characteristic time $z_0/f_c$ and infiltration rate $I(t)$ (or volumetric flux) is scaled with the infiltration capacity $f_c$ or surface saturated hydraulic conductivity $K$. Therefore, the dimensionless variables are $z'=z/z_0$, $t'=tf_c/z_0$, and $f'=I(t)/f_c$.