08 Groundwater Modeling

08-02 Numerical Schemes

Spatial/temporal discretization, stability, solution algorithms, convergence.

Contents

Index Description
08-02-001 Finite Difference Numerical Scheme
08-02-002 Finite-Difference Numerical scheme: Solver options

08-02-001Finite Difference Numerical Scheme

Type: Streamlit app Time: 15–30 minutes
Finite Difference Numerical Scheme

Figure 1: The interactive plot with the basic setup. When the computation is running, the shown head values update. (Screenshot)

Purpose and Functionality The app implements the one-dimensional finite difference method for groundwater flow with two fixed head boundary conditions. Users can specify the spatial discretization by selecting the number of cells, upon which the numerical scheme is set up and solved.

Learning Features The app visualizes the iterative development of the numerical solution and illustrates how the approximation approaches a stable state. A built-in analytical reference solution enables direct comparison, supporting the exploration of error behaviour, convergence, and numerical representation of groundwater flow processes.

LAUNCH RESOURCE

Detail Value
URL gwf-1d-conf-fd.streamlit.app · open app
Author(s) Thomas Reimann (TU Dresden); Rudolf Liedl (TU Dresden)
Keywords Numerical solution, groundwater modeling, applied hydrogeology, finite differences
Fit For self learning, online teaching, classroom teaching
Prerequisites Basic hydrogeology, 1D groundwater flow equation, analytical solutions for 1D groundwater flow,

Streamlit app details

Detail Value
Interactive plots 1 interactive plot(s)

Images

The user interface with an interactive plot that comes with an modified spatial discretization. In addition, the analytical solution is show that allows students comparison with the numerical results.

Figure 2: The user interface with an interactive plot that comes with an modified spatial discretization. In addition, the analytical solution is show that allows students comparison with the numerical results. (Screenshot)

08-02-002Finite-Difference Numerical scheme: Solver options

Type: Streamlit app Time: 15–30 minutes
Finite-Difference Numerical scheme: Solver options

Figure 1: The interactive plot shows the development of the solution. Various solver options (Screenshot)

This app illustrates the numerical solution of the 1D groundwater flow equation for a confined aquifer using a finite-difference scheme. Users can interactively compare Jacobi, Gauss–Seidel, and SOR solvers, visualize the iterative path toward convergence, and evaluate results against the analytical solution. The tool supports conceptual understanding of solver behavior, convergence characteristics, and numerical accuracy in groundwater modeling.

LAUNCH RESOURCE

Detail Value
URL gwf-1d-conf-fd-solvers.stre… · open app
Author(s) Thomas Reimann (TU Dresden)
Keywords 1D flow, finite differences, solver, solution schemes, SOR, Gauss-Seidel, Jacobi
Fit For self learning, classroom teaching, online teaching
Prerequisites Basic hydrogeology, groundwater flow equation

Streamlit app details

Detail Value
Interactive plots 1 interactive plot(s)
Co-funded by the European Union
This project is co-funded by the European Union. However, the views and opinions expressed are solely those of the author(s) and do not necessarily reflect those of the European Union or the National Agency DAAD. Neither the European Union nor the granting authority can be held responsible for them.