Finite Difference Grounwater Modeling in Python

Finite Difference Models are derived and implemented completely in Python.
The theory and construction of these models can be used in their own right
or may serve as a thorough introduction in groundwater modeling with available
codes especially with MODFLOW, MT3DMS, MODPATH and SEAWAT.
At the end of this course we have built from ground on a powerful 3D steady state and transient finite difference groundwater code completely in Python functions and also a powerful 3D particle tracking funcion capable of tracking millions of particles simultaneously. We also have seen the versatile use of this code. The finite difference model functions are compatible with MODFLOW and MODPATH. The only limitation is that the finite difference functions allow just fixed-head and prescribed flow boundaries. This is to limit clutter and keep the finite-difference model functions in this course as lean and simple to use as possible, but the full theory is presented in the first chapter. This limitation is not a problem in most cases as, it's easy to model so-called general-head boundaries by setting appropriate conductivities.
For more advanced finite difference modeling and use of more specific packages, one should use the USGS codes MODFLOW, MODPATH, MT3DMS and SEAWAT directly. A Matlab interface as developed and used by me and my students for the last 8 years in many projects is available under project mfLab on SourceForge.org. A Python interface is available under the name PyFlow as developed by the USGS.

Contents:

• Finite Difference Groundwater Modeling in Python
  • Previously Matlab-based graduate course at TUDelft
    • Abstract ABSTRACT
• Numerical groundwater modeling
• Finite difference modeling
  • Approach
  • Setup of the model by specifying its dimensions
  • IBOUND array - telling which cells are active and which have a prescribed head
  • Cell conductancies: defining the ease of flow between adjacent cells
  • Setting up the system matrix - set of water balance equations
  • Boundary conditions
    • Fixed flows
    • Fixed heads
  • Solving the matrix equation for the unknown heads
  • Plotting the heads as contours
  • Conclusion
• A finite difference model as a Python function
  • Generalize the finite difference model into a callable function
  • Apply the model
    • Generate input to run the model with
    • Call the function with the correct arguments
    • Visualization of the results: plot heads as contours
  • Conclusion
  • Examples
    • Example 1: flow between 2 fixed bounaries
  • Example 2, semi-confined flow (mazure case)
  • Example 3, same case, but using only two layers
  • Cicular island with recharge
  • Circular polder
  • More efficient coordinates
• Computing flows with the finite difference model
  • Adding flows to the output of fdm3
  • Flow output of the model
    • Flows in the cell centers
    • Some more additions been made to the model:
  • fdm3 model with computation of flows
  • Application of the model
    • Generate input to run the model with (same example)
    • Call the function with the correct arguments
    • Visualization of the results: plot heads as contours
  • Conclusion
• A Grid class to deal with any finite difference model grid
  • Using a Grid class to handle spatial information regarding the grid
  • Grid-adapted model fdm3
  • Example
  • Conclusion
• Axially symmetric modeling
  • Theory
  • Implementation; the adepted module to include axial symmetry
  • Examples
    • Circular island
    • A well in a semi-confined aquifer
  • Conclusion
• Stream lines
  • Stream lines
  • The stream function
  • The stream function implemented
  • Examples
    • Smart pumping below a building pit: a flat and an axially symmetric model
    • A partially penetrating well, analytic verification
  • Conclusion
• Transient flow
  • Theory
  • Implementation
  • Implementation; the adepted module to include axial symmetry
  • Examples
    • Preparatory work
    • A well in a confined (or unconfined) infinite aquifer (Theis)
    • Well in the center of a circular island
    • Water balance
    • A well in a semi-confined aquifer (Hantush)
  • Excercises
    • Compute / show delayed yield
    • Compute well-bore storage (Boulton)
  • Conclusion
• Particle tracking (under construction)
  • Flow lines as opposed to stream lines
  • Theory
  • Implementation
  • Verification
  • Example
  • Conclusion

Indices and tables

• Index
• Module Index
• Search Page