K2dGrFlow, 2-dimensional groundwater flow

Background

In normal words : make a GUI programm, that's free, quick and easy to use, to model a certain type of groundwaterflow. Since it's a good thing to start with the easy things, we took steady state flow (no time dependancy), under heavy asumptions :

• As said, it is steady-state, so no time variation.
• The longitudinal component of the flow is very small, so may be discarded.
  This means that we only must consider 2 directions : an x-direction in the horizontal plane, and a z-direction vertically.
• Only two types of boundary conditions, the first: impenatrable walls.
  Physically this means that the border has a conductivity several orders below the groundlayer we consider, or the border is a symmetry boundary over which we assume no flow (eg a water divide in the landscape).
• The other possible boundary condition is a Dirichlet condition that makes sence.
  If a border is given by the points (xb,zb), then the hydraulic head in that point may be zb or a X xb +b with a and b constants.
  The first possibility means the hydraulic head is the atmospheric pressure on the boundary, wich means it's the water table.
  The second condition means it's a linear function in the x term. Since our problem is time-independant, the flow through these borders must be kept constant. This means eg a steady rainfall model for the domain so that this is possible.

Extensions

1. MANY bug fixes - June 2001. Results for the designed use of the program are now 100% correct, also for d not 0. For this an extra parameter was added to correct for abberations on the Dirichlet boundary. In short, the matrix can be made to behave better by multiplication by a factor of the values that correspond to Dirichlet nodes.
2. Possibility to select the number of contours in the figure - August 2001
3. Different problem to be solved. The user can now select between two formulas that can be solved over the domain - August 2001
4. Extension, semi-infinite rectangles added as an extra division of the domain. These elements are automatically selected if the user marks the bottom boundary (which has to be a vertical line), as a imaginary boundary where the domain goes to -infinity in the z coordinate. This option has a new, third, solver, that solves for the Infinite Element Method - October 2001.

Screenshots

The code, application and galerkin solver

There are two parts, a KDE application, and a general C++ solver for the galerkin finite element method. The last is still very basic, that is, it suffices for the problem at hand. Here is the old tarbal file of the code : k2dgrflow-0.2.tar.gz. CONTAINS MANY BUGS. The bugs have now been removed but I haven't made a new tarbal yet. Mail me if you are interested.

To use the program, you first need to install the meschach 1.2b library, eg from netlib, or just search it with yahoo. Don't forget after construction to put it in /usr/lib with the name libmeschach.a. Normally the make doesn't do it for you.

Secondly, you need the EasyMesh programm. For example on www-dinma.univ.trieste.it/~nirftc/research/easymesh/ . This is the programm k2dgrFlow uses to generate a mesh

Everything is in the documentention/user manual that comes with the application. Just read the INSTALL and the README files, and also look at the FAQ before mailing me.

If you want the use the galerkin library that's the engine of the programm, check out the developers chapter in the user manual for the class diagramms, and check the API reference manual for detailed information with the classes. The links to the header files are broken in this manual. You can find these in the tarbal

ToDo List

• EasyMesh is not working very performant for domains with many nodes. To be usefull it should still perform ok with 10000 nodes. I would like to incorporate own code for the construction of the mesh.
  In the same time, it should work with curves as borders, instead of lines. The mesh has a linear interpollant of the curve as a border, but each time a node is added on the boundary, the node should be again on the curve, and not on the interpollant line. (so the outer boundary of the domain changes when you add nodes)
• It must be possible to enter domains wich contain holes.
• A procedure must be added that refines the mesh. We should start with a crude mesh, and a test function to test if the result is ok in a certain element of the mesh. If the result is not ok, the mesh should be refined in that element.
  This way of working means an iterative loop of constructing the mesh, and solving the problem, until the desired correctness has been reached
• Input of a border with a parmeter equation in stead of predefined functions. This will be difficult. Means a syntax of input like eg maple.
• A better way of working with borderconditions. Now this is a part of the K2dBorderBase class. A seperate class is better.
• A better file management. The files must be stored in the standard directory for data, not where the programm resides. On deletion of a model, also generated files must be deleted.
• Better plot functions: zooming with the mouse, a density diagram, a flow field diagram, colorscale with the values of the head, saving the figures as a .fig/.eps/.jpeg file
• Option to save the global matrices to a file. Usefull for testing