GGU-3D-SSFLOW: General
An analytical solution is only possible for simple groundwater systems. When modelling complicated systems, numerical solutions are required. In the main
finite-difference-methods (FDM) and
finite-element-methods (FEM)
are used. Using finite methods, the whole area is subdivided into a large amount of smaller (finite) areas (elements). Generally, using FEM, triangles are selected for these areas. Within these triangles simple, generally linear, approximation functions are used. The actual, complicated, whole solution is pieced together like a mosaic from the many simple partial solutions. Equation systems result, in which the number of variables corresponds to the number of system nodes. With the finite-difference-method one generally has only the possibility of defining a discrete whole using rectangular partial-areas. In contrast to FEM therefore, FDM is a lot less flexible when it comes to adjusting to complicated boundary structures. Also, in some areas, mesh refinement is not as easy. Further, the resulting equation systems are numerically more stable for FEM. The main advantage in FDM is in the theoretically simpler mathematical relationships, which generally will be of little interest to the program user. The GGU-3D-SSFLOW program uses the finite-element-method.
When using the application please remember that all finite-element or finite-difference-methods are approximation methods. The quality of the approximation compared to the actual solution increases with the fineness of the mesh. You should pay attention to the fact that in areas where the main subsurface hydraulic action takes place (e.g. wells, seepage elements), the mesh subdivisions should be finer. The type of triangle used also exerts a certain influence. Optimum conditions are achieved with equilateral triangles. You can get an overview of the solution quality by calculating the same system with a coarser and a finer mesh subdivision, and comparing the deviation of the two results.
The following general notes are important:
triangular elements are used,
Darcy's Law is valid,
the piezometric heads are calculated in a linear manner for each element,
from the linear approximation of the piezometric heads, a constant approximation of velocities results. In order to achieve a better quality of velocity approximation, the velocities for calculation of flow lines are averaged to node values in a follow-up calculation.
The procedure is:
For each element node the velocities in the neighbouring elements are added and then divided by the number of neighbouring elements. By doing this, the velocity course can be better presented. At the boundary nodes, the results are naturally not quite as exact. Further, the approximation of velocities in the region of element nodes with differing material types can be worsened in this way. If the velocities at such boundary nodes are of great interest, help is available by refining the element mesh in these areas.