GEOMESH grid generation uses three criteria to insure grid quality. They are: (1) the final grid preserves the input geometry model, (2) the grid is Delaunay (Figure 2) and (3) all coupling coefficients are positive. It is beyond the scope of this work to give the mathematical details of Delaunay triangulation. However, an intuitive definition of a Delaunay triangulation is that the circumscribed circle of any triangle contain the three points of the triangle and no other points. The extension to three dimensions is that the circumscribed sphere of any tetrahedra contains the four points of the tetrahedra and no other points. There are special cases and degeneracies when the above description is not absolutely correct, but these cases are not important to this discussion. The third constraint, that the coupling coefficients related to grid geometry produce a semi-positive definite matrix (Trease and Dean, 1990, Gable et al. 1995), insures that the solutions to nonlinear flow and transport will be stable and accurate. In addition, there are no negative transmissibilities when solving porous flow problems.
Many of the problems associated with importing data into grid generation tools results from insufficient GSIS output to completely characterize the solid geometry model. This may be a consequence of ambiguities in the output geometry model. Some GSIS packages produce beautiful graphical representations of the geometry model, but do not provide utilities or an open architecture for exporting the solid geometry model.
Examples
The first example, (Figure 3) shows a 3D grid produced from a GSIS 3D geometry model. The GSIS model is composed of hexahedral (8 node, 6 sided elements). However there are many degenerate elements that must be eliminated. For example, when a layer pinches out the GSIS model retaines zero volume elements as part of the output. While this produces a correct representation of the geometry, physics codes cannot compute on zero volume elements. Furthermore, the GSIS output produces elements without regard element shape or grid quality.
In order to produce a grid for computation from the GSIS output the following steps are taken: (1) extract the 3D geometry model, (2) convert the hexahedral elements to tetrahedral elements by subdividing, (3) eliminate the zero volume and degenerate elements, (4) reconnect the grid to insure a Delaunay grid while never disrupting material interfaces, (5) subdivide elements to insure positive coupling coefficients and(6) output node coordinates, connectivity, coupling coefficients and a list of boundary and material nodes. This grid is then used for computation of unsaturated porous flow and contaminant transport (Robinson et al. 1995).