# zone geometry-test command

Syntax

zone geometry-test <range>

Evaluate the integrity of model zones. FLAC3D has three basic tests built in to check the integrity of gridded models, to make sure that the model is adequate for simulation purposes. For example, these tests can be used to check whether there is improper mapping of gridpoints during execution of a grid-generation data file in FLAC3D, resulting in some zones being inside out and, hence, not suitable for simulation. It can also be used to check whether a zone is degenerate. Degeneracy can occur if a primitive is created without satisfying the requirements of geometry conditions, such as the number of vertices, edges and faces for that particular primitive. Warning messages are given if any of the zone primitives are degenerate or cannot support two overlays.

In addition to tests for degeneracy and overlay support, the geometric aspects of zones are further evaluated using four quantities: aspect ratio, volume ratio, orthogonality and face planarity. The quantities compare the zones to an idea one - a zone that all edges are equal, except for a degenerate brick zone whose idea one is assumed to a degenerated cube. zone geometry-test invokes the test for all four of these geometric quantities.

Aspect Ratio — The ratio of the shortest edge length to the longest edge length. This will be assumed 1.0 for an ideal zone. It will approach zero as the zone becomes stretched or flattened. The result is required to be normalized for degenerate brick zones with a multiplication factor of $$\sqrt{2}$$. See FISH function zone.aspect or zone.condition.

Volume Ratio — The ratio of the smallest tetrahedron and the averaged tetrahedron in the zone. For wedge, tetrahedron, pyramid and degenerate brick zone type with ideal shape, this measurement gives 1. However, for an ideal brick, it gives 5/6. Thus the result is required to be normalized for brick zones with a multiplication factor of 1.2. See FISH function zone.condition.

Orthogonality — A measurement of how “well” sides of the zones are inclined to each other. For each gridpoint in each zone, the determinant of the matrix defined by the three edge vectors is computed and divided by the product of their lengths. This gives 1.0 for a cube, and approaches zero as pairs of edges approach being coplanar or all three approach being coplanar. Each zone is measured by the worst orthogonality value of all gridpoints. The result is required to be normalized with a multiplication factor of $$2/\sqrt{3}$$ and with $$\sqrt{2}$$ for other non-brick zones. See FISH function zone.ortho or zone.condition.

Face Planarity — Hexahedrons are composed of 6 quadrilateral faces, just like a cube’s square faces. However, it is possible that the four vertices of a quadrilateral polygon will not be coplanar in 3D. FLAC3D allows faces to be nonplanar, but the greater the deviation, the less accurate the solution process will be. There is no clear singular method of measuring planarity. A method that compares the volume of a tetrahedron filling the 4 vertices and the area of the quadrilateral face, computing the area by adding a central point, $$m = (A + B + C + D)/4$$, and computing the 4 triangle areas, ABC, ABD, ACD, BCD, is chosen. The ratio of the cube root of the volume to the square root of the area (to get a dimensionless value) is computed. This value is zero if planar, and positive if nonplanar. This test can be “scaled” by a constant because there is no fundamental limit on how nonplanar a face can be. (Values should be << 1.0 for a face to be good.) Each zone has its six faces tested, and the worst value is reported.

Reporting average values for these tests are meaningless because some grids might be 90% good and 10% bad and give the same average as a grid with an 80% test quality. Instead, distribution of values for all of the four parameters across all zones in the range specified is reported. The distribution ranges from 0 to 1.0, with a 0.1 interval. Thus, all zones fall within these 10 intervals. This distribution helps identify the number of bad zones, and how bad these zones are. Note that these tests are useful for relative comparisons between different grids for the same geometry. For a model to perform well with FLAC3D, aspect ratio, volume ratio and orthogonality should be near 1.0, and planarity test values near 0.0. FISH functions (see zone.condition) can be written to group all zones that failed to meet minimum standards, and thus visualize the bad zones.