Using the triangle libraries

Triangular grids can be created from a simple planar straight line graph (pslg) which is specified as the pslg file in suntans.dat. The format of this file is similar to the format of the planar straight line graph file for use in triangle. The planar straight line graph file is a listing of points and edges that make up a closed contour. These edges will comprise the boundaries of the triangulation that are created by the triangle libraries. The simplest PSLG file is one which specifies a box with sides of length 1. This requires four points and four edges, as shown in the following file box.dat:

# Number of points
4
# List of points (x,y,marker)
0.0 0.0 0
0.0 1.0 1
1.0 1.0 2
1.0 0.0 3
# Number of segments
4
# List of segments and boundary markers (point #, point #, marker)
0 1 1
1 2 1
2 3 1
3 0 1
# Number of holes
0
# Minimum area
.005

The minimum area causes the triangle program to continue to add triangles until the minimum area of one of the triangles satisfies this area. Setting the pslg variable to box.dat in suntans.dat and running SUNTANS with

mpirun sun -t -g --datadir=./data

This creates a triangulation composed of 256 right triangles within a square with sides of length 1. The three columns after the number of points specification correspond to the x-y coordinates of each point, along with a marker for each point. Following the number of segments specification, the first two columns specify the indices of the points that make up the end points of each segment in C-style numbering, such that the indices go from 0 to one less than the number of points. The third column in the segment list specifies the marker for each segment. This is how the boundary conditions are specified, and is discussed in more detail in Section 4.2. The number of holes is currently not used.

Degenerate triangulations may arise when neighboring triangles are close to having right angles. In this case the distance between the Voronoi points may be close to zero and hence may severely limit the time step. This is remedied by setting the CorrectVoronoi variable to 1 in suntans.dat. If this parameter is set, then the Voronoi points are corrected when the distance between Voronoi points is less than VoronoiRatio times the distance between the cell centroids. For example, for two neighboring right triangles, the Voronoi points will be coincident and hence the distance between the Voronoi points of these neighboring triangles will be zero. If VoronoiRatio is set to 0.5, then the Voronoi points are adjusted so that the distance between them is half the distance between the cell centroids. If VoronoiRatio is set to 1, then the Voronoi points correspond to the cell centroids.

A useful m-file checkgrid.m is provided in the suntans/mfiles directory that determines the shortest distance between Voronoi points on a grid as well as a histogram of the Voronoi distances on the entire grid. It is important to remember that most grid generation packages, including triangle, are meant for finite-element calculations in which calculations are usually node-based (i.e. everything is stored at the Delaunay points). Because SUNTANS is Voronoi-based, this places a strong constraint on the distance between the Voronoi points and as a result it can be quite difficult to generate good grids in highly complex domains. We have found a great deal of success with the grid generation package GAMBIT from Fluent, Inc. and use it for most of our production-scale SUNTANS runs.