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Figure from:Efficient unstructured quadrilateral mesh generation

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Figure 16. Application of the mesh generation algorithm to adaptive computations: (a) Initial mesh (462 elements); (b) Second mesh (856 elements); (c) Third mesh (2235 elements); (d) Final mesh (3307 elements). — Figure 16 Application of the mesh generation algorithm to adaptive computations: (a) Initial mesh (462 elements); (b) Second mesh (856 elements); (c) Third mesh (2235 elements); (d) Final mesh (3307 elements).

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Figure 2. Angles formed by a candidate splitting line. Figure 1. Line r is not acceptable because it runs outside the domain, line s is acceptable. where c;, i=1,...,5, are used as weighting values. Equation (1) is evaluated for each acceptable splitting line. The best one, which will decompose the domain into two polygons, is the one that minimizes (1). The geometrical criteria are presented next.

Table I. Local structuring index values.

Figure 4. Definition of the characteristic length of a given domain. Figure 3. Influence of the splitting line length in the results. In the case on right, the centre of the domain will not be meshed with the proper density.

Figure 5. Relocation of 7; points along the splitting line: (a) general case; (b) definition of the function II(x) as two constants. actual angle from 2/2 can be computed as

Figure 6. Several steps in the mesh generation process for the two rotated squares problem.

Figure 7. Representation of the set of triangles (shadowed) around node P;.

Figure 8. Final mesh for the two rotated squares example: (a) without background mesh; (b) with background mesh.

Figure 9. Bin-tree representation of the proposed algorithm.

Table II. Slopes of the linear regressions. Notice that these examples contain all the characteristics that a general domain could show: simple- connected and multi-connected domains, constant and variable element size distributions, as well as the utilization of background meshes. For each case, the following linear regression have been performed:

Figure 10. Discretization of a dock: (a) intermediate state in the meshing process; (b) final mesh.

Figure 12. Discretization of a gear: (a) generated mesh; (b) background mesh.

Figure 11. Discretization of a rail cross section.

Figure 13. Discretization of the port of Barcelona.

Figure 14. Detail of a part of the outer dock of the port of Barcelona.

Figure 15. Detail of a part of the inner dock near the mouth of the port of Barcelona.

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