Figure 23.6: Mesh conversion: quadrilateral triangles 23.7: New node insertion New node insertion [12]: not well-shaped mesh -+ flat angle, see Figure 23.7 Pairing of adjacent triangles(tetrahedra)[14: pairing test should be performed to generate conver quadrilaterals. -pairing AABC and ACDA is unsuitable, see of triangles Mesh Smoothing Make elements better-shaped by iteratively repositioning an internal node Pi, [12 p+ where N is the number of elements connected by P Pi converges to the centroid of the polygon formed by its connected neighbors Example: After 5 iterations, Pi converges from(7, 4)to(4.5, 3), see Figure 23.9 23.1.6 Mesh Conformity If adjacent elements share a common vertex or whole edge or a whole face, see Figure 23.10, we have conforming mesh. Otherwise, mesh is non-conformin
Figure 23.6: Mesh conversion : quadrilateral → triangles Figure 23.7: New node insertion – New node insertion [12]: not well-shaped mesh → flat angle, see Figure 23.7. – Pairing of adjacent triangles (tetrahedra) [14]: pairing test should be performed to generate convex quadrilaterals. → pairing ∆ABC and ∆CDA is unsuitable, see A B D C Figure 23.8: Pairing of triangles Figure 23.8. Mesh Smoothing Make elements better-shaped by iteratively repositioning an internal node Pi , [12]. • Pi = Pi+ PN j=1 Pj N+1 , where N is the number of elements connected by Pi . → Pi converges to the centroid of the polygon formed by its connected neighbors. • Example: After 5 iterations, Pi converges from (7,4) to (4.5,3), see Figure 23.9. 23.1.6 Mesh Conformity • If adjacent elements share a common vertex or whole edge or a whole face, see Figure 23.10, we have conforming mesh. Otherwise, mesh is non-conforming. 6
Figure 23.9: Mesh smoothing (a)Conforming meshes (b) Non-conforming meshes Figure 23.10: Conforming and non-conforming mesh
Pi x y x y Figure 23.9: Mesh smoothing (a) Conforming meshes (b) Non−conforming meshes Figure 23.10: Conforming and non-conforming mesh 7