Mesh Generation Examples
(1) The transition of mesh density
The example is the problem of flood analysis in the city. The boundaries are shown in Figure 1. The 25
squares inside represent the building. The mesh size on the internal boundaries should be smaller than
on the external boundary.
Figure 1. The geometry
The mesh size on the internal boundaries is specified 30m and 100m on the external boundary. The
generated mesh is shown in Figure 2(a). The mesh near internal boundaries is magnified and shown in
Figure 2(b). The mesh size ratio of external and internal boundaries reaches to 3.3. The total 18229
elements are generated, in which the maximum internal angle is 156.40 degree and minimum internal
angle is 40.40. The number of elements whose internal angle greater than 150 degree or less than 30
degree is 3.
Figure 2. The mesh
The mesh size on the internal boundaries is specified 30m and 200m on the external boundary. The
generated mesh is shown in Figure 3(a). The mesh near internal boundaries is magnified and shown in
Figure 3(b). The mesh size ratio of external and internal boundaries reaches to 6.7. The total 8549
elements are generated, in which the maximum internal angle is 153.33 degree and minimum internal
angle is 35.06. The number of elements whose internal angle greater than 150 degree or less than 30
degree is 1.
Figure 3. The mesh
The mesh size on the internal boundaries is specified 30m and 300m on the external boundary. The
generated mesh is shown in Figure 4(a). The mesh near internal boundaries is magnified and shown in
Figure 4(b). The mesh size ratio of external and internal boundaries reaches to 10. The total 7383
elements are generated, in which the maximum internal angle is 158.85 degree and minimum internal
angle is 21.63. The number of elements whose internal angle greater than 150 degree or less than 30
degree is 10.
Figure 4. The mesh
(2) Complex geometry boundaries
Figure 5. The geometry
The example is the problem of flood analysis for dam-break. The geometry is shown in Figure 5.
The right region is reservoir and the left region is the river. The boundary of the river is relatively
complex.
The mesh size on the river boundary is specified 30m and 100m on the reservoir boundary. The
generated mesh is shown in Figure 6.
Figure 6 The mesh
(3) The mesh refinement
The example is problem of flood analysis and the geometry is shown in Figure 7. The internal two
curves represent the river dike and the fine elements are needed inside. The internal mesh size is
specified 300m and 1000m on the external boundary. The generated mesh is shown in Figure 8.
Figure 7. The geometry Figure 8. The mesh
(4) The internal feature constraints
The feature constraints include constraint lines/curves, constraint points, and local
refinement/coarseness. For some engineering analysis, the loads and boundary conditions need to
be applied along the internal lines, or directly on some fixed points in the interior. These situations
require that the nodes must be generated along the lines or on the fixed points. These internal lines
are called constraint lines and the fixed points are called constraint points. For example, in the city
flood analysis model, the roads and rivers in the city are regarded as constraint lines; in the floor
analysis system, the loads are usually applied along the lines/curves or on the fixed points on the
planar region. If the analysis model is composed of different regions, the boundaries of neighbor
regions also belong to constraint lines. For the analysis such as stress analysis or crack analysis, the
mesh needs to be refined over specific areas in order to improve calculation accuracy. Under this
situation, the mesh density needs to be specified along some lines or on some points in the interior
and the mesh generator then produce fine elements around the lines and points according to the
density. These lines are called density lines and the points are called density points.
(a)The geometry with feature constraints (b)The mesh
Figure 9. The mesh generation with internal feature constraints
Figure 9 shows the result of the mesh generation for a domain with internal feature constraints. The
domain is composed of two sub-domains as shown in Figure 9(a). There are one line constraint, four
constraint points, one density line and one density point in first sub-domain. The second sub-domain is
a circle region. The quadrilateral mesh generated based on the element size information is shown in
Figure 9(b). Figure 10 shows the mesh generation of the floor analysis model, in which the load is
applied to the constraint lines and points.
Figure 10. The mesh generation for floor analysis model
(5) Adaptive mesh generation
The optimal mesh density distribution is calculated automatically based on the element number, the
boundary curvature, geometry feature and field variable gradient etc, and then the mesh is generated
over the domain based on the mesh density.
Figure 11. Mesh generation based on the curvature Figure 12. Based on geometry feature
Figure 13. Based on density windows
Figure 14. Based on the field variable gradient
(6) The mesh density specification
The mesh density is specified on the boundaries and inside the domain manually. The smooth mesh
density distribution is calculated automatically and then the mesh is generated based on the mesh
density
Figure 15. The mesh density specification