### Tech Briefs

ADINA offers powerful meshing tools to help users generate high-quality meshes of various element types. In this Tech Brief, we give a brief educational overview of the advancing front and Delaunay triangulation methods used for generating free-form meshes. We also demonstrate ADINA’s newly enhanced boundary layer meshing. A more comprehensive description of all the meshing tools offered in ADINA is given in the new ADINA Handbook, which can be downloaded by users at the end of this brief.

The advancing front method generates meshes by progressively adding elements to the "front", which is initially located at the domain’s boundaries. The mesh advances inward from the boundaries towards the interior of the domain until the front "closes" and the domain is completely meshed.

The benefit of the advancing front method is the high quality elements generated, especially near boundaries. The main drawbacks are the difficulty in closing the front in three dimensions and poorer element quality in regions where fronts collide.

Delaunay Method

The Delaunay method generates meshes by satisfying the Delaunay criterion that states for a given set of points (nodes) in two dimensions, a triangular mesh can be constructed where circles that circumscribe the triangles contain no nodes in its interior and the minimum angle of the triangles is maximized. This same idea generalizes to three dimensions where spheres circumscribe the tetrahedrals. Delaunay meshes meet element quality demands by inserting additional nodes.

The principal strength of the Delaunay method is its ability to robustly mesh complex domains in three dimensions. In addition, several advanced options, such as curvature-based meshing, automatic grading, and size functions, are only available when using the Delaunay method.

Figure 1 shows a comparison between the advancing front and Delaunay methods. Note the regular pattern and high-quality elements formed off the boundaries on the advancing front mesh (left) as compared to the Delaunay mesh (right).

Figure 1  Two-dimensional meshes created using the advancing front method (left)
and the Delaunay method (right)

Boundary Layer Meshing

Creating boundary layer meshes is conceptually similar to advancing a front of elements from the domain’s boundary. However, rather than advancing the front one element at a time, the boundary layer "front" is advanced all at once.

In ADINA 9.1, boundary layer meshes can be applied across sharp corners where the boundary layer thickness is greater than the element thickness. Figure 2 shows a simple geometry meshed with boundary layers along all edges. The boundary layer meshes are composed of quadrilateral elements, and the internal mesh is composed of triangular elements. Note how ADINA automatically handles the regions near the sharp angles: the boundary layers mesh smoothly transitions from perpendicular to the bounding edges at the central region to a 45-degree angle at the sharp corners.

Figure 2  Two-dimensional mesh with boundary layers

Of course, boundary layer meshes can also be generated in three dimensions. When doing so, the user may select either hexahedral (brick) or prismatic (wedge) elements in the boundary layers. If hexahedral elements are chosen for the boundary layer mesh, the interior of the body is free-form mixed meshed using a combination of hexahedral, pyramid, and tetrahedral elements. If prismatic elements are chosen for the boundary layer mesh, the interior of the body is free-form tetrahedral meshed. Users can specify the total thickness, the progression type, and number of element layers in each boundary layer.

Figure 3 shows an example of a boundary layer mesh generated on all faces of a manifold pipe where a wall no slip boundary condition is applied.

Figure 3  Three-dimensional mesh generated with boundary layers along no-slip surfaces

Although boundary layer meshes are most often associated with CFD problems, they can also be useful in structural problems. For example, Figure 5 shows a contact problem with a boundary layer mesh placed along the contacting edge of the body. The resulting mesh can accurately capture the high stress gradients and location of maximum effective stress just beneath the surface. The movie above shows the stress distribution as the curved surface comes into contact with and deforms the compliant material.

Figure 4  Contact problem showing a structural application of mesh boundary layers

This Tech Brief describes the primary free-form triangulation methods used in ADINA and demonstrates ADINA’s boundary layer meshing capabilities, which allow users to generate high-quality meshes for structural, CFD, FSI and multiphysics models.

The new ADINA Handbook describes, among many ADINA features, all of ADINA’s meshing capabilities and advanced meshing options. The ADINA Handbook also includes detailed illustrations and examples, and gives the commands for each example, which readers may copy and paste directly or modify for use within their own input files of models. The ADINA Handbook helps users quickly, and confidently brings to bear ADINA’s advanced meshing features upon their own modeling challenges.