## Description

For blocks only, vertex-centered orthogonality is computed as an area-weighted
average of the orthogonality angles associated with each bounding face of the dual mesh
control volume around the vertex. For more information on how volume cells are
subdivided into sectors to form the dual mesh control volume, see the page on Vertex-Centered Volume.

The orthogonality angle (shown in red in the diagram below) for a volume cell's edge is computed as the angle between
the unit edge vector (represented as the solid black arrow) and the quadrilateral defined by the edge
midpoint, the adjacent face centroids, and the volume centroid. This quadrilateral belongs to
the boundary of the dual mesh control volume for both vertices in the edge.

The orthogonality angle (shown in red) for a volume cell's edge (shown in black). The quadrilateral formed by
the edge midpoint (blue circle), adjacent face centroids (green squares), and the volume
centroid (yellow triangle) belongs
to the boundary of the dual mesh control volume for both vertices in the edge.

This metric affects robustness for vertex-centered solvers and ranges from 0 degrees to 90
degrees, with 90 representing perfect orthogonality. For this function, the probe renders the
vertex and the bounding faces of the dual mesh control volume.

**Tip:** Use the probe
functionality while in the *Examine* command to visualize the dual mesh
control volume when examining any vertex-centered function.