HyperMesh

The following checks apply to both types of elements, but when applied to 3D elements they are generally applied to each face of the element. The value of the worst face is reported as the 3D element’s overall quality value.

Aspect Ratio

Ratio of the longest edge of an element to either its shortest edge or the shortest distance from a corner node to the opposing edge ("minimal normalized height"). HyperWorks CFD uses the same method used for the Length (min) check.

For 3D elements, each face of the element is treated as a 2D element and its aspect ratio determined. The largest aspect ratio among these faces is returned as the 3D element’s aspect ratio.

Aspect ratios should rarely exceed 5:1

Chordal Deviation

Largest distance between the centers of element edges and the associated surface.

Second order elements return the same chordal deviation as first order, when the corner nodes are used due to the expensive nature of the calculations.

Figure 1. Chordal Deviation

Interior Angles

Maximum and minimum interior angles are evaluated independently for triangles and quadrilaterals.

Jacobian

Deviation of an element from its ideal or "perfect" shape, such as a triangle’s deviation from equilateral.

The Jacobian value ranges from 0.0 to 1.0, where 1.0 represents a perfectly shaped element. The determinant of the Jacobian relates the local stretching of the parametric space which is required to fit it onto the global coordinate space.

HyperWorks CFD evaluates the determinant of the Jacobian matrix at each of the element’s integration points (also called Gauss points) or at the element’s corner nodes, and reports the ratio between the smallest and the largest. In the case of Jacobian evaluation at the Gauss points, values of 0.7 and above are generally acceptable. You can select which method of evaluation to use (Gauss point or corner node) from the Check Element settings.

Length (min)

Minimum element lengths are calculated using one of two methods.

• The shortest edge of the element. This method is used for non-tetrahedral 3D elements.
• The shortest distance from a corner node to its opposing edge (or face, in the case of tetra elements); referred to as "minimal normalized height".

Figure 2. Length Check

You can choose which method to use in the Check Element settings.

Note: This setting affects the calculation of the Aspect Ratio check.

Minimum Length / Size

Minimum element size is calculated using:

Shortest edge

Length of the shortest edge of each element is used.

Minimal normalized height

Is a more accurate, but more complex height.

For triangular elements, for each corner node (i), HyperWorks CFD calculates the closest (perpendicular) distance to the ray including the opposite leg of the triangle, h(i). MNH = min(hi) * 2/sqrt(3.0). The scaling factor 2/sqrt(3.0) ensures that for equilateral triangles, the MNH is the length of the minimum side.

Figure 3. Minimal Normalized Height for Triangular Elements

For quadrilateral elements, for each corner node, HyperWorks CFD calculates the closest (perpendicular) distances to the rays containing the legs of the quadrilateral that do not include this node. The figure above depicts these lengths as red lines. Minimal normalized height is taken to be the minimum of all eight lines and the four edge lengths, thus, the minimum of 12 possible lengths.

Figure 4. Minimal Normalized Height for Quadrilateral Elements

Minimal height

The same as minimal normalized height, but without a scaling factor.

Skew

Skew of triangular elements is calculated by finding the minimum angle between the vector from each node to the opposing mid-side, and the vector between the two adjacent mid-sides at each node of the element.

Figure 5. Skew of Triangular Elements

The minimum angle found is subtracted from ninety degrees and reported as the element’s skew.

Note: Skew for quads is part of the HyperMesh-Alt quality check.

Taper

Taper ratio for the quadrilateral element is defined by first finding the area of the triangle formed at each corner grid point.

Figure 6. Taper for Quadrilateral Element

These areas are then compared to one half of the area of the quadrilateral.

HyperWorks CFD then finds the smallest ratio of each of these triangular areas to ½ the quad element’s total area (in the diagram above, "a" is smallest). The resulting value is subtracted from 1, and the result reported as the element taper. This means that as the taper approaches 0, the shape approaches a rectangle.

$taper=1-{{\displaystyle \left(\frac{A_{tri}}{0.5\times A_{quad}}\right)}}_{\min }$

Triangles are assigned a value of 0, in order to prevent HyperWorks CFD from mistaking them for highly-tapered quadrilaterals and reporting them as "failed".

Warpage

Amount by which an element, or in the case of solid elements, an element face, deviates from being planar. Since three points define a plane, this check only applies to quads. The quad is divided into two trias along its diagonal, and the angle between the trias’ normals is measured.

Warpage of up to five degrees is generally acceptable.

Figure 7. Warpage

Minimum Length / Size

Two methods are used to calculate the minimum element size.

Shortest edge

Length of the shortest edge of each element is used.

Minimal normalized height

More accurate, but more complex.

HyperWorks CFD calculates the closest (perpendicular) distances to the planes formed by the opposite faces for each corner node.

Figure 8.

The resulting minimum length/size is the minimum of all such measured distances.

Tetra Collapse

The height of the tetra element is measured from each of the four nodes to its opposite face, and then divided by the square root of the face’s area.

Figure 9.

The minimum of the four resulting values (one per node) is then normalized by dividing it by 1.24. As the tetra collapses, the value approaches 0.0, while a perfect tetra has a value of 1.0. Non-tetrahedral elements are given values of 1 so that HyperWorks CFD will not mistake them for bad tetra elements.

Vol. Aspect Ratio

Tetrahedral elements are evaluated by finding the longest edge length and dividing it by the shortest height (measured from a node to its opposing face). Other 3D elements, such as hex elements, are evaluated based on the ratio of their longest edge to their shortest edge.

Volume Skew

Only applicable to tetrahedral elements; all others are assigned values of zero. Volume Skew is defined as 1-shape factor, so a skew of 0 is perfect and a skew of 1 is the worst possible value.

The shape factor for a tetrahedral element is determined by dividing the element’s volume by the volume of an ideal (equilateral) tetrahedron of the same circumradius. In the case of tetrahedral elements, the circumradius is the radius of a sphere passing through the four vertices of the tetrahedron.

Figure 10.