Mesh Quality and definition

8/20/2019 Mesh Quality and definition

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esh Quality and Definition

Mesh Quality Overview

Generally, there are four criteria to evaluate the qualities of the solid mesh, which are aspect ratio,

skewness, orthogonality, and smoothness. Aspect ratio is the most important criteria to evaluate the

qualities ofeach individual element. On the other hand, skewness, orthogonality and

smoothness, show the quality prediction for two adjacent elements sharing the same inner face. The

definition of each quality is explained elow.

Aspect Ratio of Triangle (Element)

The aspect ratio of a triangle is defined as !"i#"o where "i is the radius of the circle inscried in a

triangle and "o is the radius of the circle circumscried around the triangle. The aspect ratio of a

triangle lies etween $ and %. The larger aspect ratio implies the etter quality of the triangle. &or the

triangle with an area of 'ero, the aspect ratio is $. &or the equilateral triangle, the aspect ratio is %.

Fig. 1: The definition of triangle aspect ratio

Aspect Ratio of Tetrahedron

The aspect ratio of the tetrahedron is defined as ("i#"o, where "i is the radius of the sphere inscried

in the tetrahedron and "o is the radius of the sphere circumscried around the tetrahedron. The

aspect ratio of the tetrahedron also lies etween $ and %, and the larger aspect ratio implies the

etter quality of the tetrahedron. &or a tetrahedron with 'ero volume, the aspect ratio is $. &or a

equilateral tetrahedron, the aspect ratio is %. As shown in the figure elow, the left one is the frontview of an equilateral tetrahedron element, whose aspect ratio is good. The element on the right is

the tetrahedron y decreasing the height of the equilateral one , which its aspect ratio is poor.

Fig. 2: Good aspect ratio V.S. poor aspect ratio for tetrahedron element

Aspect Ratio of Prism

The aspect ratio of a prism is defined as )Aupper *Alower +#! where Aupper is the aspect ratio of the upper

triangle of a prism and Alower is the aspect ratio of the lower triangle of a prism. alculating ased

on the definition of triangle aspect ratio, the aspect ratio of the prism also lies etween $ and %. -arge

aspect ratio implies etter quality of the prism. The height of prism is not considerd into the definition

of aspect ratio. As shown elow, the aspect ratio of the left prism element seen from the top view is %,

which is good. The element on the right is the triangle y decreasing the height of the equilateral

one, which its aspect ratio is poor.



Fig. 3: Good aspect ratio V.S. poor aspect ratio for prism element

!ewness

kewness is defined as where e is inner face center, e/ is the connect center of

and A is area of face e. The inner faces may e triangles or quadrangles. 0 and 1 are centers of cells

adjacent to face e. ells may e tetra, pyramid, prism or hexa solid elements. The quality of

skewness indicates the distance etween the connect center and face center. And its value is

normali'ed y the square root of inner face area. 2f these two centers, e and e/, are coincident, theskewness is equal to %. The skewness is influenced y the area of inner face. The smaller skewness

implies a igger distance etween two centers. 3y definition, the skewness may e negative. As

shown in &ig 45%$6, the skewness is good for the left face, and is ad for the right one.

Fig. 4: The definition of skewness

Fig. 5: Good skewness V.S. poor skewness

Orthogonality

Orthogonality is defined as the angle in degrees etween , connection vector of cell centers

and " normal vector of inner face. The orthogonality lies etween $ and %6$. The value of $

implies the est situation, and the larger value indicates poor orthogonality.



Fig. : The definition of orthogonalit!

Two examples shown in elow figure descrie the good orthogonality and the poor one.

Fig. ": Good orthogonalit! V.S. poor orthogonalit!

Fig. #: Good orthogonalit! V.S. poor orthogonalit!

moothness

moothness is defined as volume ratio of two cells adjacent to the same inner face, and it is always

the ratio of the small volume to the large one. The smoothness lies etween $ and %, and the larger

smoothness implies the smoother volume of adjacent elements.

The quality ranges for each criterion are listed in the following tale.

Mesh for Plastic and Cooling

ChannelMesh for Mold Base

Mesh Quality RangeGood Quality

Range

Poor Quality

Range

Good Quality

Range

Poor Quality

Range

Aspect Ratio (0.0, 1.0 (0.!, 1.0 (0.0, 0.! (0.01, 1.0 (0.0, 0.01

"#e$ness (%∞, 1.0 (0.&, 1.0 (%∞,0.& (0.01, 1.0 (%∞,0.01



'rthogonality (0, 10 (0, )0 ()0, 10 (0, * (*, 10

"+oothness (0.0, 1.0 (0.0, 1.0 (0.0, 0.0 (0.00, 1.0 (0.0, 0.00

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Mesh Quality and definition