Mesh Quality

What is the Definition of Mesh Quality?

You can evaluate the quality of a volume mesh with Display > Plot > Cell Distribution. There are several evaluation methods, but this FAQ will only introduce the more representative ones.

Size
• Option > Size
• Mesh size [m3]

Equilateral Volume Deviation
• Option > Quality > Quality Measure > Skewness > Tri/Tet Skewness Method > Equilateral Volume Deviation
• Also known as Equi-Size-Skew (ESS) in GAMBIT
• ESS = (Seq / S) / Seq, where

• Seq is the maximum volume of the equilateral cell (maximum area in 2D) whose radius is the same as the radius of the circumcircle of the mesh element
• S is the volume of the mesh in (2D)

Equilateral Volume Deviation takes on a value between 0 and 1 (0 inclusive)

Normalized Equiangle Deviation
• Option > Quality > Quality Measure >Skewness > Tri/Tet Skewness Method > Normalized Equiangle Deviation
• Also known as Equi-Angle-Skew (EAS) in GAMBIT
• EAS = max {(θmax - θeq) / (180 - θeq), (θeq - θmin) / θeq}, where

• θmax and θmin are the maximum and minimum angles between the edges of the element
• θeq is the edge angle between isosceles cells
• θeq is 90° for a triangle (2D) or tetrahedron element (3D), and 60° for a square (2D) or hexahedron element (3D)