What are the common causes and effects of mesh distortion in CAD?

1 What is mesh distortion?

Mesh distortion is the measure of how much the mesh elements differ from their ideal shape and size. In an ideal situation, the mesh elements should be close to equilateral triangles or quadrilaterals in 2D, or tetrahedra or hexahedra in 3D. Unfortunately, due to factors such as complex geometry, boundary conditions, or mesh refinement, the mesh elements may become distorted. This skewing, stretching, or compressing of elements can have a detrimental effect on the quality of your mesh. It can reduce accuracy of results, increase computational time and cost, cause numerical errors or instability, and create visual artifacts or defects.

2 How to measure mesh distortion?

Different metrics can be used to measure mesh distortion, depending on the type and shape of the mesh elements. Common metrics include aspect ratio, skewness, Jacobian, and smoothness. Aspect ratio is the ratio of the longest to shortest edge of an element, with a high aspect ratio indicating a stretched or elongated element. Skewness is the angle between the edges of an element and the lines connecting midpoints of opposite edges, with a high skewness signifying a distorted or twisted element. Jacobian is the determinant of the transformation matrix that maps an element from physical space to reference space, with a low or negative Jacobian indicating a compressed or inverted element. Finally, smoothness is the variation of element size or shape across the mesh, with a low smoothness signifying a sudden or large change in size or shape. Most CAD software have tools or functions to calculate and display these metrics and highlight elements that exceed thresholds of distortion.

3 How to prevent mesh distortion?

To prevent mesh distortion, it is best to follow certain best practices in the mesh generation process. This includes selecting the appropriate mesh type and size for your problem, as different types of problems may require different meshes. Quality meshing algorithms and techniques should also be used, as they can generate a high-quality mesh for your geometry and handle complex features. Mesh refinement and adaptation can be useful to improve accuracy and efficiency, but they should be done sparingly and selectively and monitored carefully to ensure the mesh quality is not compromised.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?