Mesh Quality
What element quality means in Dr.Q: one number per element, and what drives it.
Mesh quality directly affects result accuracy. Distorted or inverted elements produce inaccurate results and can make the solve fail.
One number per element
Dr.Q reports mesh quality as a single value per element between 0 and 1: 1 is an ideal element, 0 is degenerate or inverted. There are no separate skewness, aspect-ratio, or Jacobian fields to read off; you get one normalized quality number. A convergence study looks at the worst element in the mesh, its minimum quality.
The formula behind that number adapts to the element type, so the single scalar stays comparable across a mixed mesh:
- Tetrahedra and triangles use a shape/collapse ratio, how flat or stretched the element is relative to an ideal one.
- Hexahedra and quadrilaterals use a Jacobian ratio, comparing the most and least stretched integration points; it drops to 0 if the element is inverted.
You don't set or tune these formulas; they are how Dr.Q measures the elements it generates.
An element at quality 0 is degenerate or inverted and cannot be solved. That is a geometry and meshing problem to resolve upstream, not a solver setting.
What drives mesh quality
Element quality is a consequence of two things you don't dial directly: the geometry and the automatic mesher. Poor quality almost always traces back to the geometry:
- Very thin or sliver faces
- Extremely small features relative to the part size
- Very thin walls, which force stretched elements
Because quality follows from the geometry, the way to improve it is upstream: clean up the CAD, not the mesh.
The quality threshold
Dr.Q uses a quality threshold as an advisory line. During a convergence study, if the mesh's worst element falls below it, Dr.Q raises a warning that reports the minimum quality and the requirement. It does not reject the mesh or stop the run: it is a reliability flag, not a gate. Results on a mesh with very low-quality elements may be less trustworthy near those elements.
If meshing fails outright or a quality warning fires, see Mesh Errors for what to do about it.