Mesh Quality Metrics: Orthogonal Quality and Aspect Ratio Limits

Numerical stability and accuracy in Finite Volume CFD solvers are highly sensitive to mesh quality. Poor grid quality leads to slow convergence or floating-point errors.

Key Metrics

• Aspect Ratio: Ratio of the longest edge to the shortest edge of a cell. For boundary layer inflation cells, high aspect ratios (up to 100) are acceptable, but in high-velocity gradient zones, it should be close to 1.
• Orthogonality: Measures the angle between the face normal vector \(\vec{A}_i\) and the vector linking cell centroids \(\vec{d}\). The orthogonality metric \(O_q\) is calculated as:
  \[O_q = \frac{\vec{d} \cdot \vec{A}_i}{\|\vec{d}\| \|\vec{A}_i\|}\]
  Values close to 1 represent ideal grid orthogonality.
• Near-Wall Mesh Spacing (\(y^+\)): Determines if near-wall modeling uses wall functions or resolves viscous sublayers:
  \[y^+ = \frac{u_\tau y}{\nu}\]
  Where \(u_\tau = \sqrt{\tau_w/\rho}\) is the friction velocity. Resolve sublayers require \(y^+ \approx 1\); wall functions require \(30 < y^+ < 300\).

References

• Roache, P. J. (1998). Verification and Validation in Scientific Computing. Hermosa Publishers.