📐 Mesh Cell Skewness
Evaluate mesh angular and equivolume skewness to avoid numerical solver instability.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Cfd
📊 Solver Telemetry
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3,976
⚡ Solves
3,110
💾 Downloads
416
📦 Fortran Code
4.4 KB
📅 Released
Jun 2026
⏱️ Latency
< 1 ms
📥 Cell Vertices $(x, y)$
📖 Equiangular Skewness Formula:
$$\text{Skewness} = \max\left( \frac{\theta_{\text{max}} - \theta_{\text{eq}}}{180^\circ - \theta_{\text{eq}}}, \frac{\theta_{\text{eq}} - \theta_{\text{min}}}{\theta_{\text{eq}}} \right)$$
$$\theta_{\text{eq}} = 60^\circ\ (\text{Triangle}), \quad \theta_{\text{eq}} = 90^\circ\ (\text{Quad})$$
0.6257
Equiangular Skewness
146.3°
Max Angle ($\theta_{\text{max}}$)
33.7°
Min Angle ($\theta_{\text{min}}$)
90°
Ideal Equiangular ($\theta_{\text{eq}}$)
💡
Solver Suitability: Acceptable (0.50 - 0.75)
Equiangular skewness is 0.626 with corner angles ranging from 33.7° to 146.3°.
Acceptable in complex geometries, but may require second-order upwind non-orthogonal corrections.
📐 2D Element Geometry & Corner Angle Visualizer
Acceptable (0.50 - 0.75)🔍 View Raw GNU Fortran Double-Precision Solver Output
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📘 Calculation Methodology: Mesh Equiangle & Equivolume Skewness
Mathematical Model & Theory
Equiangular skewness evaluates cell distortion relative to an ideal equilateral polygon ($\theta_e = 90^\circ$ for quads/hexes, $60^\circ$ for triangles/tets):
$$Q_{EAS} = \max\left( \frac{\theta_{max} - \theta_e}{180^\circ - \theta_e}, \frac{\theta_e - \theta_{min}}{\theta_e} \right)$$
$$\text{Quality Scale: } Q < 0.25 \text{ (Excellent)}, \quad Q > 0.85 \text{ (Poor)}$$
Assumptions
- Applicable to 2D and 3D volumetric unstructured meshes.
- High skewness increases linear solver iterations and numerical diffusion.
Academic References
- Frey, P. J., & George, P. L.: Mesh Generation, ISTE.
- ANSYS Meshing User's Guide.
Worked Engineering Example
Problem Statement:
A triangle has angles $\theta = [20^\circ, 135^\circ, 25^\circ]$. Calculate equiangle skewness.
Step-by-step Solution:
1. $Q_{max} = (135 - 60) / 120 = 0.625$, $Q_{min} = (60 - 20) / 60 = 0.667$.
2. $Q_{EAS} = \max(0.625, 0.667) = 0.667$.
Final Result:
Cell skewness is $Q = \mathbf{0.667}$ (Acceptable quality).
A triangle has angles $\theta = [20^\circ, 135^\circ, 25^\circ]$. Calculate equiangle skewness.
Step-by-step Solution:
1. $Q_{max} = (135 - 60) / 120 = 0.625$, $Q_{min} = (60 - 20) / 60 = 0.667$.
2. $Q_{EAS} = \max(0.625, 0.667) = 0.667$.
Final Result:
Cell skewness is $Q = \mathbf{0.667}$ (Acceptable quality).