📐 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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👁️ Views
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:
$$\text{Skewness} = \max\left( \frac{\theta_{\text{max}} - \theta_{\text{eq}}}{180^\circ - \theta_{\text{eq}}}, \frac{\theta_{\text{eq}} - \theta_{\text{min}}}{\theta_{\text{eq}}} \right)$$
$$\theta_{\text{eq}} = 60^\circ\ (\text{Triangle}), \quad \theta_{\text{eq}} = 90^\circ\ (\text{Quad})$$
0.8645
Equiangular Skewness
108.4°
Max Angle ($\theta_{\text{max}}$)
8.1°
Min Angle ($\theta_{\text{min}}$)
60°
Ideal Equiangular ($\theta_{\text{eq}}$)
💡
Solver Suitability: Poor (0.75 - 0.90)
Equiangular skewness is 0.864 with corner angles ranging from 8.1° to 108.4°.
Severely skewed element! High probability of local divergence and floating-point errors ($NaN$). Remedial remeshing recommended.
📐 2D Element Geometry & Corner Angle Visualizer
Poor (0.75 - 0.90)🔍 View Raw GNU Fortran Double-Precision Solver Output
At line 62 of file skewness.f90 (unit = 5, file = 'stdin') Fortran runtime error: End of file Error termination. Backtrace: #0 0x7fc10ce238a0 in ??? #1 0x7fc10ce243f9 in ??? #2 0x7fc10ce250bf in ??? #3 0x7fc10d0579ab in ??? #4 0x7fc10d050f04 in ??? #5 0x7fc10d051a99 in ??? #6 0x401756 in ??? #7 0x40113c in ??? #8 0x7fc10ca295cf in ??? #9 0x7fc10ca2967f in ??? #10 0x401174 in ??? #11 0xffffffffffffffff in ???
📘 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).