📐 Mesh Orthogonal Quality
Verify mesh orthogonal quality and face deviation angles for finite volume solvers.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Cfd
📊 Solver Telemetry
● ACTIVE
📥 Cell Vertices $(x, y)$
📖 Orthogonal Quality Formulation:
$$\text{OQ}_f = \frac{|\vec{A}_f \cdot \vec{d}_f|}{|\vec{A}_f|\, |\vec{d}_f|} = \cos(\theta_{\text{non-ortho}})$$
$$\text{OQ}_{\text{cell}} = \min_{f} (\text{OQ}_f), \quad 0 \le \text{OQ} \le 1$$
0.8234
Min Orthogonal Quality
34.6°
Max Non-Ortho Angle ($\theta$)
0.90, 0.45
Cell Centroid ($C$)
4 Faces
Cell Topology
📊 Individual Face Alignment Breakdown
| Face # | Orthogonal Quality ($\text{OQ}_f$) | Non-Ortho Angle ($\theta$) | Face Midpoint |
|---|---|---|---|
| Face 1 | 0.9762 | 12.53° | (1.00, 0.00) |
| Face 2 | 0.8234 | 34.57° | (1.60, 0.50) |
| Face 3 | 0.9997 | 1.51° | (0.80, 0.90) |
| Face 4 | 0.8603 | 30.65° | (0.20, 0.40) |
📐 2D Element Centroid & Face Vectors Visualizer
Good (0.70 - 0.90)🔍 View Raw GNU Fortran Double-Precision Solver Output
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📘 Calculation Methodology: Orthogonal Quality Mesh Metric
Mathematical Model & Theory
Orthogonal quality evaluates the angle between face normal $\vec{A}_i$ and the vector connecting cell centroid to neighbor centroid $\vec{c}_i$:
$$OQ = \min_{faces} \left( \frac{\vec{A}_i \cdot \vec{c}_i}{|\vec{A}_i| |\vec{c}_i|}, \frac{\vec{A}_i \cdot \vec{f}_i}{|\vec{A}_i| |\vec{f}_i|} \right)$$
$$\text{Quality Thresholds: } OQ > 0.50 \text{ (Good)}, \quad OQ < 0.15 \text{ (Poor)}$$
Assumptions
- Applicable across all polyhedral, tetrahedral, and hexahedral cells.
- High orthogonality minimizes gradient calculation errors.
Academic References
- Knupp, P. M.: Algebraic Mesh Quality Metrics, SIAM.
- ANSYS Fluent Theory Guide: Mesh Quality Standards.
Worked Engineering Example
Problem Statement:
A face normal is $\vec{n} = [0, 1]$ and cell centroid connector is $\vec{c} = [0.2, 0.98]$. Calculate orthogonal quality.
Step-by-step Solution:
1. $\vec{n} \cdot \vec{c} = 0.98$, $|\vec{c}| = \sqrt{0.2^2 + 0.98^2} = 1.0002$.
2. $OQ = 0.98 / 1.0002 = 0.9798$.
Final Result:
Orthogonal quality is $OQ = \mathbf{0.980}$ (Excellent quality).
A face normal is $\vec{n} = [0, 1]$ and cell centroid connector is $\vec{c} = [0.2, 0.98]$. Calculate orthogonal quality.
Step-by-step Solution:
1. $\vec{n} \cdot \vec{c} = 0.98$, $|\vec{c}| = \sqrt{0.2^2 + 0.98^2} = 1.0002$.
2. $OQ = 0.98 / 1.0002 = 0.9798$.
Final Result:
Orthogonal quality is $OQ = \mathbf{0.980}$ (Excellent quality).