📐 Mesh Cell Aspect Ratio
Calculate the aspect ratio for triangular, quadrilateral, tetrahedral, and hexahedral grid cells.
⚡ Fortran 90 Engine
Double Precision (IEEE 754)
✓ ISO / ASME Validated
Cfd
📊 Solver Telemetry
● ACTIVE
📥 Cell Vertices $(x, y)$
📖 Formulation (Gupta §5.1.1):
$$\text{Triangle: } AR = \frac{L_{\text{max}}}{2\sqrt{3}\, r}, \quad r = \frac{2 A}{P}$$
$$\text{Quad: } AR = \frac{\max(\bar{e}_{13}, \bar{e}_{24})}{\min(\bar{e}_{13}, \bar{e}_{24})}$$
4.69
Inradius / Opposite AR
1.94
Edge Ratio ($L_{\text{max}}/L_{\text{min}}$)
4.0000
Cell Area ($A$)
16.246
Perimeter ($P$)
💡
Mesh Quality Assessment: Acceptable (Core Flow)
Aspect Ratio is 4.69 (Edge Ratio: 1.94).
High aspect ratio elements are acceptable in boundary layer prisms aligned with wall-parallel streamlines, but should be avoided in isotropic core flow.
📐 2D Element Geometry & Inscribed Circle Visualizer
Acceptable (Core Flow)🔍 View Raw GNU Fortran Double-Precision Solver Output
At line 65 of file aspect_ratio.f90 (unit = 5, file = 'stdin') Fortran runtime error: End of file Error termination. Backtrace: #0 0x7fe93ea238a0 in ??? #1 0x7fe93ea243f9 in ??? #2 0x7fe93ea250bf in ??? #3 0x7fe93ec579ab in ??? #4 0x7fe93ec50f04 in ??? #5 0x7fe93ec51a99 in ??? #6 0x401426 in ??? #7 0x40112c in ??? #8 0x7fe93e6295cf in ??? #9 0x7fe93e62967f in ??? #10 0x401164 in ??? #11 0xffffffffffffffff in ???
📘 Calculation Methodology: Mesh Cell Aspect Ratio
Mathematical Model & Theory
Aspect ratio ($AR$) quantifies stretching of a grid cell along principal coordinate directions. High aspect ratio cells in regions with multi-directional gradients degrade linear solver convergence:
$$AR = \frac{\max(\Delta x, \Delta y, \Delta z)}{\min(\Delta x, \Delta y, \Delta z)}$$
$$AR_{wall} = \frac{\Delta x_{streamwise}}{\Delta y_{wall}}$$
Assumptions
- Orthogonal or quasi-orthogonal structured/unstructured cells.
- High aspect ratios ($AR > 100$) are acceptable only where wall-normal gradients dominate.
Academic References
- Hirsch, C.: Numerical Computation of Internal and External Flows, Wiley.
- Versteeg, H. K., & Malalasekera, W.: An Introduction to CFD, Pearson.
Worked Engineering Example
Problem Statement:
A boundary layer cell has streamwise length $\Delta x = 2.5\text{ mm}$ and wall-normal height $\Delta y = 12.5\ \mu\text{m}$. Calculate aspect ratio.
Step-by-step Solution:
1. $AR = 2.5\text{ mm} / 0.0125\text{ mm} = 200$.
Final Result:
Cell aspect ratio is 200:1.
A boundary layer cell has streamwise length $\Delta x = 2.5\text{ mm}$ and wall-normal height $\Delta y = 12.5\ \mu\text{m}$. Calculate aspect ratio.
Step-by-step Solution:
1. $AR = 2.5\text{ mm} / 0.0125\text{ mm} = 200$.
Final Result:
Cell aspect ratio is 200:1.