🥞 CFD Prism Layer Growth & Inflation Mesh Calculator
Dimension boundary layer prism/inflation layers: compute cumulative thickness $H_{tot}$, layer count $N$, last cell height $h_N$, and transition ratio to the outer volume mesh.
🧱 2D Boundary Layer Prism Mesh Visualization
True-to-Scale Layer Inflation • Bulk Mesh Interface📝 Inflation Parameters
Geometric Progression Equations:
$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$
$$h_i = h_1 \cdot r^{i-1} \quad (i = 1, \dots, N)$$ $$H_{tot} = \sum_{i=1}^N h_i = h_1 \frac{r^N - 1}{r - 1}$$ $$R_{trans} = \frac{h_N}{\Delta x_{bulk}} \quad (\text{Target: } 0.7 \le R_{trans} \le 1.3)$$
📊 Mesh Sizing Results
Boundary Layer Inflation Summary
Total Inflation Height ($H_{tot}$) across 25 Layers
3.426 mm
= 3.4260e-3 m | First layer $h_1 = 10\ \mu\text{m}$ | Last layer $h_N = 0.5311\ \text{mm}$
Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). (Ratio $h_N / \Delta x_{bulk} = \mathbf{0.354}$)
First Layer ($h_1$)10 μm
Growth Ratio ($r$)1.18
Layer Count ($N$)25
Last Layer ($h_N$)0.531 mm
Bulk Mesh ($\Delta x$)1.5 mm
Transition Ratio0.354
📈 Layer Thickness $h_i$ [mm]
📊 Cumulative Inflation Height $Y_i$ [mm]
📋 Detailed Layer-by-Layer Progression
| Layer # | Thickness [mm] | Thickness [μm] | Cumulative [mm] | Ratio |
|---|---|---|---|---|
| 1 | 0.01 | 10 | 0.01 | 1 |
| 2 | 0.0118 | 11.8 | 0.0218 | 1.18 |
| 3 | 0.01392 | 13.92 | 0.03572 | 1.18 |
| 4 | 0.01643 | 16.43 | 0.05215 | 1.18 |
| 5 | 0.01939 | 19.39 | 0.07154 | 1.18 |
| 6 | 0.02288 | 22.88 | 0.09442 | 1.18 |
| 7 | 0.027 | 27 | 0.1214 | 1.18 |
| 8 | 0.03185 | 31.85 | 0.1533 | 1.18 |
| 9 | 0.03759 | 37.59 | 0.1909 | 1.18 |
| 10 | 0.04435 | 44.35 | 0.2352 | 1.18 |
| 11 | 0.05234 | 52.34 | 0.2876 | 1.18 |
| 12 | 0.06176 | 61.76 | 0.3493 | 1.18 |
| 13 | 0.07288 | 72.88 | 0.4222 | 1.18 |
| 14 | 0.08599 | 85.99 | 0.5082 | 1.18 |
| 15 | 0.1015 | 101.5 | 0.6097 | 1.18 |
| 16 | 0.1197 | 119.7 | 0.7294 | 1.18 |
| 17 | 0.1413 | 141.3 | 0.8707 | 1.18 |
| 18 | 0.1667 | 166.7 | 1.037 | 1.18 |
| 19 | 0.1967 | 196.7 | 1.234 | 1.18 |
| 20 | 0.2321 | 232.1 | 1.466 | 1.18 |
| 21 | 0.2739 | 273.9 | 1.74 | 1.18 |
| 22 | 0.3232 | 323.2 | 2.063 | 1.18 |
| 23 | 0.3814 | 381.4 | 2.445 | 1.18 |
| 24 | 0.4501 | 450.1 | 2.895 | 1.18 |
| 25 | 0.5311 | 531.1 | 3.426 | 1.18 |
Fortran Solver Raw Output:
=============================================================== THERMOFLUIDCALC — CFD PRISM LAYER INFLATION SOLVER =============================================================== Calculation Mode = 1 First Layer h1 [m] = 1.000000E-05 First Layer h1 [mm] = 1.000000E-02 First Layer h1 [um] = 1.000000E+01 Growth Ratio (r) = 1.1800 Number of Layers (N)= 25 Total Height H [m] = 3.426035E-03 Total Height H [mm] = 3.426035E+00 Last Layer h_N [m] = 5.310901E-04 Last Layer h_N [mm] = 5.310901E-01 Bulk Cell Size [m] = 1.500000E-03 Transition Ratio = 3.540600E-01 --------------------------------------------------------------- Transition Diagnostic: WARNING: Severe step change! Last prism is too small vs bulk mesh (<0.4). =============================================================== --- PRISM LAYER DISTRIBUTION --- Layer Thickness[m] Thickness[mm] Cumulative[m] Cumulative[mm] Ratio 1 1.000000E-05 1.000000E-02 1.000000E-05 1.000000E-02 1.0000 2 1.180000E-05 1.180000E-02 2.180000E-05 2.180000E-02 1.1800 3 1.392400E-05 1.392400E-02 3.572400E-05 3.572400E-02 1.1800 4 1.643032E-05 1.643032E-02 5.215432E-05 5.215432E-02 1.1800 5 1.938778E-05 1.938778E-02 7.154210E-05 7.154210E-02 1.1800 6 2.287758E-05 2.287758E-02 9.441968E-05 9.441968E-02 1.1800 7 2.699554E-05 2.699554E-02 1.214152E-04 1.214152E-01 1.1800 8 3.185474E-05 3.185474E-02 1.532700E-04 1.532700E-01 1.1800 9 3.758859E-05 3.758859E-02 1.908585E-04 1.908585E-01 1.1800 10 4.435454E-05 4.435454E-02 2.352131E-04 2.352131E-01 1.1800 11 5.233836E-05 5.233836E-02 2.875514E-04 2.875514E-01 1.1800 12 6.175926E-05 6.175926E-02 3.493107E-04 3.493107E-01 1.1800 13 7.287593E-05 7.287593E-02 4.221866E-04 4.221866E-01 1.1800 14 8.599359E-05 8.599359E-02 5.081802E-04 5.081802E-01 1.1800 15 1.014724E-04 1.014724E-01 6.096527E-04 6.096527E-01 1.1800 16 1.197375E-04 1.197375E-01 7.293901E-04 7.293901E-01 1.1800 17 1.412902E-04 1.412902E-01 8.706804E-04 8.706804E-01 1.1800 18 1.667225E-04 1.667225E-01 1.037403E-03 1.037403E+00 1.1800 19 1.967325E-04 1.967325E-01 1.234135E-03 1.234135E+00 1.1800 20 2.321444E-04 2.321444E-01 1.466280E-03 1.466280E+00 1.1800 21 2.739303E-04 2.739303E-01 1.740210E-03 1.740210E+00 1.1800 22 3.232378E-04 3.232378E-01 2.063448E-03 2.063448E+00 1.1800 23 3.814206E-04 3.814206E-01 2.444868E-03 2.444868E+00 1.1800 24 4.500763E-04 4.500763E-01 2.894945E-03 2.894945E+00 1.1800 25 5.310901E-04 5.310901E-01 3.426035E-03 3.426035E+00 1.1800 --- END PRISM DISTRIBUTION ---