1. ASME V&V 20-2009 Standard for CFD Verification
Verification is defined as the process of determining that a computational model implementation accurately represents the developer's conceptual description and the solution to the mathematical equations.
All spatial and temporal discretization calculators on ThermoFluidCalc strictly adhere to the ASME V&V 20-2009 Standard (Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer), implementing:
- Observed Order of Convergence ($p$): Evaluated using 3 grid solutions ($N_1, N_2, N_3$) via Richardson extrapolation.
- Grid Convergence Index ($GCI$): Normalized numerical uncertainty with safety factors ($F_s = 1.25$ for 3 grids).
- Asymptotic Range Check: Verifying that $GCI_{23} / (r^p GCI_{12}) \approx 1.0$.
2. IAPWS-IF97 Industrial Formulation for Water & Steam
Thermodynamic state properties of water and steam are computed using the IAPWS-IF97 formulation adopted by the International Association for the Properties of Water and Steam.
Our Fortran 90 steam kernel divides the $P$-$T$ thermodynamic surface into 5 distinct regions (subcooled liquid, superheated steam, critical region, and high-temperature steam up to $2000^\circ\text{C}$ and $1000\text{ bar}$). All computed properties match official IAPWS verification tables to within $< 0.005\%$ relative deviation.
3. Published Analytical Benchmark Comparison Matrix
The table below compares ThermoFluidCalc outputs directly against reference analytical solutions and NIST standard reference data:
| Test Problem | Standard Reference | Input Parameters | Reference Solution | ThermoFluidCalc | Error |
|---|---|---|---|---|---|
| Rankine-Hugoniot Shock | NACA SP-3012 | $M_1 = 3.0, \; \gamma = 1.4$ | $P_2/P_1 = 10.3333$ | $10.333333$ | 0.000% |
| Prandtl-Meyer Angle | Anderson (Gas Dynamics) | $M = 2.0, \; \gamma = 1.4$ | $\nu = 26.3798^\circ$ | $26.37976^\circ$ | < 0.001% |
| Steam Tables (Region 1) | IAPWS-IF97 Table 33 | $T = 300\text{ K}, \; P = 3\text{ MPa}$ | $v = 1.00215 \times 10^{-3}$ | $1.002151 \times 10^{-3}$ | 0.000% |
| Colebrook Friction Factor | Moody (1944) | $Re = 10^5, \; \epsilon/D = 0.001$ | $f = 0.02221$ | $0.022212$ | < 0.005% |
| Dry Air Viscosity | NIST Chemistry WebBook | $T = 300\text{ K}, \; P = 1\text{ atm}$ | $\mu = 1.846 \times 10^{-5}\text{ Pa}\cdot\text{s}$ | $1.8461 \times 10^{-5}\text{ Pa}\cdot\text{s}$ | < 0.005% |
4. Fortran 90 IEEE-754 Double Precision Architecture
Unlike client-side JavaScript calculations which can suffer from 32-bit floating point precision loss, all backend solvers on ThermoFluidCalc are implemented in standalone Fortran 90 (`real(kind=8)`):
real(dp) :: gamma, mach, p_ratio
! Guaranteed 15-17 significant decimal digits IEEE-754