Methodology
THE MATH
BEHIND
EVERY
RESULT.
CFD is only as credible as the equations it solves and the process used to verify them. At Laminar Tektonix, we publish our methodology openly — governing equations, turbulence model justification, mesh independence protocol, and validation benchmarks — because that is what differentiates physics from guesswork.
Methodology at a glance
Navier-Stokes + energy equations — full viscous solver
k-ω SST turbulence — validated for indoor flow separation
GCI mesh independence — target <5% medium to fine
Churchill-Chu Nu correlation — validation benchmark
Boussinesq — justified for ΔT <30°C indoor airflow
Residual convergence — all monitors to <1×10⁻⁴
FDS (NIST-validated) — fire and smoke per IBC §909
Enthalpy-porosity method — PCM phase change modeling
Governing equations
THE PHYSICS
WE SOLVE.
Continuity — Mass Conservation
All simulations
∂ρ/∂t + ∇·(ρu) = 0
ρAir density (kg/m³)
uVelocity vector (m/s)
tTime (s)
Momentum — Navier-Stokes
All simulations
ρ(∂u/∂t + u·∇u) = −∇p + μ∇²u + ρg
pPressure (Pa)
μDynamic viscosity (Pa·s)
gGravity vector — enables buoyancy-driven flow
Energy Transport
Thermal simulations
ρcₚ(∂T/∂t + u·∇T) = ∇·(k∇T) + Φ
cₚSpecific heat (J/kg·K)
kThermal conductivity (W/m·K)
ΦViscous dissipation (negligible at low Ma)
Φ is omitted for indoor airflow (Ma ≪ 0.3). Retained for high-velocity duct simulations where viscous heating is non-trivial.
Boussinesq Approximation
Passive ventilation
ρ ≈ ρ₀[1 − β(T − T₀)]
β = 1/T₀ (ideal gas approximation)
β = 1/T₀ (ideal gas approximation)
βThermal expansion coefficient (1/K)
T₀Reference temperature (K)
Valid when β(T−T₀) ≪ 1. For ΔT = 20°C: β·ΔT ≈ 0.068. Explicitly verified and documented for each study.
PCM — Enthalpy-Porosity Method
Phase change modeling
H = href + ∫cₚ dT + β_liq · L
S = −A_mush · (1−β_liq)² / (β_liq³+ε) · u
S = −A_mush · (1−β_liq)² / (β_liq³+ε) · u
LLatent heat of fusion (kJ/kg)
β_liqLiquid fraction: 0 (solid) → 1 (liquid)
A_mushMushy zone constant (~10⁵)
Stefan number Ste = cₚ·ΔT/L calculated for every study. Ste < 0.5 confirms latent heat dominance — PCM is effective.
Churchill-Chu Validation Correlation
Validation benchmark
Nu = 0.68 + 0.670·Ra^(1/4) / [1+(0.492/Pr)^(9/16)]^(4/9)
Ra = gβΔTL³/να
Ra = gβΔTL³/να
NuNusselt number — convective heat transfer ratio
RaRayleigh number — buoyancy vs. viscous forces
PrPrandtl number — for air ≈ 0.71 (constant)
CFD Nu vs. Churchill-Chu must agree within 10–15%. Valid for Ra < 10⁹. Comparison table published in every project methodology appendix.
Verification
MESH
INDEPENDENCE
STUDY.
Every simulation is preceded by a three-mesh GCI study — the single most important verification step, and the one most commonly skipped. We include the GCI table in every project report appendix.
COARSE — ~100k cells
FINE ZONE — y⁺≈1
| Mesh | Cells | f (vel.) | GCI | Status |
|---|---|---|---|---|
| Coarse | ~100k | 0.842 m/s | — | — |
| Medium | ~420k | 0.881 m/s | 7.4% | Refine |
| Fine | ~1.6M | 0.894 m/s | 3.2% ✓ | PASS |
| Production run: Medium mesh. GCI <5% confirmed. f_exact ≈ 0.898 m/s (Richardson extrapolation). | ||||
Validation checklist
WHAT EVERY
STUDY MUST
PROVE.
✓
Mesh independence (GCI)
Three mesh densities, GCI per Roache (1994). Production run on medium mesh.
GCI < 5% between medium and fine
✓
Solver convergence
All transport residuals monitored: continuity, momentum x/y/z, energy, k, ω.
All residuals < 1×10⁻⁴
✓
Reynolds number check
Re calculated at all key openings before turbulence model is applied.
Re > 4,000 at all ventilation openings
✓
Boussinesq validity
β·(T−T₀) calculated explicitly. Full density variation used if ΔT > 30°C.
β·ΔT < 0.1 required
✓
Nu vs. Churchill-Chu (1975)
CFD wall heat flux Nu compared to published natural convection correlation.
Agreement within 10–15%
✓
ACH vs. ASHRAE 62.1
Simulated air change rate benchmarked against code minimum for occupancy type.
Passive ACH ≥ 6 for residential
✓
Stefan number (PCM studies)
Ste = cₚ·ΔT/L calculated to confirm latent heat dominance before PCM modeling.
Ste < 0.5 for effective PCM
Academic foundation
BUILT ON
PEER-REVIEWED
SCIENCE.
Every validation approach, turbulence model selection, and benchmark correlation used at Laminar Tektonix is grounded in peer-reviewed literature. We cite our sources in every project methodology appendix — because traceable physics is the foundation of credible engineering.
Perspective: a method for uniform reporting of grid refinement studies
Journal of Fluids Engineering, 116(3) — GCI mesh independence methodology
Correlating equations for laminar and turbulent free convection from a vertical plate
International Journal of Heat and Mass Transfer, 18(11) — Nu validation benchmark
Improved prediction of air flow and temperature distribution in a model room using CFD
Building and Environment, 41(12) — k-ω SST indoor flow validation
Guidebook for practical applications of CFD to pedestrian wind environment around buildings
Architectural Institute of Japan — wind comfort benchmark cases
Fifty years of CFD for room air distribution
Building and Environment, 91 — comprehensive RANS review for indoor airflow
Can CFD analysis for HVAC solve complex building engineering challenges in the USA?
axiumglobal.com — Industry application and regulatory context reference
LAMINAR
The bottom line
SIMULATION
YOU CAN
BUILD ON.
Verified. Validated. Deliverable-ready. Book a free 30-minute consultation and find out what simulation can do for your project.