Verification & Validation

The accuracy of a Physics AI model depends on the quality of its training data. Teams on the Luminary platform train Large Physics Models on data from Luminary solvers, from third-party or in-house solvers they have validated, and from experimental and operational measurements, in any combination.

This manual documents the verification and validation (V&V) of the Luminary physics solvers, for teams that generate training data with them. Its purpose is to demonstrate, on a growing library of well-characterized problems, that the solver computes correctly (verification, agreement with analytic and manufactured solutions and established numerical benchmarks) and that it predicts physical reality (validation, agreement with experimental measurement).

Each case is reproducible end to end: the geometry, mesh, and solver configuration are recorded alongside the results, and every reported quantity is compared against an authoritative reference, an analytic solution, a digitized published figure, or experimental data, with the source cited. Cases are organized by physical regime so that related problems sit together, and a coverage matrix summarizes which solver capabilities each case exercises.

Flagship benchmarks

Industry-standard prediction workshops Luminary entered and published on, recreated here from our peer-reviewed and public submissions.

Capability coverage

18 of 18 tracked solver features exercised across 56 case(s). Click any feature (a column header below, or a keyword on a case) to filter the cases and coverage matrix.

Swipe the table sideways to see all features.

Case Verification / Validation Dimensionality Flow regime Turbulence model Density relationship Time integration Energy equation Aeroacoustics Heat transfer Body forces
Verification Validation 2D 3D Inviscid Laminar RANS DES/LES Spalart–Allmaras k–ω SST Constant density Ideal gas Steady Unsteady Energy equation FW-H (solid / permeable surface) Conjugate heat transfer Buoyancy / gravity
2D Airfoil Near-Wake (Turbulent Wake) ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Asymmetric Plane Diffuser (SST) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Backward-Facing Step: Validation (SA) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Laminar Backward-Facing Step at Re = 800 ✕ ✕ ✕ ✕ ✕ ✕
Backward-Facing Step: DDES (Vogel-Eaton) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Bump-in-channel (Turbulent Boundary Layer) ✕ ✕ ✕ ✕ ✕ ✕ ✕
3D Bump-in-channel (Turbulent Boundary Layer) ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Bump-in-channel (Turbulent Boundary Layer, SST) ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Buoyancy-driven Cavity ✕ ✕ ✕ ✕ ✕ ✕ ✕
Converging–Diverging Verification Nozzle ✕ ✕ ✕ ✕ ✕ ✕
2D Coflowing Jet (Compressible Mixing Layer) ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Coflowing Jet (Compressible Mixing Layer, SST) ✕ ✕ ✕ ✕ ✕ ✕ ✕
Compressible Couette Flow (Viscous Heating) ✕ ✕ ✕ ✕ ✕ ✕
Supersonic Flow Over a Cone (Taylor-Maccoll) ✕ ✕ ✕ ✕ ✕ ✕
Plane Couette Flow (Linear Profile) ✕ ✕ ✕ ✕ ✕
Couette–Poiseuille Flow (Velocity Profiles) ✕ ✕ ✕ ✕ ✕ ✕
Laminar Cylinder at Re = 40 (Drag Coefficient) ✕ ✕ ✕ ✕ ✕
NASA CRM: AIAA Drag Prediction Workshop 6 ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
DrivAer: AutoCFD4 Case 2 (DDES) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Single Fin in Forced Flow ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Low-Prandtl Forced Convection over a Flat Plate ✕ ✕ ✕ ✕ ✕ ✕
Generic Truck Utility (GTU): DDES ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Heated Laminar Pipe (Constant Wall Heat Flux) ✕ ✕ ✕ ✕ ✕ ✕
Flow over a Heated Plate ✕ ✕ ✕ ✕ ✕ ✕ ✕
3D Hemisphere Cylinder ✕ ✕ ✕ ✕ ✕ ✕ ✕
NASA CRM-HL: High-Lift Prediction Workshop 5 ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Incompressible 2D Lattice (Decaying Vortex Array) ✕ ✕ ✕ ✕ ✕
Inviscid Isentropic Vortex Transport ✕ ✕ ✕ ✕ ✕ ✕
Joukowski Airfoil (Turbulent, SA-QCR2000-R) ✕ ✕ ✕ ✕ ✕ ✕ ✕
Laminar Flat Plate ✕ ✕ ✕ ✕ ✕ ✕
Laminar Pipe Flow at Re = 500 (Hagen–Poiseuille) ✕ ✕ ✕ ✕ ✕
Laminar Sphere at Re = 100 (Drag Coefficient) ✕ ✕ ✕ ✕ ✕
Lid-driven Cavity at Re = 1000 ✕ ✕ ✕ ✕ ✕
Manufactured Solution: Inviscid (Euler) ✕ ✕ ✕ ✕ ✕ ✕
Manufactured Solution: Viscous (Navier–Stokes) ✕ ✕ ✕ ✕ ✕ ✕
Transonic NACA 0012 (Inviscid Euler) ✕ ✕ ✕ ✕ ✕ ✕
2D NACA 0012 Airfoil: Validation (SA) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D NACA 0012 Airfoil: Validation (SST) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
3D ONERA M6 Wing ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
RAE 2822 Transonic Airfoil: Validation (SA) ✕ ✕ ✕ ✕ ✕ ✕ ✕
Stokes's First Problem (Impulsively Started Wall) ✕ ✕ ✕ ✕ ✕
Supersonic Expansion (Prandtl–Meyer Fan) ✕ ✕ ✕ ✕ ✕ ✕
Supersonic Wedge (Oblique Shock) ✕ ✕ ✕ ✕ ✕ ✕
Turbulent Natural Convection in a Tall Cavity ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Turbulent Flat Plate (Zero Pressure Gradient) ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Turbulent Flat Plate (Zero Pressure Gradient, SST) ✕ ✕ ✕ ✕ ✕ ✕ ✕
2D Wall-Mounted Hump (Separated Flow) ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Laminar Circular Cylinder at Re = 100: FW-H Against Literature ✕ ✕ ✕ ✕ ✕ ✕ ✕
Acoustic Point Source in a Uniform Flow: FW-H Against Direct CFD ✕ ✕ ✕ ✕ ✕ ✕ ✕
Acoustic Point Sources: FW-H Against Direct CFD ✕ ✕ ✕ ✕ ✕ ✕ ✕
Acoustic Point Sources in a Cube: FW-H Against Direct CFD and 1/r Decay ✕ ✕ ✕ ✕ ✕ ✕ ✕
Aeolian Tone of a Circular Cylinder: FW-H Against Direct CFD ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕
Cylinder at Re = 10⁴: FW-H Against Literature ✕ ✕ ✕ ✕ ✕ ✕ ✕
LAGOON Landing Gear: FW-H Against Literature ✕ ✕ ✕ ✕ ✕ ✕ ✕
Cylinder at Re = 3900: FW-H Against Literature ✕ ✕ ✕ ✕ ✕ ✕ ✕
Tandem Cylinders: FW-H Against Literature ✕ ✕ ✕ ✕ ✕ ✕ ✕ ✕

Cases

Inviscid 7 cases

Converging–Diverging Verification Nozzle

verification

Supersonic Flow Over a Cone (Taylor-Maccoll)

verification

Manufactured Solution: Inviscid (Euler)

verification

Transonic NACA 0012 (Inviscid Euler)

verification

Supersonic Expansion (Prandtl–Meyer Fan)

verification

Supersonic Wedge (Oblique Shock)

verification

Inviscid Isentropic Vortex Transport

verification

Laminar 19 cases

Laminar Backward-Facing Step at Re = 800

verification

Plane Couette Flow (Linear Profile)

verification

Couette–Poiseuille Flow (Velocity Profiles)

verification

Laminar Cylinder at Re = 40 (Drag Coefficient)

verification

Low-Prandtl Forced Convection over a Flat Plate

verification

Heated Laminar Pipe (Constant Wall Heat Flux)

verification

Laminar Flat Plate

verification

Laminar Pipe Flow at Re = 500 (Hagen–Poiseuille)

verification

Laminar Sphere at Re = 100 (Drag Coefficient)

verification

Lid-driven Cavity at Re = 1000

verification

Incompressible 2D Lattice (Decaying Vortex Array)

verification

Stokes's First Problem (Impulsively Started Wall)

verification

2D Buoyancy-driven Cavity

verification

Compressible Couette Flow (Viscous Heating)

verification

Manufactured Solution: Viscous (Navier–Stokes)

verification

Laminar Circular Cylinder at Re = 100: FW-H Against Literature

validation

Acoustic Point Source in a Uniform Flow: FW-H Against Direct CFD

verification

Acoustic Point Sources: FW-H Against Direct CFD

verification

Acoustic Point Sources in a Cube: FW-H Against Direct CFD and 1/r Decay

verification

RANS (turbulent) 19 cases

Turbulent Natural Convection in a Tall Cavity

validation

2D Airfoil Near-Wake (Turbulent Wake)

verification

2D Asymmetric Plane Diffuser (SST)

validation

2D Backward-Facing Step: Validation (SA)

validation

2D Bump-in-channel (Turbulent Boundary Layer)

verification

3D Bump-in-channel (Turbulent Boundary Layer)

verification

2D Bump-in-channel (Turbulent Boundary Layer, SST)

verification

2D Coflowing Jet (Compressible Mixing Layer)

verification

2D Coflowing Jet (Compressible Mixing Layer, SST)

verification

3D Hemisphere Cylinder

verification

Joukowski Airfoil (Turbulent, SA-QCR2000-R)

verification

2D NACA 0012 Airfoil: Validation (SA)

validation

2D NACA 0012 Airfoil: Validation (SST)

validation

3D ONERA M6 Wing

verification

RAE 2822 Transonic Airfoil: Validation (SA)

validation

2D Turbulent Flat Plate (Zero Pressure Gradient)

verification

2D Turbulent Flat Plate (Zero Pressure Gradient, SST)

verification

2D Wall-Mounted Hump (Separated Flow)

validation

Aeolian Tone of a Circular Cylinder: FW-H Against Direct CFD

verification

DES / LES (scale-resolving) 5 cases

Backward-Facing Step: DDES (Vogel-Eaton)

validation

Cylinder at Re = 10⁴: FW-H Against Literature

verification

LAGOON Landing Gear: FW-H Against Literature

validation

Cylinder at Re = 3900: FW-H Against Literature

verification

Tandem Cylinders: FW-H Against Literature

validation

Conjugate Heat Transfer 2 cases

Single Fin in Forced Flow

verification

Flow over a Heated Plate

verification