CFD Verification & Validation
Verifying and validating our CFD solver.
Verification and validation is how a CFD solver earns trust: verification checks that the equations are solved correctly, validation checks that the results match physical reality. Both are covered, building up from first principles.
The cases here are the first stage: verification against problems whose exact answer is known, where the solver’s error can be measured directly and shown to shrink at the rate theory predicts under refinement. Canonical benchmarks, turbulence datasets, and industrial cases follow.
Boussinesq convection: the temperature field and the buoyancy-driven circulation it sets up.
The program
From fundamental accuracy to industrial validation
The work proceeds in stages, each building on the one before. Confirming the solver’s order of accuracy comes first; broader benchmarks, turbulence modelling, and full industrial cases follow.
Order of accuracy verification
Live2D spatial accuracy
Kovasznay flow
A steady laminar wake behind a two-dimensional grid, one of the few flows with a closed-form solution to the full Navier–Stokes equations.
Spatial order (velocity)
expected 2.00→observed 1.97
3D spatial accuracy
Ethier–Steinman flow
A fully three-dimensional, time-dependent Beltrami flow with an exact Navier–Stokes solution, used to measure spatial accuracy in 3D.
Spatial order (velocity)
expected 2.00→observed 1.97
Coupled heat + flow accuracy
Boussinesq convection
A buoyancy-driven flow constructed by the Method of Manufactured Solutions to measure accuracy when temperature and momentum are two-way coupled.
Temperature order
expected 2.00→observed 2.05
Time accuracy
Stokes’ second problem
A viscous layer driven by an oscillating wall, a classical unsteady benchmark for the accuracy of the time integration.
Temporal order
expected 2.00→observed 1.99
Canonical cases
UpcomingTurbulence modelling
UpcomingIndustrial cases
UpcomingValidation on your own application
We can run the same verification workflow on your geometry, materials, and operating conditions.