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How many digits should a CFD result be quoted to?

The solver prints eight digits. How many of them mean anything is for the engineer to say, not the solver.

The solver gives you 42.8317. Writing even 42.8 in the report is often too much. The number of significant digits follows not from the computation but from the size of the error, and stating it is the engineer's job [1] [2].

The error terms are counted separately

Discretisation error. Comes from the grid independence study. The difference between the medium and fine mesh is the measure of this term.

Model error. Turbulence model, multiphase closure relations, radiation approach. This is the largest and hardest term to quantify; it can only be bounded with validation data.

Input uncertainty. Material properties, surface roughness, sealing, the actual operating condition. In thermal analyses this is often the dominant term.

Geometry difference. The modelled geometry is not the manufactured part: tolerances, weld beads, assembly gaps, fouling.

Convergence error. If convergence was done properly, this is small next to the others.

What this means in practice

In a typical industrial analysis the total uncertainty is of the order of 5–15%. That makes anything beyond three significant digits meaningless.

Instead of 1847.3 Pa for a pressure drop, write 1850 Pa, roughly ±10%. It is both more honest and more useful. With the first, the reader does not question the number; with the second, they decide knowing the margin.

Comparative use is far more reliable

Even where the uncertainty in the absolute value is large, the difference between two designs run with the same method is far more reliable: most of the model error acts in the same direction in both cases and cancels in the comparison.

That is why the strongest use of CFD is not "this device delivers exactly this value" but "design B is better than A by this much, and here is why".

What belongs in the report

The number, its range, where the range came from, and which term dominates. Stating the uncertainty does not weaken the result; it is the only thing that makes the number usable.

References

  1. ASME (2009, R2021). V&V 20 — Standard for Verification and Validation in Computational Fluid Dynamics and Heat Transfer. American Society of Mechanical Engineers, New York.
  2. Celik, I. B., Ghia, U., Roache, P. J., Freitas, C. J., Coleman, H. & Raad, P. E. (2008). Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. Journal of Fluids Engineering, 130(7), 078001. DOI: 10.1115/1.2960953

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