This is the most frequently skipped section of a CFD report. In most reports two meshes were run, the results came out close, and "grid independence was achieved" was written. That is not a demonstration; it is a hope [1] [2].
Why it is needed
Discretisation error shrinks as the mesh refines. But without knowing how much refinement is enough, you cannot say how much of your number is physics and how much is mesh.
Method
At least three meshes are needed, each systematically finer than the last. A refinement ratio between 1.3 and 2.0 per direction is the usual choice.
| Mesh | Cells | Monitored quantity |
|---|---|---|
| Coarse | 2.4 M | 41.2 m |
| Medium | 5.8 M | 42.6 m |
| Fine | 11.3 M | 42.9 m |
The monitored quantity must be the one that drives the decision — head, drag coefficient, peak temperature. Choosing something mesh-insensitive like bulk velocity lets the study fool itself.
Numerical criterion
The grid convergence index (GCI) is computed by Richardson extrapolation. In practice what you are asking is: is the difference between medium and fine large enough to change your engineering decision?
In the table above, medium-to-fine is 0.7%. Against a 5% acceptance criterion that is comfortably sufficient, and production runs can use the medium mesh.
A common mistake
Refining by cell count alone. Doubling the cells without changing the first cell height at the wall (y+) does not improve the near-wall solution. A grid independence study should report y+ as well.
References
- 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
- Roache, P. J. (1994). Perspective: A method for uniform reporting of grid refinement studies. Journal of Fluids Engineering, 116(3), 405–413. DOI: 10.1115/1.2910291
- 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.