"How many million elements?" says almost nothing about mesh quality. On the same problem, three million cells of the right type can be more accurate than fifteen million of the wrong one [1] [2].
Cell types
Hexahedral. Where it can be aligned with the flow, this is the most accurate and the cheapest option: lowest numerical diffusion, highest accuracy per cell. The price is preparation time; blocking complex geometry is skilled labour. It is the natural choice for regular geometry — pipes, ducts, blade passages.
Tetrahedral. Fills complex geometry quickly. It cannot align with the flow, so it produces numerical diffusion wherever shear dominates. Good for a fast first answer, usually not good enough for production runs.
Polyhedral. Each cell has many neighbours, which makes gradient evaluation more robust. It typically reaches accuracy comparable to a tetrahedral mesh with a third of the cells, and converges faster. For complex geometry this is the practical balance.
Cut-cell Cartesian. Generated very quickly, suited to external flow and large volumes; carries a risk of stair-stepping on curved surfaces.
What really decides it: the boundary layer prisms
Accuracy near the wall depends far less on cell type than on the prism layer structure. Drag, heat transfer coefficient and separation point all come from there.
- First cell height should follow the target y+
- The layer count should span the boundary layer; typically 10–20
- Growth rate should not exceed 1.2
- Cell volume should not jump at the transition from prisms to the volume mesh
In a mesh with no prism layers, increasing the element count does not fix the error near the wall.
Quality measures worth checking
| Measure | Target | What it degrades |
|---|---|---|
| Skewness | < 0.85 | Convergence, local accuracy |
| Orthogonality | > 0.15 | Gradient evaluation |
| Aspect ratio | May be high at walls | Convergence in the volume |
| Volume change ratio | < 1.3 | Diffusion, stability |
A single bad cell will not stop the solution, but it corrupts it locally. Look at the worst values, not the average.
A practical approach
Hexahedral where the geometry is regular; polyhedral core plus prism layers where it is complex. Do not change cell type while refining for a grid independence study — if you do, what you are measuring is not resolution but cell type.
References
- Ferziger, J. H., Perić, M. & Street, R. L. (2020). Computational Methods for Fluid Dynamics, 4th ed. Springer. DOI: 10.1007/978-3-319-99693-6
- 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