In the finite volume method the unknowns are stored at cell centres, but the fluxes are needed at cell faces. The bridge between them is the gradient estimate, and that is where mesh quality first enters the solution — on skewed cells a gradient error becomes a flux error directly.
Two common methods
Least squares. A plane is fitted to the neighbouring cell centres. More robust on irregular meshes; it weakens when the neighbours are clustered in one direction.
Green-Gauss. An integral is taken over face values. Cheap and accurate on a regular mesh; on skewed cells the interpolation of the face value degrades and the error grows.
The choice depends on mesh quality and is one of the items to check on a solution that will not converge. See the solver settings note.
What limiters protect, and what they cost
Second-order reconstruction produces unphysical overshoots at sharp gradients: negative turbulent kinetic energy, volume fractions above 100%, temperatures below absolute zero. A limiter clips them.
The cost is this: wherever the limiter engages, the solution drops locally to first order and numerical diffusion is generated. The more aggressive the limiter, the more stable and the blurrier the solution.
The practical point
Look at where the limiter engages. If it engages at a genuinely sharp transition — a shock or a free surface — that is normal. If it engages in the middle of smooth flow, that is a symptom of mesh quality: there are skewed cells or abrupt volume changes in that region.
Most cases where the mesh quality looks fine on average while the solution degrades come from exactly this — what has to be examined is the worst cells. See the cell type note.
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
- Patankar, S. V. (1980). Numerical Heat Transfer and Fluid Flow. Hemisphere Publishing. ISBN 978-0-89116-522-4.