Mesh Independence: The Study That Makes CFD Credible

The problem

Discretising a continuous domain introduces error that depends on cell size. Refine the mesh and the answer changes. If it keeps changing, you are reporting a property of your grid, not of the flow.

A grid convergence study demonstrates that further refinement would not meaningfully alter the conclusion. Without one, a CFD result is unfalsifiable.

The procedure

1. Build at least three systematically refined meshes. Refinement should be uniform across the domain, with a refinement ratio r = h_coarse / h_fine of at least 1.3. Refining only where the results look interesting invalidates the analysis, because it changes the error distribution rather than reducing it uniformly.

2. Track a quantity you actually care about. Lift coefficient, drag coefficient, pressure drop, peak wall shear stress, mass flow — a scalar tied directly to the engineering question. Field plots are not a convergence metric; two visually identical contour plots can carry meaningfully different integrated forces.

3. Compute the observed order of accuracy:

p = ln((f₃ − f₂)/(f₂ − f₁)) / ln(r)

where f₁ is the solution on the finest mesh. Compare p against the formal order of the discretisation scheme. A second-order scheme showing p ≈ 2 is behaving as expected. A p far from formal order signals that the solution is not yet in the asymptotic range, or that another error source dominates.

4. Estimate the discretisation error by Richardson extrapolation, and report a Grid Convergence Index — a conservative uncertainty band on the finest-mesh result. The GCI is what turns "the mesh looked fine" into a number a reviewer can weigh.

Boundary layer resolution

For wall-bounded flows, near-wall resolution is usually the binding constraint. The governing parameter is y⁺, the non-dimensional distance from the wall to the first cell centre.

• Wall-resolved: y⁺ ≈ 1, with 10–15 cells across the boundary layer. Required for accurate prediction of separation, wall heat transfer and skin friction.
• Wall functions: y⁺ roughly between 30 and 300, modelling the near-wall layer rather than resolving it. Considerably cheaper, and acceptable where separation is not the question being asked.

The trap is the buffer region, roughly 5 < y⁺ < 30, where neither treatment is valid. Landing there produces confident, wrong answers with no obvious symptom.

Check y⁺ after solving, not before. It depends on the computed wall shear, so any pre-solve estimate is a starting guess to be verified.

Errors that a finer mesh will never fix

Mesh independence bounds discretisation error only. It is silent on everything else:

• Model error — an inappropriate turbulence model, or steady RANS applied to a genuinely unsteady flow
• Boundary condition error — a domain too small, an inlet profile that does not match reality, or a symmetry plane imposed on an asymmetric flow
• Geometry error — a defeatured CAD model that removed something aerodynamically significant

A perfectly grid-converged solution of the wrong problem is still wrong. Grid convergence is necessary, not sufficient.

What to report

State mesh counts and refinement ratio, the tracked quantity at each refinement level, the observed order, the GCI on the finest mesh, the y⁺ range achieved, the turbulence model, and the domain extents.

That single paragraph is the difference between a result a reviewer can rely on and one they must take on trust.