# When is your mesh good enough?

A good mesh is possibly the most important component of a successful CFD simulation. But how do you know when your mesh is good enough? From your basic CFD course/training you remember terms like orthogonal angle, expansion factor and aspect ratio, and most meshing programs and CFD solvers displays these parameters as “mesh quality”. This is useful, but not sufficient to determine if your mesh is good.

Good mesh quality, bad mesh

The reason is as follows. A mesh is a spatial discretization of your domain. Depending on your solver, discretization of governing equations and so on, you will have errors that depend on (Δ𝑥)𝑛, with n= 1 or 2 as typical values. We see that the size of the elements is of absolute importance. The above-mentioned parameters do not include the size of the mesh elements, just the shape!

It is therefore clear that we need an additional measure of mesh quality. What we will use is a term called convergence. This is probably a known term for most, and the idea is to check whether your solution has converged to the exact numerical value (who knows how it compares with the real world though). The figure on the left below shows some error plotted with the number of elements in a mesh. This should be familiar. More advanced users may recognize the figure to the right as well, where the same values are plotted in a log-log plot. The right figure shows the convergence rate. It is a measure of how quickly your solution converges. It is still difficult to quantify the error, more than a visual examination.

Introducing the “Grid Convergence Index” (GCI). It is an industry-approved way of measuring the discretization error of your mesh. The details involve a bit of math, but the idea comes from the figures above; an extrapolation to the assumed converged value.

The method is remarkably simple:

• Choose a parameter defining your simulation (forces, velocities, frequencies etc.)

• Extract parameter at 3 different mesh densities

• Let the GCI do the rest

The result is a percentage value of how large your mesh error is. The detailed procedure can be found in [1].

Top tip: Use 5 minutes and create a GCI- calculator in excel. This way, checking for mesh convergence will be the easiest part of your future simulations.

[1] I. Celik, “Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications,” J. Fluids Eng., vol. 130, no. 7, pp. 078001-078001-4, Jul. 2008.