I'm wondering what alternatives there are to a grid convergence study to judge solution accuracy for a given grid resolution when doing steady-state RANS simulations on an automatically generated complex unstructured co-located grid (using OpenFOAM). Ideally, such a criterion would lend itself to automatic grid refinement.

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    $\begingroup$ If you are interested in some integral quantities like lift/drag forces, you can use grid adaptation that targets the error in these quantities. This requires solving an adjoint problem and computing cell-level error estimates. Such an approach can also give an estimate of the error in the integral quantities which can be used to judge the convergence of the solution. E.g., search for papers of Venditti and Darmofal for compressible flow case. $\endgroup$
    – cfdlab
    Sep 7, 2017 at 12:10
  • $\begingroup$ @PraveenChandrashekar Any reason you didn't add your comment as an answer? :) $\endgroup$
    – akid
    Sep 10, 2017 at 8:22
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    $\begingroup$ I was not sure if it really answered the question. Hence only a comment. $\endgroup$
    – cfdlab
    Oct 7, 2017 at 3:34

1 Answer 1


One of the conventional methods to assess the spatial convergence of RANS simulations is to perform grid refinement studies based on Richardson extrapolation. Its formulation and practice can be found in the link.

In addition, one should not select the grid refinement ratio arbitrarily. As a rule of thumb:

The grid refinement ratio (i.e. r) should be a minimum of r >= 1.1 to allow the discretization error to be differentiated from other error sources (iterative convergence errors, computer round-off, etc...).

The terms such as accuracy of a CFD simulation should always be formalised for a serious study. This link might be a good start to those who may concern.

  • $\begingroup$ This does not address the question at all unfortunately. I was explicitly looking for alternatives to a classic grid refinement study. $\endgroup$
    – akid
    Jul 9, 2017 at 16:07

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