Computational Fluid Dynamics has developed into an engineering tool that is currently applied on a daily basis to make project decisions. As a consequence, reliability and credibility of numerical simulations is an unavoidable issue. A logical step forward is then to pay due attention to the assessment of numerical errors/uncertainties (Verification) and modeling errors (Validation), which are components of Verification and Validation (V&V). The present Workshop focuses on one of the main topics of V&V: Solution Verification, i.e. the estimate of the numerical uncertainty of computational simulations, employing successive grid refinement. Furthermore, it restricts itself to the estimation of discretization errors of steady flows, i.e. parametric uncertainty is not addressed and iterative and round-off errors are assumed to be negligible and independent of the discretization error.

          Solution Verification based on a grid refinement study requires first of all the solution of one and the same problem on a number of geometrically similar grids. Afterwards, an estimate of the numerical uncertainty of (usually) the solution on the finest grid is made using some kind of procedure. It is this procedure, of which several have been proposed, that is the key of this workshop. So participants do not have to make their own numerical solutions, but just have to apply their preferred procedure on data provided by the organizers and to report their results.

          The data provided are related to six cases: flow over a flat plate for Reynolds numbers of 107, 108 and 109; flow around the NACA 0012 airfoil at Reynolds number of 6×106 and angles of attack of 0º, 4º and 10º. All test cases are statistically steady flows of an incompressible fluid that were simulated in several geometrically similar grid sets with three eddy-viscosity turbulence models: Spalart & Allmaras one-equation model; Shear-stress transport (SST) k-w two-equation model and  two-equation model. For each test case we provide the following information:


·       A list of functional and local flow quantities to estimate the uncertainties (the quantities of interest).


·       The numerical solution and the typical cell size of all quantities of interest for at least 9 levels of grid refinement that cover at least a grid refinement ratio of 4.

The requested information from the participants is:


·       Estimated numerical uncertainty for the quantities of interest for different levels of grid refinement.


·       Reference to the procedure applied or description of the procedure adopted (if not available in the open literature).

The goal of this exercise is to check the consistency of the estimated error bars for different levels of grid refinement and/or different grids with the same number of cells and flow conditions. Furthermore, this exercise will also allow us to check the consistency of the estimates performed by different users applying the same method. Hopefully, such exercise will help us to identify the main difficulties in performing reliable error estimates based on grid refinement studies.


If you require more information than that available in these pages please contact


We look forward to seeing you at the next Symposium on Verification and Validation in May 2017.


Luís Eça, Martin Hoekstra and Guilherme Vaz