Introduction
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 vv2017workshop@gmail.com.
We look
forward to seeing you at the next Symposium on Verification and Validation in
May 2017.
Luís Eça, Martin Hoekstra and Guilherme Vaz