RANS Reference Solutions for the Assessment of Discretization Error Estimators

[+] Author and Article Information
Luis Eca

Instituto Superior Técnico, ULisboa, Av. Rovisco Pais 1, 1049 001 Lisboa

Guilherme Vaz

Maritime Research Institute Netherlands, P.O. Box 28 6700AA, Wageningen, The Netherlands

Martin Hoekstra

Consultant, The Netherlands

1Corresponding author.

ASME doi:10.1115/1.4040803 History: Received December 14, 2017; Revised July 03, 2018


This article presents grid refinement studies for statistically steady, two-dimensional flows of an incompressible fluid: a flat plate at Reynolds numbers equal to $10^7$, $10^8$ and $10^9$ and the NACA 0012 airfoil at angles of attack of 0, 4 and 10 degrees with $Re=6 \times 10^6$. Results are based on the numerical solution of the Reynolds-Averaged Navier-Stokes equations supplemented by one of three eddy-viscosity turbulence models of choice: the one-equation model of Spalart \& Allmaras and the two-equation models $k-\omega$ SST and $k-\sqrt{k}L$. Sets of geometrically similar structured grids with the same number of cells but different near-wall spacings are used to generate a data set that allows more than one estimation of the numerical uncertainty for similar grid densities . The selected flow quantities include functional (integral), surface and local flow quantities. An extra set of grids significantly more refined than those proposed for the estimation of the numerical uncertainty is generated for each test case. These extra solutions are used to obtain an approximation of the exact solution that allows the assessment of the performance of the numerical uncertainty estimations performed for the basis data set. However, it must be stated that with grids up to 2.5 (plate) and 8.46 (airfoil) million cells in two-dimensions, the asymptotic range is not attained for many of the selected flow quantities. All this data is available online to the community.

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