Test cases

 

The data for the estimation of the discretization error/uncertainty of functional and local flow quantities was obtained from six statistically steady, two-dimensional flows of an incompressible fluid computed with the open-usage viscous flow code ReFRESCO (www.refresco.org):

 

·       Flow over a flat plate at three different Reynolds numbers based on the plate length, incoming velocity  and fluid kinematic viscosity ,.

                          I.          .

                        II.          .

                      III.          .

 

·       Flow around a NACA 0012 airfoil at Reynolds number based on the airfoil chord , incoming velocity  and fluid kinematic viscosity  of  at three angles of attack:

 

                     IV.          .

                       V.          .

                     VI.          .

 

For these six cases, simulations were performed with three isotropic eddy-viscosity turbulence models:

 

a.    The one-equation model of Spalart & Allmaras in the formulation without the tripping term (SAnoft2).

 

b.    The Shear-Stress Transport (SST) k-w two-equation model.

 

c.    The  two-equation model.

 

Different cases available will be designated according to the numbering presented above. For example, CASE IVb corresponds to the flow around the NACA 0012 airfoil at simulated with the SST k-w two-equation model.

 

All calculations were performed using double precision (15 digits) and iterative convergence criteria based on the maximum (norm) normalized residual  of all transport equations solved for each flow condition. Normalized residuals are equivalent to the change of dimensionless dependent variables in a simple Jacobi iteration. Reference values are the fluid density ,  and  for the plate flow and ,  and  for the flow around the airfoils.  Maximum values of  for the six test cases are given below.

 

Test Case

Flat Plate

NACA 0012

I

II

III

IV

V

VI

10-8

10-8

5×10-8

10-8

2×10-8

2×10-8