Numerical and Parameter Uncertainties: Are They Independent?

In the Validation procedure proposed by the ASME V&V 20 Standard, the quantification of the modeling error of mathematical models solved by Computational Fluid Dynamics (CFD) requires the estimation of the experimental, numerical and parameter uncertainties. In its simplest form, these uncertainties are assumed independent. Parameter uncertainty is typically a consequence of lack of exact values for the boundary conditions and/or fluid properties. Its evaluation is handled by the broad field of uncertainty quantification. However, this evaluation requires simulations that are unavoidably affected by numerical errors. Therefore, it may be questionable if parameter and numerical uncertainties are really independent or, alternatively, how small must be the numerical uncertainty to estimate parameter uncertainties without its influence. In this paper we address the relation between parameter and numerical uncertainties using two test cases: the transition from laminar to turbulent flow on a flat plate at a Reynolds number of 10⁷; the flow around the Eppler 387 airfoil at an angle of attack of 1^o and Re = 3 × 10⁵. The mathematical model for the three cases is the Reynolds-Averaged Navier-Stokes equations supplemented by the k–ω SST eddy-viscosity turbulence model and the one-equation γ transition model. Sensitivity coefficients are determined for the selected quantities of interest using the local sensitivity method and finite-differences. These estimates are performed for different levels of grid refinement to check its dependency on the estimated numerical error obtained from power series expansions. Results obtained in this study suggest that the evaluation of the parameter uncertainty only becomes independent of the numerical error when the simulation results are in the asymptotic range.