Solution Verification Test By A CFD Mixed High Order Code In Laminar-Turbulent Flow Transition

Homero Ghioti da Silva¹

¹ Faculty of Integrated Sciences at Pontal, University of Uberlandia, Brazil

doi:10.20906/CPS/COB-2015-2594

Resumo

This work treats uncertainty quantifications in CFD of high order of accuracy, in the context of Verification and Validation. The work was performed into numerical solutions by one in-house code that uses mixed high-order method, composed by compact finite difference methods at 4th to 6th order of accuracy, used to the spatial derivative calculations, and Runge Kutta method of 4th order of accuracy, used to the numerical integration calculations of the Navier/Stokes equations. The code simulates the flow laminar-turbulent transition in a channel flow. The numerical error was estimated through comparisons between numerical solutions and one reference solution by the Richardson extrapolation method on numerical solution on two different mesh level. The comparisons and the estimation to numerical error were studied in a mesh convergence test. Further, an uncertainty quantification using grid convergence index (Roache's GCI) was performed. The results confirmed great estimative to the discretization erros. The estimated order of accuracy was in agreement with the formal order of accuracy of the current numerical schemes. Because of mixed high order code adopted, the interpretation of results in the mesh refinement test was hard, but, it was possible to explain the origin and contribution of each dominant estimated numerical error.

Palavras-chave: Uncertainties quantification; Mixed high-order code; CFD in flow laminar-turbulent transition; Richardson extrapolation; ROACHE's GCI