Calculation of Numerical Uncertainty Using Richardson Extrapolation: Application to Some Simple Turbulent Flow Calculations

Abstract

Richardson extrapolation has been applied to turbulent pipe flow and turbulent flow past a backward facing step. A commercial CFD code is used for this purpose. It is found that the application of the method is not straightforward and some aspects need careful consideration. Some of the problems are elucidated. The particular code used for the present application employs a hybrid scheme, and it does not give monotonic convergence for all the variables in all regions as the grid is refined. The flow regions and the variables which converge monotonically in these regions should be identified first before the method is applied. When this is done Richardson extrapolation gives good results in calculating the apparent order of the numerical procedure used, as well as obtaining grid independent results with which discretization error bounds can be calculated as measures of numerical uncertainty. Even in cases where it does not work, the method can be used as an error indicator for some obscured user mistakes. This paper also demonstrates several shortcomings of using commercial CFD codes. The present findings should help the users of CFD software in general, to quantify discretization errors in their calculations.