Error Quantification for Computational Aerodynamics Using an Error Transport Equation

Abstract

Error quantification in computational fluid dynamics is a subject of increasing interest and research. Although solution verification is conventionally performed using systematic grid refinement, Richardson extrapolation can be restrictive in its applicability, possibly requiring more than three grids to establish monotonic behavior. Ultimately, a single grid error estimation method may prove of greater utility for practical application in computational aerodynamics. In this work, an error transport equation is implemented in a three-dimensional upwind unstructured Navier-Stokes solver. An approach for deriving errors in related quantities of interest from the solution of the error transport equation is presented. Error quantification is demonstrated in two and three dimensions for aerodynamic flows where experimental data are available for comparison. Predicted error bars are found to contain fine grid solutions, test data, and the results of Richardson extrapolation. Furthermore, the error transport equation provides meaningful error quantification for aerodynamic coefficients in cases where Richardson extrapolation cannot be applied.