An Error Transport Equation with Practical Applications

Abstract

Error quantification in Computational Fluid Dynamics (CFD) is a subject of increasing interest and research. While solution verification is conventionally performed using systematic grid refinement, Richardson extrapolation is restrictive in its ap plicability, 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 this work, an Error Transport Equation (ETE) is implemente d in a 3D upwind unstructured Navier -Stokes solver. An approach for deriving errors in related quantities of interest from the solution of the ETE is presented. Error quantification is demonstrated in 2D and 3D for aerodynamic flows where experimental da ta is available for comparison . Predicted error bars are found to contain fin e grid solutions, test data, and the results of Richardson extrapolation . Furthermore, the ETE provides meaningful error quantification in cases where Richardson extrapolation c an not be applied. Preliminary application of the ETE to a simple jet shows additional research is needed to extend the method to shear -dominated problems where turbulent mixing is significant.