Uncertainty assessment for CFD using error transport equation

While Computational Fluid Dynamics (CFD) is making extensive use of the power of computational technology, it is also facing a serious problem arising from the so-called numerical uncertainty. The overall uncertainty (or the global error) involved in CFD results can be due to different sources mainly contributed by (i) discretization error (or solution error due to incomplete grid convergence), (ii) iteration convergence error, (iii) grid generation errors (skewness, grid aspect and expansion ratio, coordinate transformation etc.), and (iv) round-off errors. In this study an in-depth discussion concerning these issues is presented with an emphasis on the discretization error in regard with the theoretical background, as well as the commonly used methods for identification and estimation of numerical errors.;The principal goal of this study is to develop a dynamic algorithm that can be used in conjunction with CFD simulation codes to quantify the discretization error in a selected process variable. The focus is on fluid dynamics applications where the conservation equations are solved for primary variables such as velocity, temperature and concentration etc., using finite difference and/or finite volume approach. A transport equation for the error (referred to as the error transport equation) is formulated and solved along with a localized residual estimation based on the modified equation concept. Spatiotemporal evolution of the error distribution is mapped and compared to exact error distributions for various benchmark test cases. A new method is proposed for deriving the error equation specifically aimed at using it with commercial CFD codes that use the finite volume approach. Finally, a blind test is performed on an unsteady 3D scalar transport problem subject to a rotational flow field. Excellent results are obtained in predicting the discretization error