Application of the grid convergence index to a laminar axisymmetric sudden expansion flow

Abstract

The use of numerical models to represent natural processes is increasingly common. The development of advanced numerical tools allows a more physically-based representation of complex flow phenomena. While more advanced systems can be solved, the uncertainty of the accuracy of the solutions obtained remains. The mere comparison between experiments and simulations is not enough proof of strength of the results. The Grid Convergence Index (GCI) methodology has been proposed with the aim to provide a mechanism to calculate and report discretization errors estimates in computational fluid dynamics (CFD) simulations. It permits the quantification of the uncertainty present in grid convergence. This method uses a grid convergence error estimator that is obtained by applying the generalized Richardson Extrapolation theory. The process is applied to an axisymmetric sudden expansion laminar flow case. Experimental results are used to verify the numerical simulation and GCI outcome. As a result of the application of this method the order of accuracy of the numerical scheme was verified. Additionally, comparing the numerical results with the experimental values, a maximum error of 6% was obtained. Finally, considering the two finest meshes, it can be concluded that the asymptotic range has been reached and that a finer Mesh won’t improve the accuracy of the solution when considering the increased numerical cost.