A Comparative Study of Gradient Reconstruction Methods for Unstructured Meshes with Application to Turbomachinery Flows

The accuracy of second-order upwind spatial discretization schemes on unstructured meshes depends strongly on the accuracy of the calculated spatial gradients. In this work the Green-Gauss and least-squares methods for the calculation of spatial gradients have been implemented in a hybrid CFD solver for turbomachinery flows and analysed in the context of both academic and industrially relevant test cases. Alongside the stability and accuracy characteristics of the methods, the issues of computational overhead and implementation complexity are discussed in detail.