Comparing the performance of preconditioning matrixes in wide range of internal and external flows

In this study, by considering jacobian matrix based on conservative variables, eigenvalues, eigenvectors, and characteristic values for three types of preconditioners which are introduced by Turkel, Choi&Merkel and Eriksson are drawn in a unified mathematical manner. For this aim, these preconditioning methods are implemented in two-dimensional density-base “Roe” upwind scheme on unstructured meshes for Euler equations. Accuracy and rate of convergence are examined by external computing flow over NACA0012 airfoil, three-element 30P-30N airfoil, and internal flow over the bump for different flow conditions. This study shows that the application of preconditioning schemes not only increases the rate of convergence for compressible and incompressible flows dramatically; but also improves accuracy for incompressible flow in comparison with the classical method. This study also indicates that all preconditioning schemes provide approximately the same accuracy, but in terms of convergence rate, the Turkel preconditioning scheme provides a better rate of convergence among all the aforementioned preconditioned matrixes.