ACCURACY VERIFICATION OF UNSTRUCTURED SECOND-ORDER FINITE VOLUME DISCRETIZATION SCHEMES BASED ON THE METHOD OF MANUFACTURED SOLUTIONS

With the great improvement in computer technology, computational fluid dynamics have progressed significantly. Even though it is fast and easy to obtain discretized results via numerical simulations, the validity and accuracy of the results need to be carefully validated and verified. As an important approach in verification and validation, the method of manufactured solutions (MMS) was widely applied in code verification, accuracy analysis and verification of boundary conditions. This paper first established the procedures for the MMS with scalar manufactured solutions and vector man-ufactured solutions. Verification of these two procedures was performed by comparing results of accuracy testing for a typical exact solution (2D inviscid isentropic vortex). The MMS procedures were then employed to the study of unstructured finite-volume discretization schemes, such as gradient reconstruction methods, convective fluxes discretization and diffusive fluxes discretization. It demonstrated that some schemes employing certain Green-Gauss based gradient degrade to 1st order on irregular meshes and discretization error increases significantly, while the least squares based gradient is insensitive to mesh irregularity. Besides, all tested convective fluxes discretization schemes were 2nd order accurate and they exhibited similar performance in terms of accuracy. But the method of computing the interface gradient was an essential factor affecting the accuracy of diffusive fluxes discretization.