Comparative study of upwind schemes for transonic and supersonic internal flows

A study of some popular upwind schemes applied to transonic internal flows using some well-known test cases is done in this paper. We focused on upwind schemes because the central space discretizations have symmetry with respect to a change in sign; therefore, the physical propagation of perturbations along characteristics, typical of hyperbolic equations is not considered in the definition of numerical model. In contrast to the central space discretizations, the upwind schemes whose origin may be due to Courant et al. [1] are directed towards the introduction of the physical properties of the flow equations into the discretized formulation that has leads to upwinding techniques such as flux vector splitting and flux difference splitting. In order to test the accuracy, robustness and efficiency of some popular upwind methods (van Leer scheme, Roe scheme and Liou's AUSM+ scheme); we used some well-known test cases.