Using JST and CUSP schemes in aerodynamic optimization based on discrete adjoint method in a viscous all-speed solver developed on unstructured grid

In this paper, using a preconditioning approach, a viscous all-speed flow solver has been developed based on JST and CUSP schemes and compared with Roe upwind scheme in unstructured database. The comparison between the preconditioning and non-preconditioning has been donned. The results show that the non-preconditioning compressible solvers hardly converged in low-speed regions while the preconditioned forms converged more rapidly. The results of all schemes were compared with experimental data that showed the all schemes have good agreement with experimental data. Although, Roe upwind and CUSP schemes have more agreement to the data. Also, the CUSP scheme is faster than the other schemes. In the next step, aerodynamic optimization based on discrete adjoint method has been developed over the schemes. The verification of the method done comparing the results with finite difference method in both preconditioning and non-preconditioning approaches. The agreement of results is good. In general, it can be concluded that the CUSP algorithm is somewhat faster than the other two algorithms and is a good option for optimization.