Hybrid Schemes of Shock Capturing Methods and Secondary Conservative Finite Difference

For compressible flow simulations, FDS, FVS, and AUSM are popular shock capturing schemes. However, these schemes do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method is useful for unsteady turbulent flow simulations, although it does not work well for flows with discontinuities. In this study, we propose a computational technique that combine the shock capturing schemes and the secondary conservative finite difference. In addition, we try to combine the secondary conservative finite difference method and LAD (localized artificial diffusivity). These methods are combined properly with the aid of a shock detected sensor. In order to demonstrate the shock capturing performance and low numerical dissipation property of the hybrid schemes, numerical tests are done on a three-dimensional periodic inviscid flow, the shock tube problem (Sod problem), and a shock-vortex interaction problem. The computational results have shown that the proposed hybrid schemes based on numerical flux have desired conservation property, shock capturing performance, and low numerical dissipation in regions without discontinuity.