Application of various compact schemes to the high-resolution simulations of compressible flow

Various compact schemes for the spatial derivatives of the compressible Navier-Stokes equations are in the evaluation, providing an improved representation of a range of scales to study structures of a compressible plane wake undergoing transition to turbulence and shock-vortex interactions. Two different kinds of compact schemes of upwind/central compact schemes are tested with a coarse grid. A local Lax-Friedrich method with upwind-biased 5th and 9th-order compact schemes is implemented for the Euler terms. Numerical differencing errors of the results calculated by the upwind and central compact schemes are investigated for the evolution of wake structure from the linear regime and the acoustic field generated by the schock-vortex interaction. A comparison between the numerical results obtained with the upwind and central compact schemes indicates that an appropriate error construction at high wave number ranges beyond an effective wavenumber of the resolution shows an advantage to resolve vortical fine structures in the wake at high Reynolds numbers. The numerical results of high-order upwind biased compact schemes show and improved representation of the vortex distortion by the vortex interaction with a relatively strong shock. The 6th-order central compact scheme with filtering by a pentadiagonal compact scheme is found to be acceptable for the shock-vortex interaction simulation.