A staggered compact finite difference formulation for the compressible Navier–Stokes equations

In this paper, a compact high order (up to 12th order) numerical method to solve the compressible Navier–Stokes equations will be presented. A staggered arrangement of the variables has been used. It is shown that the method is not only very accurate but numerically also very stable even in the case that not all the energy containing scales in the flow are resolved. This in contrast to standard (collocated) compact finite difference methods. Some results for a turbulent non-reacting and a reacting jet with a Reynolds number of 10,000 and a Mach number of 0.5 are reported.