Summary: A numerical procedure for the direct numerical simulation of compressible turbulent flow and shock-turbulence interaction is detailed and analyzed. An upwind-biased finite difference scheme with a compact centered stencil is used to discretize the convective part of the Navier-Stokes equations. The scheme has a uniformly high approximation order and allows for a spectral-like wave resolution while dissipating nonresolved wave numbers. When hybridized with an essentially nonoscillatory scheme near discontinuities, the scheme becomes schock-capturing, and its resolution properties are preserved. Diffusive parts are discretized with symmetric compact finite differences, and an explicit Runge-Kutta scheme is used for time-advancement. We describe the peculiarities of efficient upwinding and coupling procedures and give validation results. Using direct numerical simulation data, some aspects of turbulent supersonic compression ramp flow are studied to demonstrate the effectiveness of the procedure.