A high-resolution method for direct numerical simulation of shock-turbulence interaction

An approach for the direct numerical simulation of compressible turbulent flow and shock-turbulence interaction is presented. An novel upwind-biased finite-difference scheme with a compact centered stencil is used to discretize the convective part of the Navier-Stokes equations, The scheme gives uniformly high approximation order and allows for a spectral-like wave resolution while dissipating non-resolved wavenumbers. When hybridized with an essentially non-oscillatory scheme near discontinuities, the scheme becomes shock-capturing and its resolution properties are preserved. The derivation of the compact, scheme is discussed. Upwinding and coupling procedures are described. Implementational issues of the hybrid scheme are addressed. Results for test and validation computations are given.