On a method for direct numerical simulation of shear layer/compression wave interaction for aeroacoustic investigations

Direct numerical simulation (DNS) of a spatially developing mixing layer was performed. The compressible three-dimensional Navier–Stokes equations were solved for pressure, velocities and entropy for this flow using a compact finite-difference scheme of sixth-order accuracy in space, combined with Runge–Kutta three-step time advancement. On one of the transverse boundaries of the box-shaped domain, a compression wave profile was imposed in pressure and velocity components via a wave decomposition of the governing equations, in order to study the interaction of an isolated weak shock wave entering the domain with the mixed subsonic/supersonic shear layer. This flow situation is found along the shear layer of supersonic, imperfectly expanded jets containing a shock cell structure. In the present work, an isolated compression–expansion structure constitutes the model problem. The domain setup and the boundary conditions were chosen such as to allow analysis of the sound field generated by the turbulent flow and the shock–turbulence interaction. The numerical method used to impose the boundary conditions and solve the compressible Navier–Stokes equations, and the choice of numerical parameters, are described in detail. Some results on the two-dimensional and three-dimensional flow field computed are presented as well.