Compressible large eddy simulations of wall-bounded turbulent flows using a semi-implicit numerical scheme for low Mach number aeroacoustics

Large eddy simulations (LES) of low-speed, wall-bounded turbulent flows were conducted by numerically integrating the compressible Navier–Stokes equations in a generalized curvilinear coordinate system. An efficient numerical scheme based on a third-order additive semi-implicit Runge–Kutta method for time advancement and a sixth-order accurate, compact finite-difference scheme for spatial discretization were used. The convective terms in the wall-normal direction were treated implicitly to remove the time-step limitation associated with the use of fine meshes in the near-wall region for high Reynolds number viscous flows. The dynamic Smagorinsky subgrid-scale eddy viscosity model was used to close the filtered equations. Generalized characteristic-based non-reflecting boundary conditions were used together with grid stretching and enhanced damping in the exit zone. The accuracy and efficiency of the numerical scheme was assessed by simple acoustic model problems and by comparing LES predictions for fully developed turbulent channel flow and turbulent separated flow in an asymmetric diffuser to previous direct numerical simulation (DNS) and experimental data, respectively. LES predictions for both flows were in reasonable agreement with the DNS and experimental mean velocity and turbulence statistics. The findings suggest that the numerical approach employed here offers comparable accuracy to similar recent studies at approximately one-third of the computational cost and may provide both an accurate and efficient way to conduct computational aeroacoustics studies for low Mach number, confined turbulent flows.