Acoustic upwinding for sub- and super-sonic turbulent channel flow at low Reynolds number

A recently developed asymmetric implicit fifth-order scheme with acoustic upwinding for the spatial discretization for the characteristic waves is applied to the fully compressible, viscous and non-stationary Navier-Stokes equations for sub- and super-sonic, mildly turbulent, channel flow (Re=360). For a Mach number of 0.1, results are presented for uniform (323, 643 and 1283) and non-uniform (expanding wall-normal, 323 and 643) grids and compared to the (incompressible) reference solution found in (J. Fluid. Mech. 1987; 177:133-166). The results for uniform grids on 1283 and 643 nodes show high resemblance with the reference solution. Expanding grids are applied on 643- and 323-node grids. The capability of the proposed technique to solve compressible flow is first demonstrated by increasing the Mach number to 0.3, 0.6 and 0.9 for isentropic flow on the uniform 643-grid. Next, the flow speed is increased to Ma=2. The results for the isothermal-wall supersonic flows give very good agreement with known literature results. The velocity field, the temperature and their fluctuations are well resolved. This means that in all presented (sub- and super-sonic) cases, the combination of acoustic upwinding and the asymmetric high-order scheme provides sufficient high wave-number damping and low wave-number accuracy to give numerically stable and accurate results.