Large eddy Simulation of turbulent compressible wavy channels

Large-eddy simulations of compressible flows over a wavy turbulent channel are performed to investigate the effects of wavy roughness. The simulation are performed using our recently developed framework that incorporates subgrid-scale model LES and sharp interface immersed boundary method. The equations are discretized using a fourth-order hybrid discretization comprising a fourth-order skew-central scheme and a third-order weighted essentially nonoscillatory (WENO) scheme. To ensure that our framework can resolve turbulent wall flows properly, the LES has been first validated for turbulent channel with flat walls. The simulations were validated at Reynolds numbers $(Re_{\tau}=u_{\tau}H/\nu=180$, H: channel half width, $u_\tau$: friction velocity, and $\nu:$ kinematic viscosity) and two Mach numbers (M), M=0.5 and M=1.5 against the previous numerical studies. The wavy channel simulations are performed with a non-dimensional amplitude a/H=0.075 and a wavelength of $\lambda/H=\pi/2$ for three Mach numbers M=0.5, M=1.5, and M=3.0. It is observed that the flow separates at the troughs of the wave and flow separation is not affected by the fluid compression. However, it can be observed that the wavy surface imparts strong shock patterns that go all from the peak of the wave to the upper surface and reflect from the upper wall to the domain.