This work investigates the application of a high-order finite difference method for compressible large-eddy simulations on stretched, curvilinear and dynamic meshes. The solver utilizes 4th and 6th-order compact-differencing schemes for the spatial discretization, coupled with both explicit and implicit time-marching methods. Up to 10th order, Pade-type low-pass spatial filter operators are also incorporated to eliminate the spurious high-frequency modes which inevitably arise due to the lack of inherent dissipation in the spatial scheme. The solution procedure is evaluated for the case of decaying compressible isotropic turbulence and turbulent channel flow. The compact/filtering approach is found to be superior to standard second and fourth-order centered, as well as third-order upwind-biased approximations. For the case of isotropic turbulence, better results are obtained with the compact/filtering method (without an added subgrid-scale model) than with the constant-coefficient and dynamic Smagorinsky models. This is attributed to the fact that the SGS models, unlike the optimized low-pass filter, exert dissipation over a wide range of wave numbers including on some of the resolved scales. For channel flow simulations on coarse meshes, the compact/filtering and dynamic models provide similar results, with no clear advantage achieved by incorporating the SGS model. However, additional computations at higher Reynolds numbers must be considered in order to further evaluate this issue. The accuracy and efficiency of the implicit time-marching method relative to the explicit approach are also evaluated. It is shown that a second-order iterative implicit scheme represents an effective choice for large-eddy simulation of compressible wall-bounded flows.

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A viscous-inviscid interaction is produced when a compressible laminar boundary layer encounters a corner. The correct mathematical structure for such interactions at large Reynolds number is given by the asymptotic triple-deck theory. In the present work the triple-deck equations for supersonic and hypersonic flows are solved for both compression and expansion corners. Results are presented for a range of corner angles, including separated cases, and are compared with experimental data and with finite Reynolds number calculations based on an interacting boundary-layer model.