Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes

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.