The success of Large-Eddy Simulations (LES) of wall-bounded turbulence depends strongly on an accurate representation of the flow near the boundaries. Since in implicit LES the truncation error of the numerical discretization itself functions as SGS model, the order of accuracy of the discretization should be maintained near the boundary. In this paper, we analyze the performance of implicit LES for predicting turbulent flows along complex geometries. For the representation of wall-boundaries two different approaches are compared: (A) the case of body-fitted grids, and (B) a novel second-order accurate Conservative Immersed Interface Method (CIIM) for representing boundaries of arbitrary shape on Cartesian grids. The need for mapping domain boundaries on the grid raises the question whether a comparable accuracy with body-fitted grids can be achieved. In both (A) and (B) we employ the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The assessment is carried out on the example of the flow over a circular cylinder at Re=3900. Two simulations with comparable numerical resolution are performed and compared to experimental reference data. Both methods result in similar accuracy for turbulent statistics and mean integral quantities. This demonstrates that ALDM on Cartesian grids is a feasible and efficient approach to simulate turbulent flows on complex domains.@en

We propose a conservative, second-order accurate immersed interface method for representing incompressible fluid flows over complex three dimensional solid obstacles on a staggered Cartesian grid. The method is based on a finite-volume discretization of the incompressible Navier-Stokes equations which is modified locally in cells that are cut by the interface in such a way that accuracy and conservativity are maintained. A level-set technique is used for description and tracking of the interface geometry, so that an extension of the method to moving boundaries and flexible walls is straightforward. Numerical stability is ensured for small cells by a conservative mixing procedure. Discrete conservation and sharp representation of the fluid-solid interface render the method particularly suitable for Large-Eddy Simulations of high-Reynolds number flows. Accuracy, second-order grid convergence and robustness of the method is demonstrated for several test cases: inclined channel flow at Re= 20, flow over a square cylinder at Re= 100, flow over a circular cylinder at Re= 40, Re= 100 and Re= 3900, as well as turbulent channel flow with periodic constrictions at Re= 10,595.@en

This work presents an immersed interface method for representing complex boundaries in Implicit Large-Eddy Simulation on three-dimensional, staggered Cartesian Grids. The immersed obstacle in the fluid domain is characterized by a levelset field. Initial flux calculations are carried out for the entire domain in the same way. Cells intersected by the immersed interface then undergo a special treatment: only the fluid part is considered, no-slip condition and no-through-flux condition are imposed by changing the flux balance and a homogeneous Neumann condition for pressure is enforced in the pressure projection. To deal with the small cell problem a cell-mixing procedure is applied. The approach is fully conservative and we demonstrate the method is second-order accurate. The validation and the performance of the approach are done with some numerical examples of 2D and 3D flow configurations.@en