Computational fluid dynamics for complex industrial applications up to now usually refers to RANS (Reynolds-Averaged Navier Stokes) simulations with appropriate statistical turbulence models. Existing RANS turbulence models, however, often fail to accurately predict separated and reattached flows. Better results but higher computational costs are expected from Large-Eddy Simulations (LES). It is therefore a common interest to develop efficient and robust LES approaches for the prediction of complex flows with industrial relevance. An efficient representation of physically complex flows can be achieved with an Implicit LES approach, where the truncation error of the numerical discretization itself functions as turbulence model. We employ an Adaptive Local Deconvolution Method (ALDM) implemented in a solver for the incompressible Navier-Stokes equations where the domain is discretized on a Cartesian grid. Boundaries of arbitrary shape are represented by a second-order accurate Conservative Immersed Interface Method (CIIM). In this report we point out the computational aspects of CIIM in the framework of ILES on the example of the flow over a circular cylinder at Re = 3,900. As benchmark an ILES with ALDM on body-fitted grids and with a usual formulation of the wall-boundary condition is taken. Two simulations with similar numerical resolution are compared with experimental reference data. Also compared are their computational cost.