This paper discusses the implementation of a direct-forcing Immersed Boundary Method (IBM) in the CFD software by ONERA, DLR and AIRBUS CODA to solve the compressible Reynolds-Averaged Navier-Stokes (RANS) equations around geometrically complex geometries. Developed in close collaboration between ONERA and DLR, this method explicitly forces the flow solution at the integration points located near the immersed boundaries using Immersed Boundary Conditions (IBCs). As the mesh does not need to conform to the obstacles within the flow to handle intricate geometries, the current approach uses Cartesian meshes to simplify and automate the mesh generation process.Both the Cartesian mesh generation and the specific IBM pre-processing to locate the integration and donor points are handled via Cassiopee package. Unlike other IBM implementations, unstructured AMR-type meshes are favored over structured octree-based grids to reduce the final number of cells by multiple orders of magnitude and to leverage the unstructured architecture of CODA. A collection of offsets defined from the immersed boundary (surface edges or surface meshes, depending on the simulation dimension) is then used to determine the different levels of refinement. Recent improvements brought to the mesh adaptation tool algorithm have significantly increased the efficiency of the mesh generation and have overcome prior memory limitations. The solution at integration points located on the immersed boundaries is computed using the weakly imposed boundary condition formulation in CODA, adapted for the IBM approach. Wall functions are applied to avoid Cartesian cells with y+=1 near the walls, which would be too prohibitive in terms of cell count for high Reynolds number simulations. RANS simulations are compared against body-fitted wall-resolved solutions, as well as other Cartesian IBM solutions, in order to assess the accuracy, the robustness and the performance of this IBM methodology, especially in terms of skin pressure and skin friction coefficients. To that end, various academic 2D and 3D test cases have been envisioned and thoroughly tested. The conclusions and details of these validations can be found in a companion paper.