Coanda wall jets in technical applications are almost always turbulent. Since reliable prediction tools are not available, wind/water tunnel tests are indispensable for validating any new design. Still, complete confidence in Coanda wall jet applications can only be obtained if the intricate fluid dynamics are understood. Ongoing research efforts, both experimentally and numerically, aim at broadening our understanding of the physical mechanisms involved in Coanda wall jet flows. This paper explores the feasibility of several Reynolds averaged Navier-Stokes (RANS) turbulence models for calculating a Coanda wall jet over a circular cylinder in a quiescent ambient. Neither one of the models captures all aspects of the flow correctly. It is shown how a finite ambient velocity affects both, jet separation location and generated aerodynamic forces. The grid resolution requirements can make direct numerical simulations (DNS) of turbulent Coanda wall jet flows unaffordable. Hybrid turbulence modeling approaches such as detached eddy simulation (DES) and the flow simulation methodology (FSM) combine the advantages of DNS, large eddy simulation (LES), and RANS. The dynamics of the large scale coherent structures are captured while the small scale and more homogeneous turbulence motion is modeled. Using 3-D FSM it is shown how streamwise vortices generated at the nozzle exit can significantly alter the wall jet characteristics.