Numerical computations are commonly used for better understanding the unsteady processes in internal combustion engine components and their acoustic behavior. The acoustic characterization of a system requires that reflections from duct terminations are avoided, which is achieved either by using highly dissipative terminations or, when an impulsive excitation is used, by placing long ducts between the system under study and the duct ends. In the latter case, the simulation of such a procedure would require a large computational domain with the associated high computational cost, unless non-reflecting boundary conditions are used. In this paper, first the different non-reflecting boundary conditions available in ANSYS-FLUENT are evaluated. Then, the development and implementation of an anechoic termination in a 3D-CFD code is presented. The performance of the new implementation is first validated in the classic Sod's shock tube problem, and then checked against numerical and experimental results of the flow and acoustic fields in automotive exhaust mufflers. The results obtained compare favorably with those from the conventional CFD approach and experiments, while the computational cost is significantly reduced.