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A cylindrical complex-frequency-shifted perfectly matched layers (CFS-PML) absorbing boundary condition (ABC) is applied in the bi-dimensional (2-D) finite volume (FV) method. The impact of CFS-PML parameters on the wave absorption, as well as on the condition number of the associated system matrix is examinated by comparing the performance of two PML loss profiles, viz., polynomial and geometric grading. The discretization error due to FV approximation is also studied. FV results are validated against analytical solution. Results show that both profiles have similar performance in terms of absorption wave and conditioning of the associated system matrix.