In order to study acoustic noise generation and propagation while considering that internal viscosity of the propagation medium affects the results of aeroacoustics numerical simulation, a decomposition technique and a turbulent model were introduced in time-domain. Based on an unstructured collocated grid and finite volume method, the compressible N-S equation was divided into a viscous incompressible N-S equation and the viscous perturbation equation, and a SimpleC algorithm was used to solve the problem of velocity-pressure decoupling. Appropriate non-reflecting boundary conditions were adopted at the inflow and outflow boundaries. The governing acoustic equations of boundaries are discretized over finite volume method and the transient term is discretized by the second-order Euler implicit scheme. Numerical simulation of noise induced by flow around a circular cylinder at small and big Reynolds number has been conducted and compared with the aeroacoustic theory in time domain, in order to study the effect of viscosity on aeroacoustic numerical simulation. Comparing the two results, good results and more details about flow and sound could be obtained by splitting method, which could be used to provide some information for reducing the noise in actual engineering. The work demonstrated that the numerical algorithm can be used for the simulation and analysis of flow-induced noise at a flow with low speed.