A finite-difference scheme for the analysis of high frequency sound radiation

A finite-difference formulation is developed for sound propagation in 2-D straight and cylindrical hard walled ducts with uniform flow. The procedure that has been developed is able to treat very high frequency problems without having to use a correspondingly high resolution grid. The idea is to solve for the real amplitude and phase angle of a complex potential instead of solving for its real and imaginary parts. The governing equations are recast in terms of amplitude and phase angle which do not show oscillatory behavior and hence are not difficult to solve when compared to solving for real and imaginary parts of the complex potential. Also the solution procedure is stable at very high reduced frequencies. Time marching, which utilizes the harmonic time factorization is used to solve these equations. This method has been programmed and sample calculations are presented for 2-D and cylindrical straight hard walled ducts which show excellent agreement with the analytical solutions.