An algorithm is proposed to combine Kirchhoff integral and an unsteady flow computation. Axisymmetric jet flows are given by DNS using 5-order accurate upwind compact scheme and 3-order accurate Runge-Kutta scheme. Kirchhoff integral is used to predict the far-field sound. Numerical results show that far-field sound pressure has the directivity and reaches maximal value at 20° diverged from the flow direction. The directivity is attenuating while the propagation distance is increasing.

The flow fields of 2-D compressible axisymmetric jet are simulated by solving N-S equations. The discretization method has high order accuracy. The information and development of the large vortical structure and it's role in the jet development are studied. The Kelvin-Helmholtz wave appears firstly when jet losts it's stability, and then the single vortex rolls up. After that, with the development of jet, the vortex structures begin to pair and merge because of the increasement of non-linear effects. It is also shown that the pressure distribution is directly relative to the large vortical structures.