Using High-Order Accurate Essentially Non-Oscillatory (ENO) Schemes for Aeroacoustic Applications

Figures 1 through 3 depict the interaction of a vortex and a shock wave. Such an interaction is believed to be one of the fundamental mechanisms that are responsible for shock-associated noise in jets. The figures represent a computational solution of the axisymmetric Euler equations in the upper x-r plane. The initial conditions are implemented in two steps. First, a normal shock plane is positioned in a steady, rectilinear flow that is parallel to the axis of symmetry (x-axis) and with a pre-shock Mach number is 1.3. At t=0, a toroidal vortex is imposed upstream of the shock (Fig. 1). For t>0, the vortex convects downstream and passes through the shock (Fig. 2). The shape of the shock is distorted, the vortex strength is altered by the post-shock state, and an acoustic wave is produced (Fig. 3).

Figure 1 Initial conditions.

Figure 2 Vortex core interacts with shock wave.

Figure 3 An acoustic wave front emerges downstream of the shock.

Details can be obtained from the AIAA Journal paper:
Casper, J. and Meadows, K.R., "Using High-Order Accurate Essentially Non-Oscillatory Schemes for Aeroacoustic Applications", AIAA Journal, Vol. 34, No. 2, February, 1996.