Two-dimensional, unsteady, compressible flow fields produced by
the interactions
between a single vortex or a pair of vortices and a shock wave are simulated
numerically. The Navier–Stokes equations are solved by a finite difference
method.
The sixth-order-accurate compact Padé scheme is used for spatial
derivatives, together
with the fourth-order-accurate Runge–Kutta scheme for time integration.
The detailed
mechanics of the flow fields at an early stage of the interactions and
the basic nature
of the near-field sound generated by the interactions are studied. The
results for both
a single vortex and a pair of vortices suggest that the generation and
the nature of
sounds are closely related to the generation of reflected shock waves.
The flow field
differs significantly when the pair of vortices moves in the same direction
as the shock
wave than when opposite to it.