Simulation of the KelvinHelmholtz instability of a supersonic slip surface with the PiecewiseParabolic Method (PPM)
Abstract
The PiecewiseParabolic Method (PPM) was used to study the nonlinear development of the KelvinHelmholtz instability of a Mach 2 slip surface in both a gamma law gas and in an isothermal gas. A simplified version of PPM appropriate to this and other problems with only weak shocks is described. The instability calculations demonstrate the usefulness of discontinuity steepening in PPM and illustrate the complexity in a flow problem which this method treats accurately on CrayIclass computers. The simulations also bring to light characteristic combinations of nonlinear waves which arise from finite amplitude perturbations of the slip surface and which exhibit an approximately self similar growth. After passing through a fairly chaotic phase of development, the mixing layer generated by the instability achieves a relatively ordered state which does not appear to depend greatly upon the nature of the initial perturbation, but which does depend upon the length scale over which strict periodicity is enforced in the simulation.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 March 1984
 Bibcode:
 1984STIN...8432768W
 Keywords:

 Gas Flow;
 KelvinHelmholtz Instability;
 Nonlinearity;
 Slip Flow;
 Supersonic Flow;
 Compressible Flow;
 Computerized Simulation;
 Cray Computers;
 Euler Equations Of Motion;
 Mach Number;
 Mixing Layers (Fluids);
 Perturbation;
 Fluid Mechanics and Heat Transfer