wiki:u/johannjc/scratchpad27

Version 2 (modified by Jonathan, 6 years ago) ( diff )

Dealing with supercritical exterior inward flows

  1. Want to find steady state solution interior of super-critical boundary point
  2. Problem is that none exist with adiabatic EOS
  3. Would like interior solution to be steady state and inflowing
  4. This constrains the velocity and sound speed to give critical (or sub-critical) values for xi and u
  5. And the density can also be arbitrary.
  6. This interface can therefore generate three waves (with a shock/rarefaction, contact, and shock/rarefaction)
  7. We would like there to be no inward waves - so only a right moving shock or rarefaction.

Single Shock

  1. For shocks, the mach number is the only 'free' parameter.
  2. There is a lower limit for the mach number so that the inward solution is critical (or subcritical).
  3. And there is an upper limit for the mach number if we require the flow to remain inward.
  4. As the shocks move, the post shock values do not fill in the bondi curve - nor do they satisfy the jump conditions for a single shock. Instead a rarefaction forms

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