Changes between Version 2 and Version 3 of u/johannjc/scratchpad27


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Timestamp:
10/16/18 11:16:22 (6 years ago)
Author:
Jonathan
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  • u/johannjc/scratchpad27

    v2 v3  
    1 == Dealing with supercritical exterior inward flows ==
     1== Dealing with super-critical exterior inward flows ==
    221.  Want to find steady state solution interior of super-critical boundary point
    3 2.  Problem is that none exist with adiabatic EOS
     32.  Problem is that none exist that connect to the exterior point with the adiabatic EOS
    443.  Would like interior solution to be steady state and inflowing
    5 4.  This constrains the velocity and sound speed to give critical (or sub-critical) values for xi and u
    6 5.  And the density can also be arbitrary.
    7 6.  This interface can therefore generate three waves (with a shock/rarefaction, contact, and shock/rarefaction)
     54.  This constrains the velocity and sound speed to give critical (or sub-critical) Bondi solutions
     65.  The density can be arbitrary.
     76.  This interface can therefore generate three waves
    887.  We would like there to be no inward waves - so only a right moving shock or rarefaction.
    99
     
    13131.  There is a lower limit for the mach number so that the inward solution is critical (or subcritical).
    14141.  And there is an upper limit for the mach number if we require the flow to remain inward.
    15 1.  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
     151.  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
    1616
    1717
     18This shows the evolution of a run in 1D to verify the shock jump conditions
    1819
     20[[Image(Image2.png,width=400)]]
     21
     22
     23And here is the same run but in 3D with the interior and exterior profiles
     24
     25[[Image(Image3.png,width=400)]]
     26
     27
     28And here is a run where the initial post-shock conditions are held fixed (to suppress any interior waves)
     29
     30[[Image(Image1.png,width=400)]]
     31
     32
     33As the shock moves outwards, the upstream values seen by the shock change - which cause the downstream values to change - but they do not continue to lie along the steady state Bondi curve.  This leads to additional waves to form in the post shock flow.
     34