Changes between Version 5 and Version 6 of u/erica/CFringanalysis


Ignore:
Timestamp:
07/01/15 17:11:01 (10 years ago)
Author:
Erica Kaminski
Comment:

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  • u/erica/CFringanalysis

    v5 v6  
    11=== Developing a model to describe the position of the ring found in the simulations
    22
    3 Model 1 - Normal shock (head on collision case), ignore magnetic fields
     3'''Model 1 - Normal shock (head on collision case), ignore magnetic fields
    44
    55-Ignore one side of the flow [[br]]
    … …  
    2424|| [[latex($ P_{ram} = \rho_2 v_2^2$)]]
    2525
    26 We can then look to where this outward ram pressure equals the pressure of the ambient medium. The ambient medium is not in HSE, so it will begin to fall inward toward the cylinder. We can approximate this a uniform collapse, which will specify density and velocity as a function of distance away from the cylinder, thus giving a ram pressure of the ambient medium. At that radius where these ram pressures are equal, we can expect a ring will build up.
     26We can then look to where this outward ram pressure equals the pressure of the ambient medium. The ambient medium is not in HSE, so it will begin to fall inward toward the cylinder. We can approximate this a uniform collapse, which will specify density and velocity as a ''function of distance'' away from the cylinder, thus giving a ram pressure of the ambient medium. At that radius where these ram pressures are equal, we can expect a ring will build up.
     27
     28Here are the shock parameters (1 is pre-shock, 2 is post-shock), in physical units (cgs):
     29
     30|| gamma || 5/3 ||
     31|| kB || 1.38*10^-16^ ||
     32|| G || ||
     33|| mH || 1.67*10^-24^ ||
     34|| M1 || 1.5 ||
     35|| M2 || 0.7 ||
     36|| T1 || 4931 ||
     37|| T2 || 7370 ||
     38|| rho1 || 1.67*10^-24^ ||
     39|| rho2 || 2.86286 * 10^-24^ ||
     40|| Cs1 || 733530 ||
     41|| Cs2 || 1.00754*10^6^ ||
     42|| v1 || 1 100 376 ||
     43|| v2 || 641 920 ||
     44|| pram2 || 1.48*10^-12^ ||
    2745
    2846'''Uniform Collapse of the ambient'''
    … …  
    3553----
    3654
    37 Model 2 - Assume ambient is stationary, and outflowing material is a parker type wind
     55'''Model 2 - Assume ambient is stationary, and outflowing material is a parker type wind
    3856
    3957*Note - can choose which is dominant by considering time scales -- freefall time compared to radius of splashed/ v_2, for instance
    … …  
    4159----
    4260
    43 Model 3 - Reflected shock, hydro case
     61'''Model 3 - Reflected shock, hydro case
    4462
    4563-Same as above, but now treat the shock as being reflected off of a wall (i.e. the opposing flow)
    … …  
    4866----
    4967
    50 Model 4 - Include magnetic pressures
     68'''Model 4 - Include magnetic pressures