Changes between Version 19 and Version 20 of u/BonnorEbert


Ignore:
Timestamp:
01/15/16 14:55:52 (9 years ago)
Author:
Erica Kaminski
Comment:

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  • u/BonnorEbert

    v19 v20  
    7676In numerical simulations, it is meaningful to constrain Pin=Pext at the outer boundary of the sphere, as the Bonnor Ebert sphere is in pressure balance and no external pressures are considered in its derivation. This gives the following useful relationship:
    7777
    78 {{{#!latex
    79 P_i =  P_o \Rightarrow
    80 }}}
     78[[latex($P_i =  P_o \Rightarrow $)]]
    8179
    8280
    83 {{{#!latex
    84 P_i = C_s^2 \times\rho_i = C_s^2\times\rho_o = P_o
    85 }}}
     81[[latex($P_i = C_s^2 \times\rho_i = C_s^2\times\rho_o = P_o $)]]
    8682
    8783That is, by requiring that the pressures remain equal at the sphere's edge implies that reducing the density outside of the sphere concomitantly increases the external temperature (Fig. 1). This can lead to more realistic conditions, as well as prove helpful in managing the mass outside of the sphere during simulations (refer to Results: Non-Rotating, Non-MHD). Figure 2 shows the set-up without adjusting any external parameters.