Changes between Version 19 and Version 20 of u/BonnorEbert
- Timestamp:
- 01/15/16 14:55:52 (9 years ago)
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u/BonnorEbert
v19 v20 76 76 In 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: 77 77 78 {{{#!latex 79 P_i = P_o \Rightarrow 80 }}} 78 [[latex($P_i = P_o \Rightarrow $)]] 81 79 82 80 83 {{{#!latex 84 P_i = C_s^2 \times\rho_i = C_s^2\times\rho_o = P_o 85 }}} 81 [[latex($P_i = C_s^2 \times\rho_i = C_s^2\times\rho_o = P_o $)]] 86 82 87 83 That 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.