Changes between Version 11 and Version 12 of u/erica/AccretionModelingBlog
- Timestamp:
- 03/20/18 19:08:29 (7 years ago)
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u/erica/AccretionModelingBlog
v11 v12 1 1 == Bondi Accretion == 2 2 3 === 3/18/2018 ===3 === 3/18/2018 ($\gamma=1.66$ case)=== 4 4 5 5 Am working on a 3D simulation of Bondi Flow onto a central sink particle and studying the accretion properties using the Krumholz accretion algorithm. … … 25 25 $y\_=\frac{v_r}{C_\infty}$ 26 26 27 In the above, $\lambda$ is a numerical coefficient which controls the strength of the accretion flow. At its critical value, $\lambda=\lambda_{crit}$, $\dot{M}$ is strongest. In the code, $\lambda_{crit}$ is solved for using Eqn. 18 in Bondi's paper. In this simulation, these parameters are:27 In the above, $\lambda$ is a numerical coefficient which controls the strength of the accretion flow. At its critical value, $\lambda=\lambda_{crit}$, $\dot{M}$ is strongest. In the code, $\lambda_{crit}$ is solved for using Eqn. 18 in Bondi's paper. 28 28 29 || $\lambda_{crit}$ || .2526 || 30 || $\gamma$ || 1.66 || 31 32 Additionally, we have: 29 The IC's for this simulation include: 33 30 34 31 || $C_{\infty}$ || 1.291 || … … 37 34 || $M_*$ || .14318E+13 || 38 35 || $R_{BH}$ || 25.63 || 39 || $R_{s}$ || .0128 ||40 36 || $\dot{M}$ || 2692.17 || 41 37 42 38 The case of $\gamma=5/3$ flow is an extreme limit for the solution space. This value of $\gamma$ has a few interesting features: 43 39 40 In other words, when $\gamma=5/3$ exactly, we have no accretion flow. 41 44 42 45 43 === Results === 44 ==== $\gamma=1.66$ case ==== 45 46 || $\gamma$ || 1.66 || 47 || $\lambda_{crit}$ || .2526 || 48 || $R_{s}$ || .0128 || 46 49 47 50 The simulation setup reproduces the correct nondimensional profiles. Here's a comparison of the t=0 nondimensional density and velocity profiles astrobear calculates for the bondi module (left), compared to the Bondi solutions for $\gamma=5/3$ (curves II and III for the case of $\lambda=\lambda_{crit}$). 48 51 49 52 [[Image(Bondi_Comparison.png, 50%)]] 53 54 The profiles are cut-off within an inner radius of $r=.875$ to avoid extremely high speeds there (am going to get rid of this in the next round of sims). Sampling the mass flux across a spherical shell less than this radius doesn't match up with the theoretical prediction of $\dot{M}=2692$ since the solution is getting stepped on there. Sampling the mass flux across a shell larger than this, however, produces agreement. 55 56 50 57 51 58 However, the accretion rate onto the particle does not match the theoretical value. Sampling the mass of the particle over 10 different times shows the accretion rate to be fairly constant at,