| | 67 | == Accretion == |
| | 68 | Federrath accretion removes just enough density from cells within 4 zones of the particle to keep them below the truelove limit. |
| | 69 | |
| | 70 | Bondi accretions is a bit more involved. |
| | 71 | The host cell of the particle first estimates [[latex($c_{\infty}$)]] and [[latex($v_{\infty}$)]] using the host cell and calculates the bondi radius from the particles mass. It then calculates the surrounding mean density using [[latex($\bar{\rho}=\frac{\sum{\rho wdV}}{\sum{wdV}}$)]], and estimates [[latex($\rho_{\infty}$)]] using the solution to bondi accretion [[latex($\rho_{\infty}=\frac{\bar{\rho}}{\alpha(1.2\Delta x/r_{BH})}$)]]. It then calculates the accretion rate as |
| | 72 | |
| | 73 | [[latex($\dot{M}=4\pi\rho_{\infty}r_{BH}^2 \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}$)]] |
| | 74 | |
| | 75 | The accretion rate can be written as [[latex($\dot{M}=\frac{4\pi r_{BH}^2}{\alpha(1.2\Delta x/r_{BH})} \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}\frac{\sum{\rho wdV}}{\sum{wdV}}=\sum{d\rho dV}$)]]. The Krumohlz paper suggests the amount of accreted material from each cell should be proportional to the weight factor [[latex($d \rho \propto w$)]] but it makes more sense to make it proportional to the density times the weight factor [[latex($d \rho = A \rho w$)]] . If [[latex($d\rho \propto \rho w$)]] then [[latex($\sum{d\rho dV}= \sum{A \rho wdV} = A \sum{\rho wdV}$)]] which then gives [[latex($A=\frac{4\pi r_{BH}^2}{\alpha(1.2\Delta x/r_{BH})\sum{wdV}} \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}$)]] |
| | 76 | |
| | 77 | This makes implementation easier since each processor only needs to calculate A for local particles and then share them with other processors. This quantity is stored in {{{particle%AccretionRate}}} |
| | 78 | |
