Changes between Version 8 and Version 9 of SinkParticlesDevel

Timestamp:

02/09/12 14:52:43 (13 years ago)

Author:

Jonathan

Comment:

—

SinkParticlesDevel

@@ -73 +73 @@
 [[latex($\dot{M}=4\pi\rho_{\infty}r_{BH}^2 \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}$)]]
 
-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($A=\frac{4\pi r_{BH}^2}{\alpha(1.2\Delta x/r_{BH})\sum{wdV}} \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}$)]]
+The accretion rate can be written as [[latex($\dot{M}=\frac{4\pi r_{BH}^2}{\alpha(1.2\Delta x/r_{BH})} \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}\frac{\sum{\dot{\rho}  wdV}}{\sum{wdV}}=\frac{\sum{d\rho dV}}{\Delta t}$)]].  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($d \rho = A \rho w \Delta t$)]] .  If [[latex($d\rho \propto \rho w$)]] then [[latex($\sum{d\rho dV}= \sum{A \rho wdV \Delta t} = A \Delta t \sum{\rho wdV}$)]] which then gives [[latex($A=\frac{4\pi r_{BH}^2}{\alpha(1.2\Delta x/r_{BH})\sum{wdV}} \left ( \lambda^2 c_{\infty}^2 +v_{\infty}^2 \right )^{1/2}$)]]
 
 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}}}