Changes between Version 4 and Version 5 of u/erica/angularmomentumoutflows

Timestamp:

08/01/16 16:23:25 (9 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/angularmomentumoutflows

@@ -8 +8 @@
 these represent the total *accreted* mass (m_acc), center of mass (COM_acc), momentum (p_acc) and angular momentum (L_acc) from all the cells within the accretion volume surrounding the sink particle.
 
-We use these quantities to (conservatively) update the particle's mass, COM, and so on, following:
+We use these quantities to update the particle's mass, COM, and so on, following (to maintain conservation between grid zones and particle):
 
 [[latex($m'=m + m_{acc}$)]] [[br]]
@@ -20 +20 @@
 [[latex($L'\neq L+L_{acc}$)]]
 
-as we might expect. This is because the position of the sink during the accretion event can change ever so slightly over the course of the accretion step, and thus, the angular momentum can change slightly as well (to maintain conservation of the com).. Thus, we instead write the angular momentum, post-accretion, as:
+which is somewhat unexpected. This is because the position of the sink can change ever so slightly over the course of the accretion step, and thus, the angular momentum can change slightly as well (to maintain conservation of the com).. Thus, we instead write the angular momentum, post-accretion, as:
 
 [[latex($L'=m'r'\times v'$)]]
+
+
+That is, the cross product of the updated particle's com and velocity. Given this may be a slight over (or under) shoot of the updated angular momentum, due to the fact that the particle may have lost (or gained) some angular momentum over the accretion time step, we create a new vector to absorb this difference, the 'spin' vector (S). We want the total angular momentum (L+S) to maintain conservation over the accretion time step. That is, we want:
+
+[[latex($L'+S'=(L+S)+L_{acc}$)]]
+
+and thus, we can define the spin vector using:
+
+[[latex($S'=S+L-L'+L_{acc}$)]]
+
+Thus, we can say the conserved accreted angular momentum per time step is:
+
+[[latex($S'-S=(L-L')+L_{acc}$)]]
+
+Notes: calling it 'spin' might be slightly confusing.