Changes between Version 3 and Version 4 of u/adebrech/Papers

Timestamp:

12/06/16 16:08:07 (8 years ago)

Author:

adebrech

Comment:

—

u/adebrech/Papers

@@ -2 +2 @@
 
 [attachment:'Schneiter ea 2016 PhotIon.pdf' Schneiter et al.] calculate effects of radiative transfer and photoionization, but do not launch the wind this way. [attachment:'Murry-Clay ea 2009 AtmoEscHJ.pdf' Murray-Clay et al.] calculate 1D wind from UV flux. [attachment:'Tripathi ea 2015 HJ Blowoff.pdf' Tripathi et al.] calculate multidimensional wind due to heating from UV flux. [attachment:Krumholz_2007_ApJ_671_518.pdf Krumholz, Stone, and Gardiner] present the simulation method used by Tripathi et al in the Athena code.
+
+Summary of Krumholz, Stone, Gardiner: No assumption of equilibrium (thermal or ionization). Usual MHD equations:
+{{{
+#!latex
+$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho v) = 0$
+
+$\frac{\partial}{\partial t}(\rho v) + \nabla \cdot (\rho v v - B B) + \nabla P^* = 0$
+
+$\frac{\partial B}{\partial t} + \nabla \cdot (vB - Bv) = 0$
+
+$\frac{\partial E}{\partial t} + \nabla \cdot [(E+P^*)v-B(B \cdot v)] = \mathcal G - \mathcal L$
+
+$\frac{\partial \rho_n}{\partial t} + \nabla \cdot (\rho_n v) = \mathcal R - \mathcal I$
+}}}
+
+Still need to specify rates of radiative processes.
+
+Algorithm:
+
+q vector of information now includes neutral densities: 
+
+$\vec q^n = \begin{pmatrix} \rho^n \\ \vec p^n \\ \vec B^n \\ E^n \\ \rho^n_n \end{pmatrix}$
+
+Flow control diagram:
+
+[[Image(control_flow.png)]]
+
+In order to update radiation, start by calculating cells through which rays from each source pass - start with 12, but may split into 4 child rays at any time (ref Abel and Wandelt 2002). Need length of rays that intersect each cell for calculating absorbed flux (usual exponential dependence on optical depth, given by number densities). Similar calculations for photoionization and photoionization heating - calculation ends at edge of domain or when only a small fraction of the photons are left. Sum heating and photoionization for every ray which passes through a given cell. Since collisional ionization, recombination, and optically thin heating and cooling are local effects, just calculate these for current state of fluid. Calculate time step from relative size of changes, then change in q is:
+
+$\Delta q = \Delta t \begin{pmatrix} 0 \\ \vec 0 \\ \vec 0 \\ \mathcal G - \mathcal L \\ \mathcal R - \mathcal I \end{pmatrix}$
+
+Iterate until particular conditions (relating to time step or change in energy) are met, at which point feed to conservative MHD update.
 
 = [http://arxiv.org/pdf/1206.5003v3.pdf Tremblin & Chiang], Computational Charge Exchange =