Changes between Version 26 and Version 27 of u/bliu/pnfldiff

Timestamp:

08/15/18 16:55:16 (6 years ago)

Author:

Baowei Liu

Comment:

—

u/bliu/pnfldiff

@@ -59 +59 @@
 
 {{{
+
 Data has computational units of the density of neutral hydrogen, ionized hydrogen, ionization rate, and heating rate
 tau =sigmaH*nH+sigmad*nHII
 
 }}}
+
+== Discretization ==
+Discretize the equation of $n_{e}$ in the same way as [https://astrobear.pas.rochester.edu/trac/wiki/ThermalConduction Thermal Conduction]
+
+$\partial_{t}n_{e} +\partial_{i}(n_{e}u_{i})=I-r$
+
+Replace $n_{e}$ with $n_{e}^{*}$ where[[BR]]
+$n_{e}^{*}=(1-\Phi)n_{e}+\Phi n_{e}^{'}$[[BR]]
+and
+$\Phi=1$ for backward Euler, $\Phi=1/2$ for Crank Nicholson
+
+$\partial_{t}n_{e} +u_{i}\partial_{i}n_{e}^{*}+n_{e}^{*}\partial_{i}u_{i}=I-r$
+
+
+
 
 == Links and References ==