Changes between Version 26 and Version 27 of u/bliu/pnfldiff
 Timestamp:
 08/15/18 16:55:16 (6 years ago)
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u/bliu/pnfldiff
v26 v27 59 59 60 60 {{{ 61 61 62 Data has computational units of the density of neutral hydrogen, ionized hydrogen, ionization rate, and heating rate 62 63 tau =sigmaH*nH+sigmad*nHII 63 64 64 65 }}} 66 67 == Discretization == 68 Discretize the equation of $n_{e}$ in the same way as [https://astrobear.pas.rochester.edu/trac/wiki/ThermalConduction Thermal Conduction] 69 70 $\partial_{t}n_{e} +\partial_{i}(n_{e}u_{i})=Ir$ 71 72 Replace $n_{e}$ with $n_{e}^{*}$ where[[BR]] 73 $n_{e}^{*}=(1\Phi)n_{e}+\Phi n_{e}^{'}$[[BR]] 74 and 75 $\Phi=1$ for backward Euler, $\Phi=1/2$ for Crank Nicholson 76 77 $\partial_{t}n_{e} +u_{i}\partial_{i}n_{e}^{*}+n_{e}^{*}\partial_{i}u_{i}=Ir$ 78 79 80 65 81 66 82 == Links and References ==