Changes between Version 19 and Version 20 of FluxLimitedDiffusion
 Timestamp:
 03/20/13 10:12:58 (12 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

FluxLimitedDiffusion
v19 v20 124 124 where 125 125 126 [[latex(\Gamma = \frac{ dT}{dE} = \frac{(\gamma1)}{n k_B})]]126 [[latex(\Gamma = \frac{\partial T}{\partial e} = \frac{(\gamma1)}{n k_B})]] 127 127 128 128 Then the system of equations becomes … … 134 134 === 1D === 135 135 Which we can discretize for (1D) as 136 137  [[latex(E^{n+1}_iE^{n}_i = \left [ \alpha^n_{i+1/2} \left ( E^{*}_{i+1}E^{*}_{i} \right )  \alpha^n_{i1/2} \left ( E^{*}_{i}E^{*}_{i1} \right ) \right ] + \epsilon^n_i \left ( \frac{4 \pi}{c} B \left ( T^n_i \right ) \left ( 1  4\Gamma \frac{e^n_i}{T^n_i} + 4\Gamma \frac{e^{*}_i}{T^n_i} \right ) E^{*}_i \right ) )]]  138  [[latex(e^{n+1}_ie^{n}_i =  \epsilon^n_i \left ( \frac{4 \pi}{c} B\left ( T^n_i \right ) \left ( 1  4\Gamma \frac{e^n_i}{T^n_i} + 4\Gamma \frac{e^{*}_i}{T^n_i} \right )  E^{*}_i \right ) )]]  139 140 141 142 136 143 137 144  [[latex(E^{n+1}_iE^{n}_i = \left [ \alpha^n_{i+1/2} \left ( E^{n+1}_{i+1}E^{n+1}_{i} \right )  \alpha^n_{i1/2} \left ( E^{n+1}_{i}E^{n+1}_{i1} \right ) \right ] + \epsilon^n_i \left ( \frac{4 \pi}{c} B(T^n_i)E^{n+1}_i \right ) )]] 