Changes between Version 29 and Version 30 of FluxLimitedDiffusion
 Timestamp:
 03/20/13 12:37:07 (12 years ago)
Legend:
 Unmodified
 Added
 Removed
 Modified

FluxLimitedDiffusion
v29 v30 78 78 79 79 80 For static diffusion, the terms in blue with v^2^/c can be dropped and the system can be split into the usual hydro update (black), radiative source terms (green) using time centered radiation energy, and a coupled implicit solve (red) for the radiation energy density and thermal energy density (ie temperature). If the opacity is independent of temperature and radiation energy density, then the implicit solve only involves the radiation energy density. Otherwise some sort of subcycling would be required.80 For static diffusion, the terms in blue with v^2^/c can be dropped and the system can be split into the usual hydro update (black), radiative source terms (green), and a coupled implicit solve (red) for the radiation energy density and thermal energy density (ie temperature). 81 81 82 82 … … 105 105 * Do ER,,0,,  Terms with grad E can be done without ghosting since EH did not change E. The del dot vE term needs time centered face centered velocities which can be stored during the hydro update. 106 106 107 == Implicit Discretization ==107 == Implicit Equation == 108 108 109 109 For now we will assume that [[latex(\kappa_{0P})]] and [[latex(\kappa_{0R})]] are constant over the implicit update and we will treat the energy as the total internal energy ignoring kinetic and magnetic contributions. In this case we can solve the radiation energy equations: … … 132 132 133 133 134 === 1D===134 === Implicit Discretization === 135 135 Which we can discretize for (1D) as 136 136 … … 163 163 [[latex(\frac{\Delta t}{\Delta x}\mathbf{F}^n_{i+1/2} = \alpha^n_{i+1/2} \left ( E^{*}_{i+1}  E^{*}_i \right ) )]] 164 164 165 === Time Discretization === 165 166 166 167 Now all the terms on the right hand side that are linear in E or e have been written as E^*^ or e^*^ because there are different ways to approximate E^*^ (e^*^). For Backward Euler we have