Changes between Version 59 and Version 60 of FluxLimitedDiffusion
 Timestamp:
 03/24/13 20:44:44 (12 years ago)
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FluxLimitedDiffusion
v59 v60 3 3 Most of what follows is taken from [http://adsabs.harvard.edu/abs/2007ApJ...667..626K Krumholz et al. 2007] 4 4 5 [[CollapsibleStart(Physics of Flux Limited Diffusion)]]6 5 = Physics of Radiation Transfer = 7 6 … … 11 10  [[latex(\tau >> 1 \mbox{, } \beta \tau >> 1)]]  dynamic diffusion limit  12 11 12 [[CollapsibleStart(Equations of Radiation Hydrodynamics)]] 13 13 == Equations of Radiation Hydrodynamics == 14 14 … … 32 32 If we had a closure relation for the radiation pressure then we could solve this system. For gas particles, collisions tend to produce a Boltzmann Distribution which is isotropic and gives a pressure tensor that is a multiple of the identity tensor. Photons do not "collide" with each other and they all have the same velocity 'c' but in various directions. If the field were isotropic than [[latex(P^{ij}=\delta^{ij} 1/3 E)]] but in general [[latex(P^{ij}=f^{ij} E)]] where 'f' is the Eddington Tensor. 33 33 34 [[CollapsibleEnd()]] 35 [[CollapsibleStart(Simplifiying assumptions)]] 34 36 == Simplifying assumptions == 35 37 * If the flux spectrum of the radiation is directionindependent then we can write the radiation fourforce density in terms of the moments of the radiation field … … 48 50 which implies that [[latex(\kappa_{0F}^{1}=\kappa_{0R}^{1}=\frac{\int_0^\infty d \nu_0 \kappa_0(\nu_0)^{1}[\partial B(\nu_0,T_0)/\partial T_0]}{\int_0^\infty d \nu_0 [\partial B(\nu_0, T_0)/\partial T_0]})]] 49 51 * In the optically thin regime, [[latex(\mathbf{F}_0(\nu_0) \rightarrow cE_0(\nu_0))]] so we would have [[latex(\kappa_{0F}=\kappa_{0E})]] however assuming a blackbody temperature in the optically thin limit may be any more accurate than assuming that [[latex(\kappa_{0F}=\kappa_{0R})]] 50 52 [[CollapsibleEnd()]] 53 54 [[CollapsibleStart(Flux limited diffusion)]] 51 55 == Flux limited diffusion == 52 56 … … 73 77 74 78 [[CollapsibleEnd()]] 75 [[CollapsibleStart(Numerics of Flux Limited Diffusion)]] 79 76 80 = Numerics of Flux Limited Diffusion = 77 81 … … 85 89 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). 86 90 87 91 [[CollapsibleStart(Operator Splitting)]] 88 92 == Operator splitting == 89 93 Krumholz et al. perform Implicit Radiative, Explicit Hydro, Explicit Radiative … … 109 113 * Do second EH,,0,, 110 114 * 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. 115 [[CollapsibleEnd()]] 111 116 112 117 [[CollapsibleStart(Explcit Update)]] … … 302 307 303 308 [[CollapsibleEnd()]] 304 [[CollapsibleEnd()]]