Changes between Version 34 and Version 35 of FluxLimitedDiffusion
 Timestamp:
 03/20/13 14:19:14 (12 years ago)
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FluxLimitedDiffusion
v34 v35 5 5 = Physics of Radiation Transfer = 6 6 7  [[latex(\tau = l \kappa=\frac{l}{\lambda_p})]]  8  [[latex(\beta = \frac{u}{c})]]  7  [[latex(\tau = l \kappa=\frac{l}{\lambda_p})]]  [[latex(\beta = \frac{u}{c})]]  9 8  [[latex(\tau << 1 )]]  streaming limit  10 9  [[latex(\tau >> 1 \mbox{, } \beta \tau << 1)]]  static diffusion limit  … … 19 18  [[latex(\frac{1}{c^2} \frac{\partial \mathbf{F}}{\partial t} + \nabla \cdot \mathbf{P} = \mathbf{G})]]  20 19 21 where 20 where the moments of the specific intensity are defined as 22 21 23 22  [[latex(cE=\int_0^\infty d \nu \int d \Omega I(\mathbf{n}, \nu))]]  … … 25 24  [[latex(c\mathbf{P}=\int_0^\infty d \nu \int d \Omega \mathbf{nn} I(\mathbf{n}, \nu))]]  26 25 27 and 26 and the radiation 4momentum is given by 28 27 29 28  [[latex(cG^0 = \int_0^\infty d \nu \int d \Omega \left [ \kappa (\mathbf{n}, v)I(\mathbf{n}, \nu)\eta(\mathbf{n},v) \right ])]]  30 29  [[latex(c\mathbf{G} = \int_0^\infty d \nu \int d \Omega \left [ \kappa (\mathbf{n}, v)I(\mathbf{n}, \nu)\eta(\mathbf{n},v) \right ] \mathbf{n})]]  31 30 31 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. 32 32 33 33 == Simplifying assumptions ==