Changes between Version 165 and Version 166 of FluxLimitedDiffusion

Timestamp:

04/03/13 11:36:14 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -388 +388 @@
 
   [[latex(\frac{\partial }{\partial t} \left ( \rho \mathbf{v} \right ) + \nabla \cdot \left ( \rho \mathbf{vv} \right ) = -\nabla P\color{green}{-\lambda \nabla E})]]   
-  [[latex(\frac{\partial e}{\partial t}  + \nabla \cdot \left [ \left ( e + P \right ) \mathbf{v} \right ] = \color{red}{-\kappa_{0P}(4 \pi B-cE)} \color{orange}{+\lambda \left ( 2 \frac{\kappa_{0P}}{\kappa_{0R}}-1 \right ) \mathbf{v} \cdot \nabla E} \color{orange}{-\frac{3-R_2}{2}\kappa_{0P}\frac{v^2}{c}E})]]  
-  [[latex(\frac{\partial E}{\partial t}  \color{red}{ - \nabla \cdot \frac{c\lambda}{\kappa_{0R}} \nabla E} = \color{red}{\kappa_{0P} (4 \pi B-cE)} \color{orange}{-\lambda \left(2\frac{\kappa_{0P}}{\kappa_{0R}}-1 \right )\mathbf{v}\cdot \nabla E} \color{orange}{-\nabla \cdot \left ( \frac{3-R_2}{2}\mathbf{v}E \right )} \color{orange}{+\frac{3-R_2}{2}\kappa_{0P}\frac{v^2}{c}E}  )]]  
+  [[latex(\frac{\partial e}{\partial t}  + \nabla \cdot \left [ \left ( e + P \right ) \mathbf{v} \right ] = \color{red}{-\kappa_{0P}(4 \pi B-cE)} \color{red}{+\lambda \left ( 2 \frac{\kappa_{0P}}{\kappa_{0R}}-1 \right ) \mathbf{v} \cdot \nabla E} \color{red}{-\frac{3-R_2}{2}\kappa_{0P}\frac{v^2}{c}E})]]  
+  [[latex(\frac{\partial E}{\partial t}  \color{red}{ - \nabla \cdot \frac{c\lambda}{\kappa_{0R}} \nabla E} = \color{red}{\kappa_{0P} (4 \pi B-cE)} \color{red}{-\lambda \left(2\frac{\kappa_{0P}}{\kappa_{0R}}-1 \right )\mathbf{v}\cdot \nabla E} \color{red}{-\nabla \cdot \left ( \frac{3-R_2}{2}\mathbf{v}E \right )} \color{red}{+\frac{3-R_2}{2}\kappa_{0P}\frac{v^2}{c}E}  )]]  
 
 It is possible that with included the terms in orange in a semi-implicit method, the dynamic diffusion regime may be stable...  In any event, it costs very little to add all of the terms in orange to the implicit solve (using the old velocity).  Then the momentum update can be done explicitly - though using a time centered radiation field.