Changes between Version 144 and Version 145 of FluxLimitedDiffusion


Ignore:
Timestamp:
03/31/13 15:47:28 (12 years ago)
Author:
Jonathan
Comment:

—

Legend:

Unmodified
Added
Removed
Modified

  • FluxLimitedDiffusion

    v144 v145  
    533533#!latex
    534534\begin{eqnarray}
    535  & \left ( 1 + \psi \left ( \alpha^n_{i+1/2} +  \alpha^n_{i-1/2} - \zeta^n_{i+1/2} v^n_{x,i+1/2} + zeta^n_{i-1/2} v^n_{x,i-1/2} + \frac{\epsilon + \xi}{1-\psi \phi} \right ) \right ) E^{n+1}_i   \\
    536 + & \left ( \psi \left (  -alpha^n_{i+1/2} - \zeta^n_{i+1/2} v^n_{x,i+1/2} - \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n+1}_{i+1}  \\
    537 + & \left ( \psi \left (  -alpha^n_{i-1/2} + \zeta^n_{i-1/2} v^n_{x,i-1/2} + \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n+1}_{i-1}  \\
    538 = & \left ( 1 + \bar{\psi} \left ( -\alpha^n_{i+1/2} - \alpha^n_{i-1/2} + \zeta^n_{i+1/2} v^n_{x,i+1/2} -  \zeta^n_{i-1/2} v^n_{x,i-1/2} - \frac{\epsilon + \xi}{1-\psi \phi} \right ) \right ) E^{n}_i  \\
    539 + & \left ( \bar{\psi} \left (  alpha^n_{i+1/2} + \zeta^n_{i+1/2} v^n_{x,i+1/2} + \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n}_{i+1}  \\
    540 + & \left ( \bar{\psi} \left (  alpha^n_{i-1/2} - \zeta^n_{i-1/2} v^n_{x,i-1/2} - \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n}_{i-1}  \\
     535 & \left ( 1 + \psi \left ( \alpha^n_{i+1/2} +  \alpha^n_{i-1/2} - \zeta^n_{i+1/2} v^n_{x,i+1/2} + \zeta^n_{i-1/2} v^n_{x,i-1/2} + \frac{\epsilon - \xi}{1-\psi \phi} \right ) \right ) E^{n+1}_i   \\
     536- & \left ( \psi \left (  \alpha^n_{i+1/2} + \zeta^n_{i+1/2} v^n_{x,i+1/2} - \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n+1}_{i+1}  \\
     537- & \left ( \psi \left (  \alpha^n_{i-1/2} - \zeta^n_{i-1/2} v^n_{x,i-1/2} + \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n+1}_{i-1}  \\
     538= & \left ( 1 - \bar{\psi} \left ( \alpha^n_{i+1/2} + \alpha^n_{i-1/2} - \zeta^n_{i+1/2} v^n_{x,i+1/2} +  \zeta^n_{i-1/2} v^n_{x,i-1/2} + \frac{\epsilon - \xi}{1-\psi \phi} \right ) \right ) E^{n}_i  \\
     539+ & \left ( \bar{\psi} \left (  alpha^n_{i+1/2} + \zeta^n_{i+1/2} v^n_{x,i+1/2} - \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n}_{i+1}  \\
     540+ & \left ( \bar{\psi} \left (  alpha^n_{i-1/2} - \zeta^n_{i-1/2} v^n_{x,i-1/2} + \frac{\omega v^n_x}{1-\psi \phi} \right ) \right ) E^{n}_{i-1}  \\
    541541- & \frac{\theta}{1-\psi \phi}   \\
    542542\end{eqnarray}