Changes between Version 185 and Version 186 of FluxLimitedDiffusion


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Timestamp:
04/03/13 17:27:58 (12 years ago)
Author:
Jonathan
Comment:

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  • FluxLimitedDiffusion

    v185 v186  
    611611#!latex
    612612\begin{eqnarray}
    613  & \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   \\
    614 - & \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}  \\
    615 - & \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}  \\
    616 = & \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  \\
    617 + & \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}  \\
    618 + & \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}  \\
    619 - & \frac{\theta}{1-\psi \phi}   \\
     613 & \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   \\
     614- & \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}  \\
     615- & \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}  \\
     616= & \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  \\
     617+ & \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}  \\
     618+ & \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}  \\
     619+ & \frac{\theta}{1+\psi \phi}   \\
    620620\end{eqnarray}
    621621}}}