Changes between Version 133 and Version 134 of FluxLimitedDiffusion


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Timestamp:
03/31/13 10:26:09 (12 years ago)
Author:
Jonathan
Comment:

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  • FluxLimitedDiffusion

    v133 v134  
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    462 [[latex(g = \epsilon \left ( \psi E^{n+1}_i + \bar{\psi} E^n_i \right ) + \omega v^n_x \left ( \psi E^{n+1}_{i+1} - \psi E^{n+1}_{i-1} + \bar{\psi} E^n_{i+1}- \bar{\psi} E^n_{i-1} \right ) - \xi \left ( \psi E^{n+1}_i + \bar{\psi} E^{n}_i \right )]]
     462[[latex(g = \epsilon \left ( \psi E^{n+1}_i + \bar{\psi} E^n_i \right ) + \omega v^n_x \left ( \psi E^{n+1}_{i+1} - \psi E^{n+1}_{i-1} + \bar{\psi} E^n_{i+1}- \bar{\psi} E^n_{i-1} \right ) - \xi \left ( \psi E^{n+1}_i + \bar{\psi} E^{n}_i \right ) )]]
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    464464which along with the other terms gives
    465 
    466    [[latex(E^{n+1}_i-E^{n}_i = \left [ \alpha^n_{i+1/2} \left ( \psi E^{n}_{i+1} + \bar{\psi} E^{n+1}_{i+1}- \psi E^{n+1}_{i} - \psi E^n_{i} \right ) - \alpha^n_{i-1/2} \left ( \psi E^{n+1}_{i} + \bar{\psi} E^n_i - \psi E^{n+1}_{i-1} - \bar{\psi}E^{n}_{i-1} \right ) \right ] + \left [ \zeta^n_{i+1/2} \left ( \psi E^{n}_{i+1} + \bar{\psi} E^{n+1}_{i+1} + \psi E^{n+1}_{i} + \psi E^n_{i} \right ) - \zeta^n_{i-1/2} \left ( \psi E^{n+1}_{i} + \bar{\psi} E^n_i + \psi E^{n+1}_{i-1} + \bar{\psi}E^{n}_{i-1} \right ) \right ] - \frac{1}{1-\psi \phi} \left [ \epsilon \left ( \psi E^{n+1}_i + \bar{\psi} E^n_i \right ) - \omega v^n_x \left ( \psi E^{n+1}_{i+1} - \psi E^{n+1}_{i-1} + \bar{\psi} E^n_{i+1}- \bar{\psi} E^n_{i-1} \right ) + \xi \left ( \psi E^{n+1}_i + \bar{\psi} E^{n}_i \right ) \right ] )]]   
     465{{{
     466#!latex
     467\begin{eqnarray}
     468E^{n+1}_i-E^{n}_i = & \left [ \alpha^n_{i+1/2} \left ( \psi E^{n}_{i+1} + \bar{\psi} E^{n+1}_{i+1}- \psi E^{n+1}_{i} - \psi E^n_{i} \right ) - \alpha^n_{i-1/2} \left ( \psi  E^{n+1}_{i} + \bar{\psi} E^n_i - \psi E^{n+1}_{i-1} - \bar{\psi}E^{n}_{i-1} \right ) \right ] \\
     469 + & \left [ \zeta^n_{i+1/2} \left ( \psi E^{n}_{i+1} + \bar{\psi} E^{n+1}_{i+1} + \psi E^{n+1}_{i} + \psi E^n_{i} \right ) - \zeta^n_{i-1/2} \left ( \psi E^{n+1}_{i} + \bar{\psi} E^n_i + \psi E^{n+1}_{i-1} + \bar{\psi}E^{n}_{i-1} \right ) \right ] \\
     470- & \frac{1}{1-\psi \phi} \left [ \epsilon \left ( \psi E^{n+1}_i + \bar{\psi} E^n_i \right ) - \omega v^n_x \left ( \psi E^{n+1}_{i+1} - \psi E^{n+1}_{i-1} + \bar{\psi} E^n_{i+1}- \bar{\psi} E^n_{i-1} \right ) + \xi \left ( \psi E^{n+1}_i + \bar{\psi} E^{n}_i \right ) \right ] )]]   
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