Changes between Version 121 and Version 122 of FluxLimitedDiffusion
- Timestamp:
- 03/30/13 22:41:15 (12 years ago)
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FluxLimitedDiffusion
v121 v122 401 401 so that the first equation can be written as 402 402 403 [[latex(\frac{\partial e}{\partial t} = f \left ( e_0 \right ) + \frac{\partial f}{\partial e} \left ( e - e_0 \right ) )]]403 [[latex(\frac{\partial e}{\partial t} = f \left ( e_0 \right ) + g \left ( E,\nabla E \right ) + \frac{\partial f}{\partial e} \left ( e - e_0 \right ) )]] 404 404 405 405 and then discretized as 406 406 407 [[latex(e^{n+1}_i-e^{n}_i = \frac{\Delta t}{\Delta x} \left ( f \left ( e _n \right ) + g \left ( e_n,E^*,\nabla E^* \right ) \right ) + \left ( \left ( \bar{\psi} - 1 \right ) \phi \right ) e_n + \psi \phi e^{n+1}_i]]407 [[latex(e^{n+1}_i-e^{n}_i = \frac{\Delta t}{\Delta x} \left ( f \left ( e^i_n \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) + \left ( \left ( \bar{\psi} - 1 \right ) \phi \right ) e^n_i + \psi \phi e^{n+1}_i) ]] 408 408 409 409 which can be solved for [[latex(e^{n+1} = \frac{1}{1-\psi \phi} \left ( \left ( \bar{\psi} - 1 \right ) \phi e^n_i + f \left ( e^n_i \right ) + g \left ( e^n_i,E^*,\nabla E^* \right ) \right ) )]]
