Changes between Version 50 and Version 51 of u/bliu/pnfldiff


Ignore:
Timestamp:
09/04/18 16:53:59 (6 years ago)
Author:
Baowei Liu
Comment:

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  • u/bliu/pnfldiff

    v50 v51  
    5353
    5454$I^{n+1}_{i}+\Delta t \phi (D_{i}^{n+1}(I,n_{H})+L_{I,i}^{n+1}(I,n_{H}))=I^{n}_{i}+\Delta t (\phi -1) (D^{n}_{i}(I,n_{H})+L_{I,i}^{n}(I,n_{H})$
     55
    5556$n_{H,i}^{n+1}+\Delta t\phi L^{n+1}_{n_{H},i}(I, n_{H})=n_{H,i}^{n}+\Delta t(\phi -1) L^{n}_{n_{H},i}(I,n_{H})$
     57
    5658$e_{i}^{n+1}+\Delta t\phi L^{n+1}_{e,i}(I,n_{H})=e_{i}^{n}+\Delta t (\phi -1) L^{n}_{e,i}(I,n_{H})$
    5759
     60where the diffusion operator
     61
     62$D(I,n_{H})=\nabla \cdot(\frac{c\lambda}{\sigma n_{H}}\nabla I)$
     63
     64and local reaction operators
     65
     66$L_{I}(I,n_{H})=-\sigma n_{H} I$
     67
     68$L_{n_{H}}(I,n_{H})=-\sigma n_{H}c I +\alpha n_{e} n_{H}$
     69
     70$L_{e}(I,n_{H})=\Lambda\sigma n_{H} c I$
     71
     72and
     73
    5874$\phi=1$ for backward Euler method and $\phi=1/2$ for Crank-Nicolson method.
     75
     76
     77Let
     78
     79 $ U=(I, n_{H}, e)^{T}$
     80
     81 
    5982
    6083