Changes between Version 50 and Version 51 of u/bliu/pnfldiff
- Timestamp:
- 09/04/18 16:53:59 (6 years ago)
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u/bliu/pnfldiff
v50 v51 53 53 54 54 $I^{n+1}_{i}+\Delta t \phi (D_{i}^{n+1}(I,n_{H})+L_{I,i}^{n+1}(I,n_{H}))=I^{n}_{i}+\Delta t (\phi -1) (D^{n}_{i}(I,n_{H})+L_{I,i}^{n}(I,n_{H})$ 55 55 56 $n_{H,i}^{n+1}+\Delta t\phi L^{n+1}_{n_{H},i}(I, n_{H})=n_{H,i}^{n}+\Delta t(\phi -1) L^{n}_{n_{H},i}(I,n_{H})$ 57 56 58 $e_{i}^{n+1}+\Delta t\phi L^{n+1}_{e,i}(I,n_{H})=e_{i}^{n}+\Delta t (\phi -1) L^{n}_{e,i}(I,n_{H})$ 57 59 60 where the diffusion operator 61 62 $D(I,n_{H})=\nabla \cdot(\frac{c\lambda}{\sigma n_{H}}\nabla I)$ 63 64 and 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 72 and 73 58 74 $\phi=1$ for backward Euler method and $\phi=1/2$ for Crank-Nicolson method. 75 76 77 Let 78 79 $ U=(I, n_{H}, e)^{T}$ 80 81 59 82 60 83