Changes between Version 11 and Version 12 of u/johannjc/scratchpad4


Ignore:
Timestamp:
09/30/15 17:37:34 (9 years ago)
Author:
Jonathan
Comment:

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  • u/johannjc/scratchpad4

    v11 v12  
    9494
    9595$\alpha_{\pm i, \pm j} = \pm \pm \frac{E_{ij}\Delta t}{4 \Delta x^2}$
     96
     97
     98
     99Now in the limit where we ignore spatial derivatives in density and magnetic field orientation, we can throw away the C terms - and if we also assume backward Euler, we can set
     100
     101$\psi=1$
     102
     103$\phi' = \frac{-\lambda}{\lambda+1}$
     104
     105$E_{ij}=\kappa_\parallel n b_i b_j$
     106
     107
     108If we are using Crank-Nicholson, then
     109
     110$\psi=1/2$
     111
     112$\phi' = \frac{1-\lambda}{\lambda+1}$
     113
     114$E_{ij}=\frac{1}{2}\kappa_\parallel n b_i b_j$