Changes between Version 20 and Version 21 of u/johannjc/scratchpad


Ignore:
Timestamp:
01/10/14 16:31:34 (11 years ago)
Author:
Jonathan
Comment:

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  • u/johannjc/scratchpad

    v20 v21  
    113113}}}
    114114
    115 in the limit of [[latex($T \rightarrow 0$)]] with a flux from the left...
     115== Limiting case ==
    116116
    117 are equation becomes [[latex($\rho_i c_v T_i^{j+1} = \rho_i c_v T_i^j + \frac{\Delta t}{\Delta x} Q \delta_i^1$)]]
     117In the limit of [[latex($T \rightarrow 0$)]] with a flux from the left boundary:
     118
     119our equation becomes [[latex($\rho_i c_v T_i^{j+1} = \rho_i c_v T_i^j + \frac{\Delta t}{\Delta x} Q \delta_i^1$)]]
    118120
    119121and the total energy [[latex($E^{j+1}=\rho c_v \sum T_i^{j+1} \Delta x = E^{j} + \Delta t Q$)]]