Changes between Version 6 and Version 7 of u/johannjc/scratchpad4

Timestamp:

09/30/15 17:03:58 (9 years ago)

Author:

Jonathan

Comment:

—

u/johannjc/scratchpad4

@@ -59 +59 @@
 we get expressions for
 
-$A = \frac{1}{\Delta t}$
-
 $B_j =  \frac{\kappa_\parallel \left ( \phi-\psi\lambda \right )}{\lambda+1} \partial_i n b_i b_j $
 
@@ -71 +69 @@
 We then need expressions for
 
-$ \partial_t T = A \left ( T'_0 - T_0 \right )$
+$ \partial_t T = \frac{ T'_0 - T_0}{\Delta t}$
 
 $ \partial_j T^{\lambda+1} = \frac{T^{\lambda+1}_{\hat{j}} - T^{\lambda+1}_{-\hat{j}}}{2 \Delta x}$
@@ -91 +89 @@
 $\alpha_{\pm j} = \pm C_jT^\lambda_{\pm \hat{j}} + \frac{E_{jj}}{\Delta x^2}T_{\pm \hat{j}}^\lambda$
 
-$\alpha_{\pm i \pm j} = \pm \pm \frac{E_{ij}}{4 \Delta x^2}T^\lambda_{\pm \hat{i} \pm \hat{j}}$
+$\alpha_{\pm i, \pm j} = \pm \pm \frac{E_{ij}}{4 \Delta x^2}T^\lambda_{\pm \hat{i} \pm \hat{j}}$
 
+$\beta = -\frac{T_0}{\Delta t} \pm \frac{B_j}{2 \Delta x} T^{\lambda+1}_{\pm \hat{j}} \pm \pm \frac{D_{ij}}{4 \Delta x^2} T^{lambda+1}_{\pm \hat{i} \pm \hat{j}}\left ( 1 - \delta_{ij} \right )  + \frac{D_{jj}}{\Delta x^2} T^{lambda+1}_{\pm \hat{j}} - 2 \frac{D_{jj}}{\Delta x^2}T^{\lambda+1}_0$