mirror of
https://git.gfz-potsdam.de/naaice/tug.git
synced 2025-12-13 17:38:23 +01:00
Update applicable equation
This commit is contained in:
parent
1fb3b85b65
commit
899e00bec1
@ -163,11 +163,17 @@ C_0^{j+1} & = C_0^{j} + \frac{\alpha \cdot \Delta t}{\Delta x^2} \cdot \left( C
|
||||
& = C_0^{j} + \frac{\alpha \cdot \Delta t}{\Delta x^2} \cdot \left( C^{j+1}_{1}- 3 C^{j+1}_{0} +2l \right)
|
||||
\end{align}
|
||||
|
||||
Which leads to the following term applicable to our approach:
|
||||
Now we define variable $s_x$ as following:
|
||||
|
||||
\begin{equation}
|
||||
s_x = \frac{\alpha \cdot \Delta t}{\Delta x^2}
|
||||
\end{equation}
|
||||
|
||||
Substituting with the new variable $s_x$ and reordering of terms leads to the equation applicable to our model:
|
||||
|
||||
#+NAME: eqn:5
|
||||
\begin{equation}\displaystyle
|
||||
-C^j_0} = \left[\frac{\alpha \cdot \Delta t}{\Delta x^2}\right] \cdot \left(C^{j+1}_1 + 2l \right) + \left[ -1 - 3 \cdot \frac{\alpha \cdot \Delta t}{\Delta x^2} \right] \cdot C^{j+1}_0
|
||||
-C^j_0} = s_x \cdot C^{j+1}_1 + (2s_x) \cdot l + (-1 - 3s_x) \cdot C^{j+1}_0
|
||||
\end{equation}
|
||||
|
||||
In case of constant right boundary, the finite difference of point
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user