Changes between Version 31 and Version 32 of u/erica/MusclHancock

Timestamp:

06/18/13 11:50:36 (11 years ago)

Author:

Erica Kaminski

Comment:

—

u/erica/MusclHancock

@@ -36 +36 @@
   [[latex($u_i(x) = u_i^n + (x - x_i) \frac{\triangle _i }{\triangle x}, x \in [0, \triangle x]$)]]
 
-  where [[latex($ \triangle _i $)]] is called a 'slope' for [[latex($ u_i ^n $)]], that is, for the elements of [[latex($ \vec{u} $)]] in cell i on the nth time level. Using a linear function produces 2 extreme values of each cell, one on the left and on the right: [[latex($ u_l $)]] and [[latex($ u_r $)]], respectively. These values are crucial in the MH scheme and their role will be presented shortly. Their values are given by [[latex($ u_l = u_i(0) = u_i ^n - \frac{1}{2} \triangle_ i $)]] and [[latex($ u_r = u_i(0) = u_i ^n + \frac{1}{2} \triangle_ i $)]]. A schematic of the situation is as follows:
+  where 
+
+  [[latex($ \triangle _i $)]] 
+
+  is called a 'slope' for 
+  
+  [[latex($ u_i ^n $)]],
+  
+  that is, for the elements of 
+  [[latex($ \vec{u} $)]] 
+  in cell i on the nth time level. Using a linear function produces 2 extreme values of each cell, one on the left and on the right: 
+
+  [[latex($ u_l $)]] 
+  and 
+
+  [[latex($ u_r $)]], 
+  respectively. These values are crucial in the MH scheme and their role will be presented shortly. Their values are given by 
+  [[latex($ u_l = u_i(0) = u_i ^n - \frac{1}{2} \triangle_ i $)]]
+  and
+   [[latex($ u_r = u_i(0) = u_i ^n + \frac{1}{2} \triangle_ i $)]]
+   A schematic of the situation is as follows:
 
   [[Image(MusclReconstruction.png, 35%)]]
@@ -44 +64 @@
   [[latex($ \frac{\partial \vec{u}}{\partial t} + \frac{\partial f(\vec{u})}{\partial x} = 0 $)]]
 
-  [[latex($ u(x,0) = { \frac{u_i^r, x\<0}{u_{i+1}^l, x\>0} $)]]
+  [[latex($ u(x,0) =  \frac{u_i^r, x\<0}{u_{i+1}^l, x\>0} $)]]
 
  where 0 is the local origin, i.e. any given intercell boundary.