Changes between Version 29 and Version 30 of u/erica/MusclHancock

Timestamp:

06/18/13 09:07:42 (11 years ago)

Author:

Baowei Liu

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 - \{1}{2} \triangle_ i $)]] and [[latex($ u_r = u_i(0) = u_i ^n + \{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%)]]