Changes between Version 29 and Version 30 of u/erica/MusclHancock
 Timestamp:
 06/18/13 09:07:42 (11 years ago)
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u/erica/MusclHancock
v29 v30 36 36 [[latex($u_i(x) = u_i^n + (x  x_i) \frac{\triangle _i }{\triangle x}, x \in [0, \triangle x]$)]] 37 37 38 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 $)]]. A schematic of the situation is as follows:38 where [[latex($ \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: 39 39 40 40 [[Image(MusclReconstruction.png, 35%)]]