Scaling - Revision history

RosDeath at 16:55, 2 November 2007

2007-11-02T16:55:16Z

2007-11-02T16:54:47Z

2007-11-02T16:54:08Z

2007-11-02T16:53:25Z

2007-11-02T16:50:40Z

2007-11-02T16:48:46Z

2007-11-02T16:41:20Z

2007-11-02T16:40:40Z

2007-11-02T16:38:47Z

2007-11-02T16:36:56Z

← Older revision		Revision as of 16:54, 2 November 2007
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−	~~[[Skadia]]~~
−
	In this section, subscript ''0'' is used to denote scales; primed symbols denote scaled quantities; unadorned symbols denote unscaled quantities; and finite difference approximations are denoted using <math>\Delta\,</math>.		In this section, subscript ''0'' is used to denote scales; primed symbols denote scaled quantities; unadorned symbols denote unscaled quantities; and finite difference approximations are denoted using <math>\Delta\,</math>.

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	</math>		</math>
		+
		+	Back to [[Skadia]]

← Older revision		Revision as of 16:54, 2 November 2007
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		+	[[Skadia]]
		+
	In this section, subscript ''0'' is used to denote scales; primed symbols denote scaled quantities; unadorned symbols denote unscaled quantities; and finite difference approximations are denoted using <math>\Delta\,</math>.		In this section, subscript ''0'' is used to denote scales; primed symbols denote scaled quantities; unadorned symbols denote unscaled quantities; and finite difference approximations are denoted using <math>\Delta\,</math>.

@@ Line 39: / Line 39: @@
-Note that ''diff'' is not simply the scaled diffusivity but carries the appropriate time and grid steps (final bracketed quantity).  To find ice flux,
+Note that ''diff'' is not simply the scaled diffusivity but carries the appropriate time and grid steps (final bracketed quantity).  To find the ice flux,
 <math>
@@ Line 47: / Line 47: @@
-however, in the code, need to remember to reset grid steps so,
+however, in the code, we need to remember to reset the grid steps so,
 <math>
@@ Line 55: / Line 55: @@
+Finally, we need to look at the convergence term.  In this case, nothing needs to be done because the various grid steps are needed however some averaging between grids is required,
-Finally, we need to look at the convergence term.  In this case, nothing needs to be done because the various grid steps are needed however some averaging between grids is required
+</math>

@@ Line 50: / Line 50: @@
 <math>
-Q' = - diff w' \frac{\Delta\, s'} {\Delta\,x'} \left [\frac{\left (\Delta\,x'\right )^2}{Delta\,t'}\right ]
+Q' = - diff w' \frac{\Delta\, s'} {\Delta\,x'} \left [\frac{\left (\Delta\,x'\right )^2}{\Delta\,t'}\right ] = - diff w'\Delta\, s'\left [\frac{\Delta\,x'}{\Delta\,t'}\right ]
-</math>
+</math>.

← Older revision		Revision as of 16:48, 2 November 2007
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−	however, in the code, need to remember to reset grid steps	+	however, in the code, need to remember to reset grid steps so,
		+
		+	<math>
		+	Q' = - diff w' \frac{\Delta\, s'} {\Delta\,x'} \left [\frac{\left (\Delta\,x'\right )^2}{Delta\,t'}\right ]
		+
		+	</math>
		+



	Finally, we need to look at the convergence term. In this case, nothing needs to be done because the various grid steps are needed however some averaging between grids is required		Finally, we need to look at the convergence term. In this case, nothing needs to be done because the various grid steps are needed however some averaging between grids is required

@@ Line 42: / Line 42: @@
 <math>
-Q' = - D'w' \frac{\Delta\, s'} {\Delta\,x'\right ]
+Q' = - D'w' \frac{\Delta\, s'} {\Delta\,x'}
 </math>

@@ Line 34: / Line 34: @@
 <math>
-diff = - \frac{2fA}{n+2} (\rho\,g)^n \left ( \frac{\sum H}{2} \right ) ^{n+2} \left | \frac{\Delta s}{\Delta x} \right |^{n-1}\left [\frac{H_{0}^{2n+1}}{X_{0} ^{n+1} D_{0}}\right ]\left [\frac{\Delta\, t} ^{n+1} D_{0}}\right ]
+diff = - \frac{2fA}{n+2} (\rho\,g)^n \left ( \frac{\sum H}{2} \right ) ^{n+2} \left | \frac{\Delta\, s}{\Delta\, x} \right |^{n-1}\left [\frac{H_{0}^{2n+1}}{X_{0} ^{n+1} D_{0}}\right ]\left [\frac{\Delta\, t} {\left (\Delta\,x\right )^2}\right ]
 </math>