Changeset 7124 for anuga_core/documentation/user_manual/anuga_user_manual.tex

Timestamp:

May 28, 2009, 11:03:22 AM (14 years ago)

Author:

ole

Message:

Updated manual in regard to flux limiter

File:

• anuga_core/documentation/user_manual/anuga_user_manual.tex (modified) (1 diff)

anuga_core/documentation/user_manual/anuga_user_manual.tex

@@ -3352 +3352 @@
 \]
 In general, for multiples of the minimal depth $N H_0$ one obtains
-\[
+\begin{equation}
   \left[ \frac{\mu}{h + h_0/h} \right]_{h = N H_0} =
-  \frac{\mu}{H_0 (1 + 1/N^2)}
-\]
+  \frac{\mu}{N H_0 + H_0/N} =  
+  \frac{\mu}{h (1 + 1/N^2)}
+  \label{eq:flux limit multiple}
+\end{equation}
 which converges quadratically to the true value with the multiple N.
+
+Although this equation can be used for any depth, we have restricted its use to depths less than $10 * H_0$ (or 1 cm) to computational resources. 
+According to Equation \ref{eq:flux limit multiple} this cutoff   
+affects the calculated velocity by less than 1 \%.   
 
 %The developed numerical model has been applied to several test cases