Changes between Version 4 and Version 5 of doc/tec/bc

Timestamp:

Apr 5, 2016 1:38:57 PM (9 years ago)

Author:

maronga

Comment:

--

doc/tec/bc

@@ -162 +162 @@
 \end{equation*}
 \begin{equation*}
-Ri_\mathrm{b,Ne} = - \dfrac{g z_\mathrm{MO} \overline{v^{\prime\prime} \theta_\mathrm{v}^{\prime\prime}}_0}{\kappa^2 u_\mathrm{h}^3 \theta_v}\;,
+Ri_\mathrm{b,Ne} = - \dfrac{g z_\mathrm{MO} \overline{v^{\prime\prime} \theta_\mathrm{v}^{\prime\prime}}_0}{\kappa^2 u_\mathrm{h}^3 \theta_v}\;.
 \end{equation*}
 }}}
+In case of {{{most_method = 'newton'}}}, the above equations are solved for ''L'' by Newton iteration, i.e. finding the root of the equation
+{{{
+#!Latex
+\begin{equation*}
+f = Ri_\mathrm{b} - \dfrac{z}{L} \cdot \dfrac{[\ldots]^x}{[\ldots]^y}
+\end{equation*}
+}}}
+where ''x'' and ''y'' depend on the chosen boundary conditions (see above). The solution is given by iteration of
+{{{
+#!Latex
+\begin{equation*}
+L^{t+1} = L^t - \dfrac{f(L^t)}{f'(L^t)}
+\end{equation*}
+}}}
+with
+#!Latex
+\begin{equation*}
+f'(L) = \dfrac{df}{dL}
+\end{equation*}
+}}}