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Next: Running the full code Up: Coupled neutronics thermal-hydraulics model Previous: Evaluating the nuclear cross Contents Index

Solution of the coupled model

With the interface in place we can move to a description of the solution algorithm for the coupled model. A flow chart of the algorithm we use is depicted in Figure 13.2. In every iteration we check if certain accuracy criteria are fulfilled. All five accuracy criteria are of the following form

$\begin{displaymath} E^{(k)} < \varepsilon \end{displaymath}$

(13.28)

where k denotes the iteration number, $\varepsilon$ is a user specified accuracy requirement and the error estimate, E^(k), is defined by

$\begin{displaymath} E^{(k)} \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scripts... ...ace{0.2ex}\underline{x}{}\hspace{0.15ex}^{(k-1)} \Vert _\infty \end{displaymath}$

(13.29)

where the vector $\hspace{0.2ex}\underline{x}{}\hspace{0.15ex}$ holds the calculated values of one of the dependent variables $\{\mbox{$<\!{\alpha}\!>$},\mbox{$<\!{x}\!>$},p,\overline{T}{}_f,q'\}$ at discrete z-values.

The accuracy requirements are by default

$\begin{eqnarray*} \varepsilon_\alpha &=& 1\cdot 10^{-3} \\ \varepsilon_x &=& ... ...\varepsilon_{T_f} &=& 10.0 {\mbox{ \mbox{${}^\circ\mbox{C}$}}} \end{eqnarray*}$

$\textstyle \parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

These default values can be altered by a factor which is input at the command line--see section 13.4.

$\begin{figure} % latex2html id marker 42253\rule{\textwidth}{0.2mm} \rule{0cm}... ...ce names in the parenthesis are {\em module} names (ie file names).}\end{figure}$

The typical iteration course for the described iterative solution algorithm is depicted in Figures 13.3 to 13.7. As we can see we obtain a linear convergence and surprisingly the error constant is very close to 0.3 for all the dependent variables!

In all the cases we have encountered it is the requirement on q' which is the limiting one.

$\begin{figure} % latex2html id marker 42439\rule{\textwidth}{0.2mm} \rule{0cm}... ...el_E}) for the linear heat generation rate (for one element), $q'$.}\end{figure}$

$\begin{figure} % latex2html id marker 42485\rule{\textwidth}{0.2mm} \rule{0cm}... ...led_model_E}) for the average fuel temperature, $\overline{T}{}_f$.}\end{figure}$

$\begin{figure} % latex2html id marker 42532\rule{\textwidth}{0.2mm} \rule{0cm}... ...ef{coupled_model_E}) for the core flow quality, \mbox{$<\!{x}\!>$}.}\end{figure}$

$\begin{figure} % latex2html id marker 42577\rule{\textwidth}{0.2mm} \rule{0cm}... ...pled_model_E}) for the core void fraction, \mbox{$<\!{\alpha}\!>$}.}\end{figure}$

$\begin{figure} % latex2html id marker 42622\rule{\textwidth}{0.2mm} \rule{0cm}... ...tect\ref{coupled_model_E}) for the core pressure distribution, $p$.}\end{figure}$

Next: Running the full code Up: Coupled neutronics thermal-hydraulics model Previous: Evaluating the nuclear cross Contents Index

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