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Test cases

Most of the tests are based on the general reactor geometry depicted in Figure 4.1. The idea and data for this reactor type is taken from [7, p. 56, 58]. These data enable us to perform tests using two energy groups, a fast and a thermal group, which constitute the simplest possible multi-group description.

In [7] the following elevation data is specified

$$\begin{eqnarray*} z_{\mbox{\protect\scriptsize c,bot}} &=& 40 \mbox{cm}\\ z_{... ...x{cm}\\ z_{\mbox{\protect\scriptsize top}} &=& 500 \mbox{cm} \end{eqnarray*}$$

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

and the quantity $z_{\mbox{\protect\scriptsize abs}}$ is chosen as appropriate.

The four different slabs have the following reactor physical data

.

Reflector and absorber:

$\overline{\Sigma}{}_f^1 = \overline{\Sigma}{}_f^2 = 0 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{1 \rightarrow 2} = 0.0048 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{2 \rightarrow 1} = 0 \mbox{cm}^{-1}$

$\overline{\Sigma}{}_a^{1} = 0 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_a^{2} = 0.0011 \mbox{cm}^{-1}$ $\overline{D}{}^1 = 1.1 \mbox{cm}$ $\overline{D}{}^2 = 0.8 \mbox{cm}$

.

Fuel and absorber:

$\overline{\Sigma}{}_f^1 = 0.00014 \mbox{$\mbox{cm}^{-1}$}$ $\overline{\Sigma}{}_f^2 = 0.0024 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{1 \rightarrow 2} = 0.0024 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{2 \rightarrow 1} = 0 \mbox{cm}^{-1}$

$\nu^1 = 2.5$ $\nu^2 = 2.4$

$\overline{\Sigma}{}_a^{1} = 0.00086 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_a^{2} = 0.0050 \mbox{cm}^{-1}$ $\overline{D}{}^1 = 1.4 \mbox{cm}$ $\overline{D}{}^2 = 1.1 \mbox{cm}$

.

Fuel:

$\overline{\Sigma}{}_f^1 = 0.00014 \mbox{$\mbox{cm}^{-1}$}$ $\overline{\Sigma}{}_f^2 = 0.0024 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{1 \rightarrow 2} = 0.0024 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{2 \rightarrow 1} = 0 \mbox{cm}^{-1}$

$\nu^1 = 2.5$ $\nu^2 = 2.4$

$\overline{\Sigma}{}_a^{1} = 0.00086 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_a^{2} = 0.0041 \mbox{cm}^{-1}$ $\overline{D}{}^1 = 1.4 \mbox{cm}$ $\overline{D}{}^2 = 1.1 \mbox{cm}$

.

Reflector:

$\overline{\Sigma}{}_f^1 = \overline{\Sigma}{}_f^2 = 0 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{1 \rightarrow 2} = 0.0048 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_s^{2 \rightarrow 1} = 0 \mbox{cm}^{-1}$

$\overline{\Sigma}{}_a^{1} = 0 \mbox{cm}^{-1}$ $\overline{\Sigma}{}_a^{2} = 0.0002 \mbox{cm}^{-1}$ $\overline{D}{}^1 = 1.1 \mbox{cm}$ $\overline{D}{}^2 = 0.8 \mbox{cm}$

Furthermore we assume that all neutrons are born in the fast energy group, ie we specify

$$\begin{eqnarray*} \chi^1 = 1.0 \\ \chi^2 = 0.0 \end{eqnarray*}$$

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

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