Numerical Results II

In this section we provide results for two dimensional XY geometry cases in one and two energy groups. Test problems 1 and 2 are for one energy group cases. Configurations for problems 1 and 2 are specified in figure 2.9. The first test problem is a 8 cm by 8 cm square region with homogeneous cross sections of $\Sigma_t$=1.0 cm^-1, $\bar\nu\Sigma_f$ = 0.11 cm^-1, and $\Sigma_s$ = 0.9 cm^-1; and with vacuum boundary conditions on all sides. The second test problem is an 8 cm by 8 cm square region with an interior 4 cm by 4 cm square region and vacuum boundary conditions on all sides. The inner square region has cross sections of $\Sigma_t$=1.0 cm^-1, $\bar\nu\Sigma_f$ = 0.21 cm^-1, and
$\Sigma_s$ = 0.9 cm^-1, and the rest of the system has cross sections of $\Sigma_t$=1.0 cm^-1,
$\bar\nu\Sigma_f$ = 0.11 cm^-1, and $\Sigma_s$ = 0.9 cm^-1. Test problems 1 and 2 were simulated for 120 active batches, 40 inactive batches and with 4000 neutrons per batch. Test problem 3 is a homogeneous square region with vacuum boundary conditions on all sides and two energy groups. Cross sections for test problem 3 and the configuration is shown in figure 2.10. Test problem 3 was simulated with 120 active batches, 40 inactive batches and 2500 neutrons per batch. Results for the two dimensional problems are shown in table 2.3. The reference TWODANT results are for S₁₆ quadrature sets and with inner and outer iteration convergence criteria of 10^-12.

 

1|cProblem 1|c|TWODANT 1|c|Source iteration 1c|Fission matrix

$${\pm} {\pm}$$ Test Problem 1 0.640792

$${\pm} {\pm}$$ Test Problem 2 1.004494

$${\pm} {\pm}$$ Test Problem 3 1.489619

 

Figure: Configuration of Two-Dimensional One Energy Group Problems.

 

Figure: Configuration of Two-Dimensional Two Energy Group Problem.