Homework Problem #4As we have studied, deterministic methods require that the dimensions of space, energy, and direction be discretized as part of the numerical treatment. These decisions are made in the following way:
1. Energy: The user (you) picks the cross section library as part of the input. (We have been using the 56- group library.) In the output file, you can find the energy group boundaries in an output array just below the words "neutron group parameters".
2. Direction: The calculation requires that an angular quadrature be specified. Although we learned that a quadrature requires the specification of a weight and a cosine value for each direction, the quadratures built into SCALE are specified by the number of directions (2,4,6,8,16,32,64, ...).
3. Spatial: The spatial subdivisions of the spherical layers are chosen automatically by SCALE. The number of divisions are chosen according to the actual cross sections in the layer material, so is problem-dependent.
The user can over-ride the default values from SCALE by adding a "MORE DATA" block (which should be between the END ZONE line and the END CELLDATA line).
The syntax is:
The SCALE manual gives all of the keywords that can be used. The ones we will use in this exercise are:
ISN = number where "number" gives the number of directions you want SCALE to use
SZF = value where "value" of 1.0 means you want SCALE to use its default choices. 0.5 gives you smaller (i.e., roughly twice as many) divisions; 2.0 gives larger (i.e., roughly half as many) divisions.
In this assignment, I want you to take the CSAS1 problem we used in HW#3:
=csas1 parm=bonami fig. 2-2, point 1 v7-56 read composition pu 1 1 293 94239 100 end h2o 2 1 293 end end composition read celldata multiregion spherical left_bdy=reflected right_bdy=vacuum cellmix=500 end 1 5 end zone end celldata end
and test the effect on the eigenvalue of:
a. Halving the default angular quadrature (which is 8, so run 4)
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