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the arrays T and II, respectively.
Finally, a record per line keeps the following information:
W, L0, LLL, (T(k), k=1,2,,...,LLL), (II(k),k=1,2,...,LLL)
where W is the weight of a line given by
W =1 for slab (7.1-73a)
W = ω r r ) for r i−1 < ρ < ri
for cylinder (7.1-73b)
g ( i − i− 1
W = ρ ω r − r ) for ri
−1 < ρ < ri
for sphere (7.1-73c)
× g ( i i−1
W = Δ ρ × Δϕ
=constant for two-dimensional cylinder (7.1-73d)
where ω g is the weight for the Gaussian quadrature at the point r g in the range between r i-1 and r i , and
L0 : number of intersects of the source cell,
LLL : total number of intersects on a line (Unless the mirror or periodic boundary
condition is taken, LLL = L0),
T(k) : distance between intersects which produces the optical thickness λ k by
multiplying the macroscopic cross-section of the region II(k),
I(k) : region numbers of k-th intersect.
The total number of lines LCOUNT (records) required to achieve the integration varies widely
depending on the complexity of the geometry, for example, LCOUNT= 2 for slab, LCOUNT= several
tens for one-dimensional cylinder and sphere, and LCOUNT= a few thousands for the most
complicated two-dimensional case.
After storing the trace tables for all lines, a numerical integration of region volumes and an
array of integrated to exact volume ratios is printed as an indicator of the adequacy of the integration
mesh. The numerical integration is performed by
V(II(k)) = V(II(k)) + W× T(k) for k=1,2,...,L0
and accumulated by line. ( 7.1-74)
The resultant array V gives the numerically integrated region volumes.
(2) Process for Numerical Integration
Being given the cross sections of an energy group, the integration of collision probabilities is
performed line by line. Actually, the symmetric element Δ ij (=V i P ij / Σ j ) and Δ is (=V i P is ) are integrated
instead of P ij and P is , respectively.
We shall show the computer process repeated by each line in the computational flow diagram
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