Code Manual for CONTAIN 2.0 - Federation of American Scientists

T 2,eff = T2
h I,eff = hlz
whereas for Xlzxz, it is given by
T 2,eff = (fT2h12+(1-f)Tlhl@l,.ff
h 1,eff = f hlz +(1-f)h14
(10-107) ~
(10-108)
where f = rnin(xl,xz)/max(x l,xz). These boundary conditions allow the conduction solution to be
obtained for region 1, in the manner discussed below. A similar set of boundary conditions allow
the conduction solution to be carried out in region 3.
In the following, structure 1 is assumed to belong to the first of the two cells to be processed by
CONTAIN for the present system timestep AK. The flux ~ leaving region 1 over all cell timesteps
At: in the present system timestep is calculated as discussed below and used to define an averaged
flux
~;= ~ qlm AtCm/At,” (10-109)
m
where the sum is carried out over the cell timesteps in the present system timestep. When the ~
temperature profile in region 2 is calculated (after regions 1 and 3 in structure 1 are processed for
the entire system timestep), a flux-matching boundary condition is used for all cell timesteps in the
system timestep for regions 2 and 4 in structure 2. The definition of the flux ~mfor xl < Xzis given
by
(10-110)
where f’= (X2- xl)/(l - xl), ~ ~’+fi and ~ ~’+h are extrapolated temperatures as described below,
m’ corresponds to the cell timestep at the end of the last system timestep, and Am corresponds to the
number of cell timesteps in the present system timestep. On the other hand, for xl > x2,the flux is
given by
It is tempting to define qlmexplicitly in terms of Tz,,~~according to
(10-111)
R O 10 56 6/30/97