April 4, 2017

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By Jess C Gehin

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_,,rat, ka,d _ e" _,dat... ,\eAt. 14) M(,,, ....... I). quatmn .... Nicholson) of the choice of tOwill be given in ('hapter The value of the precursor densities 4. at lhe new time step appears in Eq,(3,14). This term may be eliminated by using the result of the direct integration of the precur- sor equation. Thus, substituting Eq. 13} into (3,14) and subsequent 49 rearranging, we obtain the followin_ equation f,,r the tluxes , ]} O _". _dii . averKged ttuxes at the new time _tep. tion of the point kinetics equlttions [H-4], The shape function i, defined for Pitch node ttttd enerly+group, and energy independetlt quantity.

DCdg(_), D. difference equations we now define Vg = An N x N diagonal matrix of the group speeds, {vg}, Fmo, An N:, Cdg A column vector of length N of {X,0c_JJ'}, Fa,go, An N× N diagonal matrix of {X,ovE_)_k,}, N diagonal matrix of { _:,t#_,;E_}. _ An NG _ NG diagonalmatrixofthe groupspeeds,{V_}, L = An NG _ NG matrix of {Ngbatr - _g_,(t)}, Mp _---. An NG _ NG matrix of prompt fission production terms, {Fp,_0,}, Md = An NG _. Dependent of the neutron diffusion equation, Polynomial Nodal Equations When the polynomial nodal method is applied 1o tile transient the expansion coettlcients determine the expansion become time dependent.

Correct for spatial, homogenization Since the quartic polynomial al proxmlatlon t l ri,_. Note that the discontinuity fat'tors which occur are different from thote introduced JI these discontinuity ,g_, factors and diffuaioii theory errors. leads to small spatial errors their ' q | _ I ,_rill primary purpose is to provide homogenization correct|on. ,, will he ¢Olllttant throughout -I/U 8. 17) D_ 'Fhe_e equations very time consuming further manipulation, represent a 8(;' ( _,,,,,, .... ,,_,,,,.

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