Efficient and accurate depletion calculations via two-block decomposition of nuclide concentration vector

A new method of depletion calculation is introduced by decomposing nuclide concentration vector into two blocks (short-lived nuclide block and long-lived nuclide block). For short-lived nuclide block calculation, general Bateman solution of each short-lived nuclide is used. An "importance" concept is introduced for selecting important parents for producing a particular short-lived nuclide so that computational burden for Bateman solution calculation is reduced. Long-lived nuclide block is solved by the method of variation of parameters, in which matrix exponentials are calculated efficiently since the norm of long-lived nuclide block matrix is small. The two-block decomposition method is tested on UO₂ PWR fuel depletion problems and compared to existing depletion methods, i.e.; ORIGEN code and Krylov subspace methods. The numerical results show that the two-block decomposition method gives much more accurate results than those of the ORIGEN code for similar computing time. For similar accuracy computing time of the two-block decomposition method is ∼10 times less than that of the Krylov subspace method.