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.

► Nuclide density vector is decomposed into two blocks by effective decay constant.
► Short-lived nuclide block is solved by the general Bateman solution method.
► An importance concept, related to Bateman solution method, is introduced to reduce computational burden.
► Long-lived nuclide block is solved by the method of variation of parameters with matrix exponential with reduced norm.
► The new method shows significantly improved results compared to existing methods.