ERRORS IN THE NUCLEAR FUEL BURNUP SIMULATIONS WITH THE USE OF STATISTICAL METHODS
D. G. Modestov
VANT. Ser.: Mat. Mod. Fiz. Proc 2019. Вып.1. С. 33-43.
The fuel burnup problem is a Cauchy problem for some system of ordinary differential equations, where the right-hand side of equation is a set of the transport equation solution functionals. To estimate such functionals, the statistical methods of simulation are often used, which require the least number of physical and technical approximations in comparison with other methods. Errors in estimating functionals lead, in turn, to errors in the calculated results for the nuclear composition of fuel, which are classified as statistical and systematic errors. The paper describes the asymptotical behavior of the latter at small integration steps. It is also demonstrated that statistical errors are slightly dependent on these integration steps. This property allows mitigating, to some extent, the pessimistic prediction of impossibility to construct higher-order schemes, which was discussed in an earlier published article by the author. The paper presents results of methodological simulations for a simple thermal-neutron reactor model, which are in a good agreement with theoretical estimates. Keywords: nuclei kinetics, numerical methods, Cauchy problem, integration scheme, the particle transport equation, the generation method.
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