TIME CONSTANT ESTIMATION WITH STATISTIC SIMULATION METHODS IN PARTICLE TRANSPORT PROBLEMS
D. G. Modestov
VANT. Ser.: Mat. Mod. Fiz. Proc 2021. Вып.3. С. 59-69.
The asymptotic behavior of the transport equation solution at large times is determined by the transport operator eigenvalue with a maximum real part, i.e. a time constant. Accordingly, this value is an important characteristic of the radiation field dynamics. To calculate it with the statistic simulation methods that allow solving the transport equation with least approximations, the most common approach is based on solving the conditionally critical problem with an added auxiliary reaction parametrized by a trial value of time constant. The true value is obtained by selecting values according to the operator criticality condition. A restricted range of applicability is a disadvantage of the current methods based on the approach above. The paper describes the approach with an auxiliary operator which is time dependent and, at the same time, smoothly depends on the trial time-constant value which has no such disadvantage. To solve the problem, an algorithm similar to the method of generations with a quadratic rate of convergence, in optimal case, is used. Issues of convergence are considered. Comparison between the numerical and analytical solutions is presented including the case of no convergence. Keywords: particle transport equation, time constant, method of generations, statistical simulation.
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