Efficiently realized approximate models of random functions in stochastic problems of the theory of particle transfer

G. A. Michailov^ab, G. Z. Lotova^ab, I. N. Medvedev<sup>ab

a</sup> Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
^b Novosibirsk State University, Russia

Abstract: The paper presents efficiently realized approximations of random functions, which are developed by the authors and numerically modeled for the study of stochastic processes of particle transport, including criticality fluctuations of processes in random media with multiplication. Efficient correlation randomized algorithms for approximating an ensemble of particle trajectories using the correlation function or only the correlation scale of a medium are constructed. A simple grid model of an isotropic random field is formulated reproducing a given average correlation length, which ensures high accuracy in solving stochastic transfer problems for a small correlation scale. The algorithms are tested by solving a test problem of photon transfer and a problem of estimating the overexponential average particle flux in a random medium with multiplication.

Key words: numerical statistical modeling, random medium, Voronoi tessellation, maximum cross-section method (Woodcock tracking), correlation randomized algorithms, grid approximation, particle flow, overexponential asymptotics, estimation error, computation cost.

UDC: 519.245

Received: 27.11.2023
Revised: 27.12.2023
Accepted: 04.03.2024

DOI: 10.15372/SJNM20240205

 English version: Numerical Analysis and Applications, 2024, 17:2, 152–168