New Computer Efficient Approximations of Random Functions for Solving Stochastic Transport Problems

A new grid approximation of a homogeneous isotropic random field with a given average correlation length is developed. The approximation is constructed by partitioning the coordinate space into an ensemble of cubes whose size reproduces the average correlation length in the case of a field value chosen independently from a given one-dimensional distribution in each partition element. The correlative randomized algorithm recently proposed by the authors for modeling particle transport through a random medium is formulated. The accuracy and computational cost of corresponding Monte Carlo algorithms intended to compute gamma radiation transfer through a random medium of Voronoi diagram type are compared. To test the hypothesis that the one-dimensional distribution and the correlation length of the optical density of the medium have a large effect on radiation transfer, additional computations are performed for a random Poisson “field of air balls” in water. The grid approximation is generalized to anisotropic random fields.