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Stochastic Methods For Uncertainty Quantification In Radiation Transport, Erin D. Fichtl Jul 2009

Stochastic Methods For Uncertainty Quantification In Radiation Transport, Erin D. Fichtl

Nuclear Engineering ETDs

The use of stochastic spectral expansions, specifically generalized polynomial chaos (gPC) and Karhunen-Loeve (KL) expansions, is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of random variables. The KL expansion is a Fourier-type expansion that represents a second-order random process with known covariance function in terms of a set of uncorrelated random variables and the eigenmodes of the covariance function. The flux and, in multiplying materials, the k-eigenvalue, which are the problem unknowns, are always expanded in a gPC expansion since their covariance functions are also unknown ...