Effects of Truncation on Polynomial Chaos ...

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XVI International Conference on Computational Methods in Water Resources (CMWR-XVI) Ingeniørhuset

Effects of Truncation on Polynomial Chaos Coefficients in Stochastic Transient Groundwater Flow
Author:Carl Rupert <crupert@email.unc.edu> (University of North Carolina at Chapel Hill)
Cass Miller <casey_miller@unc.edu> (University of North Carolina at Chapel Hill)
Presenter:Carl Rupert <crupert@email.unc.edu> (University of North Carolina at Chapel Hill)
Date: 2006-06-18     Track: General Sessions     Session: General
DOI:10.4122/1.1000000385

Our inability to fully characterize heterogeneous subsurface systems at appropriate scales motivates continuing interest in the careful stochastic treatment of subsurface fluid flow and contaminant transport. Unfortunately, existing methods often appear to require restriction to low variability regimes, and significant challenges remain as heterogeneity increases, In the last decade, models based on Wiener polynomial chaos and Karhunen-Loeve expansion have been developed for a range of scientific fields. The present work contributes to the assessment of these techniques for application to subsurface systems. It is known that chaos methods may rapidly become intractable as the number of random variables or degree increases. Truncation, however, can have several effects: in addition to the error resulting directly from the omitted terms, there is also an error induced in the estimated numerical values of the retained terms, as a result of the truncation. We therefore examine chaos approximation of a transient, two-dimensional groundwater flow problem with a random log-normally distributed hydraulic conductivity field, with particular attention to the effect of higher order terms and additional random variables on the values obtained for prior terms in the expansion and discuss the implications for applicability of chaos methods.