Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation
Joint Authors
Ossiander, Mina E.
Vasylkivska, Veronika S.
Peszynska, Malgorzata
Source
Journal of Applied Mathematics
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-21, 21 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-14
Country of Publication
Egypt
No. of Pages
21
Main Subjects
Abstract EN
We derive a new method of conditional Karhunen-Loève (KL) expansions for stochastic coefficients in models of flow and transport in the subsurface, and in particular for the heterogeneous random permeability field.
Exact values of this field are never known, and thus one must evaluate uncertainty of solutions to the flow and transport models.
This is typically done by constructing independent realizations of the permeability field followed by numerical simulations of flow and transport for each realization and assembling statistical estimates of moments of desired quantities of interest.
We follow the well-known framework of KL expansions and derive a new method that incorporates known values of the permeability at given locations so that the realizations of the permeability field honor this data exactly.
Our method relies on projections to an appropriate subspace of random weights applied to the eigenfunctions of the covariance operator.
We use the permeability realizations constructed with our stochastic simulation method in simulations of flow and transport and compare the results to those obtained when realizations are constructed with sequential Gaussian simulation (SGS).
We also compare efficiency and stochastic convergence with that of stochastic collocation.
American Psychological Association (APA)
Ossiander, Mina E.& Peszynska, Malgorzata& Vasylkivska, Veronika S.. 2014. Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation. Journal of Applied Mathematics،Vol. 2014, no. 2014, pp.1-21.
https://search.emarefa.net/detail/BIM-1039751
Modern Language Association (MLA)
Ossiander, Mina E.…[et al.]. Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation. Journal of Applied Mathematics No. 2014 (2014), pp.1-21.
https://search.emarefa.net/detail/BIM-1039751
American Medical Association (AMA)
Ossiander, Mina E.& Peszynska, Malgorzata& Vasylkivska, Veronika S.. Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation. Journal of Applied Mathematics. 2014. Vol. 2014, no. 2014, pp.1-21.
https://search.emarefa.net/detail/BIM-1039751
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1039751