Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/652594 |
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| author | Mina E. Ossiander Malgorzata Peszynska Veronika S. Vasylkivska |
| author_facet | Mina E. Ossiander Malgorzata Peszynska Veronika S. Vasylkivska |
| author_sort | Mina E. Ossiander |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-152a2f3b3ccc495da5052f826cea48bc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-152a2f3b3ccc495da5052f826cea48bc2025-02-03T01:22:04ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/652594652594Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian SimulationMina E. Ossiander0Malgorzata Peszynska1Veronika S. Vasylkivska2Department of Mathematics, Oregon State University, Corvallis, OR 97331, USADepartment of Mathematics, Oregon State University, Corvallis, OR 97331, USADepartment of Mathematics, Oregon State University, Corvallis, OR 97331, USAWe 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.http://dx.doi.org/10.1155/2014/652594 |
| spellingShingle | Mina E. Ossiander Malgorzata Peszynska Veronika S. Vasylkivska Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation Journal of Applied Mathematics |
| title | Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation |
| title_full | Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation |
| title_fullStr | Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation |
| title_full_unstemmed | Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation |
| title_short | Conditional Stochastic Simulations of Flow and Transport with Karhunen-Loève Expansions, Stochastic Collocation, and Sequential Gaussian Simulation |
| title_sort | conditional stochastic simulations of flow and transport with karhunen loeve expansions stochastic collocation and sequential gaussian simulation |
| url | http://dx.doi.org/10.1155/2014/652594 |
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