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Probabilistic collocation and Lagrangian sampling for tracer transport in randomly heterogeneous porous media

by F. Müller and D. W. Meyer and P. Jenny

(Report number 2011-34)

Abstract
The Karhunen–Loeve (KL) decomposition and the polynomial chaos (PC) expansion are elegant and efficient tools for uncertainty propagation in porous media. Over recent years, KL/PC-based frameworks have successfully been applied in several contributions for the flow problem in the subsurface con- text. It was also shown, however, that the accurate solution of the transport problem with KL/PC techniques is more challenging. We propose a framework that utilizes KL/PC in combination with sparse Smolyak quadrature for the flow problem only. In a subsequent step, a Lagrangian Monte Carlo sampling technique is used for transport, where the flow field samples are calculated very efficiently based on the solutions at relatively few quadrature points. To increase the computational efficiency of the PC-based flow field sampling, a new reduction method is applied. Compared to a conventional full MC method that includes both flow and transport, the proposed PC/MC method (PCMCM) for flow/transport, respectively, saves on the computational cost of the flow problem. The applicability of PCMCM is demonstrated for transport simulations in multivariate Gaussian log-conductivity fields that are unconditional and conditional on conductivity measurements.

Keywords: Probabilistic collocation, Karhunen-Loeve expansion, Polynomial chaos, Smolyak sparse grid, Heterogeneous porous media, Tracer transport

@Techreport{MMJ11_136,
  author = {F. M\"uller and D. W. Meyer and P. Jenny},
  title = {Probabilistic collocation and Lagrangian sampling for tracer transport in randomly heterogeneous porous media},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2011-34},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2011/2011-34.pdf },
  year = {2011}
}

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