Probabilistic collocation and Lagrangian sampling for tracer transport in randomly heterogeneous porous media
Meyer, Daniel W.
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. Mehr anzeigen
Zeitschrift / SerieResearch reports
VerlagSeminar für Angewandte Mathematik, ETH
ThemaProbabilistic collocation; Karhunen–Loeve expansion; Polynomial chaos; Smolyak sparse grid; Heterogeneous porous media; Tracer transport
Organisationseinheit03644 - Jenny, Patrick / Jenny, Patrick
03435 - Schwab, Christoph / Schwab, Christoph