Probabilistic collocation and lagrangian sampling for advective tracer transport in randomly heterogeneous porous media |
| |
Authors: | Florian Müller Patrick JennyDaniel W Meyer |
| |
Institution: | Institute of Fluid Dynamics, ETH Zurich, Switzerland |
| |
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 context. 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 sampling technique is used for transport. The flow field samples are calculated based on a PC expansion derived from 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. For advection dominated transport scenarios, where a Lagrangian approach is applicable, the proposed PC/Monte Carlo method (PCMCM) is very efficient and avoids accuracy problems that arise when applying KL/PC techniques to both flow and transport. 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 Advective tracer transport |
本文献已被 ScienceDirect 等数据库收录! |
|