A Stochastic Finite Element Heterogeneous Multiscale Method for Seepage Field in Heterogeneous Ground

Abstract

The finite element heterogeneous multiscale method (FEHM) combined with stochastic collocation method (SCM) called SHMFE is applied to studying the seepage field of naturally heterogeneous multiscale subsurface formations. Kinds of stochastic finite element (SFEM) are mainly computational techniques for the class of problems. But those methods do not report the multiscale nature of the properties of subsurface formations. When the random permeability field is heterogeneous in fine scale comparing to study domain, the simulation by the classic SFEM is not a trivial task. The SHMFE can efficiently solve the problems. In the method, Karhunen-Loµeve (KL) decomposition is used to represent the log hydraulic conductivity Y = lnKεin fine scale. The SCM which couples the generalized polynomial chaos is used to make the problem determined, and then the FEHM method is used to solve it. Sparse grid stochastic collocation method is used when KL expansion has many random variables. The numerical examples demonstrate that the SHMFE approach can efficiently simulate the flow in naturally multiscale heterogeneous subsurface formations with relatively lower computational cost comparing with the SFEM methods.