Simulation of Heterogeneous Stable Seepage Field by Stochastic Heterogeneous Multiscale Finite Element Method
Xia Yan-hua · Wanxi Xueyuan xuebao · 2012
This paper studies on the stable seepage field of heterogeneous strata in small scale by stochastic multiscale finite element method.The method is different from traditional stochastic finite elements for such as problems.The mulitiscale propriety of strata is not considered by traditional methods,so those methods cannot resolve the multiscale propriety of nature strata in a trivial means.So a new method called stochastic heterogeneous multiscale finite element method(SHMFE) is introduced to resolve the problem efficiently.The ln permeability Y=lnKe in micro-scale is described by Karhunen-Loμeve expansion.In order to make the problem well-defined,the stochastic collocation method is adopted by combining generalized polynomial chaos to disperse the probability space.If Karhunen-Loμeve expansion has a lot of random variable,sparse grid stochastic collocation method is used.The well-defined problem is solved by stochastic multiscale finite element method.The numerical example argues that stochastic multiscale finite element method is better than traditional methods in the aspects of computational resource and cost.It can resolve the nature of multiscale heterogeneous porous media which classical methods do not.