Smoothed multiscale stochastic collocation method for flow in fractured rocks
Meng Guang-we · Journal of Hydraulic Engineering · 2015
A smoothed multiscale stochastic collocation method(SMs SCM) was proposed to solve stochasticproblems of fluid flow in heterogeneous fractured rocks. The basic idea of this method is to simplify the sto-chastic problem into a series of deterministic problems at the collocation points based on the sparse gridstochastic collocation method,then construct multiscale basis functions using limited global information todemonstrate material heterogeneity and coupled relationship of fluid flow in porous and fractured media,and finally solve the coarse scale problem by reflecting the small scale heterogeneity on large scale materi-al,with the adoption of gradient smoothing technique when assembling the coarse element correlation ma-trix. Comparing with the traditional multiscale stochastic collocation method,SMs SCM transforms inner inte-gral of the interest domain into boundary integral without solving the continuous form and derivatives of thebasis functions when assembling the correlation matrix of coarse element. Correspondingly,the programminghas been simplified and the finite element system is fairly softened. The results indicate that SMs SCM ismore accurate and efficient than the traditional multiscale stochastic collocation method.