In this paper we develop a Stochastic Collocation Method(SCM)for flow in randomly heterogeneous porous media.At first,the Karhunen-Lo`eve expansion is taken to decompose the log transformed hydraulic conductivity fiel...In this paper we develop a Stochastic Collocation Method(SCM)for flow in randomly heterogeneous porous media.At first,the Karhunen-Lo`eve expansion is taken to decompose the log transformed hydraulic conductivity field,which leads to a stochastic PDE that only depends on a finite number of i.i.d.Gaussian random variables.Based on the eigenvalue decay property and a rough error estimate of Stroud cubature in SCM,we propose to subdivide the leading dimensions in the integration space for random variables to increase the accuracy.We refer to this approach as adaptive Stroud SCM.One-and two-dimensional steady-state single phase flow examples are simulated with the new method,and comparisons are made with other stochastic methods,namely,the Monte Carlo method,the tensor product SCM,and the quasiMonte Carlo SCM.The results indicate that the adaptive Stroud SCM is more efficient and the statistical moments of the hydraulic head can be more accurately estimated.展开更多
基金National Natural Science Foundation of China(NSFC)grants 10401004the National Basic Research Program under the grant 2005CB321704+2 种基金.D.Zhang is grateful to the supports by NSFC through grant 50688901by the National Basic Research Program through grant 2006CB705800P.Zhang is supported by the special funds for Major State Research Projects through grant 2005CB321704.
文摘In this paper we develop a Stochastic Collocation Method(SCM)for flow in randomly heterogeneous porous media.At first,the Karhunen-Lo`eve expansion is taken to decompose the log transformed hydraulic conductivity field,which leads to a stochastic PDE that only depends on a finite number of i.i.d.Gaussian random variables.Based on the eigenvalue decay property and a rough error estimate of Stroud cubature in SCM,we propose to subdivide the leading dimensions in the integration space for random variables to increase the accuracy.We refer to this approach as adaptive Stroud SCM.One-and two-dimensional steady-state single phase flow examples are simulated with the new method,and comparisons are made with other stochastic methods,namely,the Monte Carlo method,the tensor product SCM,and the quasiMonte Carlo SCM.The results indicate that the adaptive Stroud SCM is more efficient and the statistical moments of the hydraulic head can be more accurately estimated.
