A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media

2017 ◽  
Vol 330 ◽  
pp. 828-845 ◽  
Author(s):  
Qinzhuo Liao ◽  
Dongxiao Zhang ◽  
Hamdi Tchelepi
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Collocation Method ◽  
Sparse Grids ◽  
Heterogeneous Porous Media ◽  
Stochastic Collocation ◽  
Two Stage ◽  
Stochastic Collocation Method

scholarly journals A stochastic collocation method based on sparse grids for a stochastic Stokes-Darcy model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhipeng Yang ◽  
Xuejian Li ◽  
Xiaoming He ◽  
Ju Ming
Keyword(s):  
Hydraulic Conductivity ◽  
Collocation Method ◽  
Grid Method ◽  
Sparse Grids ◽  
Sparse Grid ◽  
Stochastic Collocation ◽  
Discrete Form ◽  
Darcy Model ◽  
Stochastic Collocation Method ◽  
Sparse Grid Method

<p style='text-indent:20px;'>In this paper, we develop a sparse grid stochastic collocation method to improve the computational efficiency in handling the steady Stokes-Darcy model with random hydraulic conductivity. To represent the random hydraulic conductivity, the truncated Karhunen-Loève expansion is used. For the discrete form in probability space, we adopt the stochastic collocation method and then use the Smolyak sparse grid method to improve the efficiency. For the uncoupled deterministic subproblems at collocation nodes, we apply the general coupled finite element method. Numerical experiment results are presented to illustrate the features of this method, such as the sample size, convergence, and randomness transmission through the interface.</p>

scholarly journals Uncertainty Quantification in Small-Timescale Model-Based Fatigue Crack Growth Analysis Using a Stochastic Collocation Method

Metals ◽  
2020 ◽  
Vol 10 (5) ◽  
pp. 646
Author(s):  
Hesheng Tang ◽  
Xueyuan Guo ◽  
Songtao Xue
Keyword(s):  
Fatigue Crack ◽  
Fatigue Crack Growth ◽  
Uncertainty Quantification ◽  
Crack Growth ◽  
Collocation Method ◽  
Life Prediction ◽  
Remaining Useful Life ◽  
Stochastic Collocation ◽  
Stochastic Collocation Method ◽  
Model Based

Due to the uncertainties originating from the underlying physical model, material properties and the measurement data in fatigue crack growth (FCG) processing, the prediction of fatigue crack growth lifetime is still challenging. The objective of this paper was to investigate a methodology for uncertainty quantification in FCG analysis and probabilistic remaining useful life prediction. A small-timescale growth model for the fracture mechanics-based analysis and predicting crack-growth lifetime is studied. A stochastic collocation method is used to alleviate the computational difficulties in the uncertainty quantification in the small-timescale model-based FCG analysis, which is derived from tensor products based on the solution of deterministic FCG problems on sparse grids of collocation point sets in random space. The proposed method is applied to the prediction of fatigue crack growth lifetime of Al7075-T6 alloy plates and verified by fatigue crack-growth experiments. The results show that the proposed method has the advantage of computational efficiency in uncertainty quantification of remaining life prediction of FCG.

Experimental observations of multiphase flow in heterogeneous porous media

1989 ◽  
Vol 5 (1) ◽  
pp. 83-95 ◽  
Author(s):  
Bernard H. Kueper ◽  
Wesley Abbott ◽  
Graham Farquhar
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Heterogeneous Porous Media

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

2012 ◽  
Vol 594-597 ◽  
pp. 2545-2551
Author(s):  
Yan Hua Xia
Keyword(s):  
Finite Element ◽  
Collocation Method ◽  
Multiscale Method ◽  
Computational Techniques ◽  
Stochastic Collocation ◽  
Fine Scale ◽  
Stochastic Finite Element ◽  
Seepage Field ◽  
Stochastic Collocation Method ◽  
Heterogeneous Multiscale

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.

Sign in / Sign up

Export Citation Format

Share Document