Application of the finite difference heterogeneous multiscale method to the Richards' equation

2008 ◽  
Vol 44 (7) ◽  
Author(s):  
Fulai Chen ◽  
Li Ren
Keyword(s):  
Finite Difference ◽  
Multiscale Method ◽  
Richards Equation ◽  
Heterogeneous Multiscale

scholarly journals New Scheme of Finite Difference Heterogeneous Multiscale Method to Solve Saturated Flow in Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-19
Author(s):  
Fulai Chen ◽  
Li Ren
Keyword(s):  
Porous Media ◽  
Finite Difference ◽  
Sudden Change ◽  
Multiscale Method ◽  
Flow In Porous Media ◽  
Computational Time ◽  
Saturated Water ◽  
Comparable Accuracy ◽  
Multiscale Finite Element ◽  
Heterogeneous Multiscale

A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media. In the discretization framework of FDHMM, we follow some ideas from the multiscale finite element method and construct basic microscopic elliptic models. Tests on a variety of numerical experiments show that, in the case that only about a half of the information of the whole microstructure is used, the constructed scheme gives better accuracy at a much lower computational time than FDHMM for the problem of aquifer response to sudden change in reservoir level and gives comparable accuracy at a much lower computational time than FDHMM for the weak drawdown problem.

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.

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